MESHMAKER (MM) V1.5

DOE Office of Scientific and Technical Information (OSTI.GOV)

MORIDIS, GEORGE

2016-05-02

MeshMaker v1.5 is a code that describes the system geometry and discretizes the domain in problems of flow and transport through porous and fractured media that are simulated using the TOUGH+ [Moridis and Pruess, 2014] or TOUGH2 [Pruess et al., 1999; 2012] families of codes. It is a significantly modified and drastically enhanced version of an earlier simpler facility that was embedded in the TOUGH2 codes [Pruess et al., 1999; 2012], from which it could not be separated. The code (MeshMaker.f90) is a stand-alone product written in FORTRAN 95/2003, is written according to the tenets of Object-Oriented Programming, has amore » modular structure and can perform a number of mesh generation and processing operations. It can generate two-dimensional radially symmetric (r,z) meshes, and one-, two-, and three-dimensional rectilinear (Cartesian) grids in (x,y,z). The code generates the file MESH, which includes all the elements and connections that describe the discretized simulation domain and conforming to the requirements of the TOUGH+ and TOUGH2 codes. Multiple-porosity processing for simulation of flow in naturally fractured reservoirs can be invoked by means of a keyword MINC, which stands for Multiple INteracting Continua. The MINC process operates on the data of the primary (porous medium) mesh as provided on disk file MESH, and generates a secondary mesh containing fracture and matrix elements with identical data formats on file MINC.« less

Toward performance portability of the Albany finite element analysis code using the Kokkos library

DOE Office of Scientific and Technical Information (OSTI.GOV)

Demeshko, Irina; Watkins, Jerry; Tezaur, Irina K.

Performance portability on heterogeneous high-performance computing (HPC) systems is a major challenge faced today by code developers: parallel code needs to be executed correctly as well as with high performance on machines with different architectures, operating systems, and software libraries. The finite element method (FEM) is a popular and flexible method for discretizing partial differential equations arising in a wide variety of scientific, engineering, and industrial applications that require HPC. This paper presents some preliminary results pertaining to our development of a performance portable implementation of the FEM-based Albany code. Performance portability is achieved using the Kokkos library. We presentmore » performance results for the Aeras global atmosphere dynamical core module in Albany. Finally, numerical experiments show that our single code implementation gives reasonable performance across three multicore/many-core architectures: NVIDIA General Processing Units (GPU’s), Intel Xeon Phis, and multicore CPUs.« less

Toward performance portability of the Albany finite element analysis code using the Kokkos library

DOE PAGES

Demeshko, Irina; Watkins, Jerry; Tezaur, Irina K.; ...

2018-02-05

Performance portability on heterogeneous high-performance computing (HPC) systems is a major challenge faced today by code developers: parallel code needs to be executed correctly as well as with high performance on machines with different architectures, operating systems, and software libraries. The finite element method (FEM) is a popular and flexible method for discretizing partial differential equations arising in a wide variety of scientific, engineering, and industrial applications that require HPC. This paper presents some preliminary results pertaining to our development of a performance portable implementation of the FEM-based Albany code. Performance portability is achieved using the Kokkos library. We presentmore » performance results for the Aeras global atmosphere dynamical core module in Albany. Finally, numerical experiments show that our single code implementation gives reasonable performance across three multicore/many-core architectures: NVIDIA General Processing Units (GPU’s), Intel Xeon Phis, and multicore CPUs.« less

2nd-Order CESE Results For C1.4: Vortex Transport by Uniform Flow

NASA Technical Reports Server (NTRS)

Friedlander, David J.

2015-01-01

The Conservation Element and Solution Element (CESE) method was used as implemented in the NASA research code ez4d. The CESE method is a time accurate formulation with flux-conservation in both space and time. The method treats the discretized derivatives of space and time identically and while the 2nd-order accurate version was used, high-order versions exist, the 2nd-order accurate version was used. In regards to the ez4d code, it is an unstructured Navier-Stokes solver coded in C++ with serial and parallel versions available. As part of its architecture, ez4d has the capability to utilize multi-thread and Messaging Passage Interface (MPI) for parallel runs.

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

NASA Technical Reports Server (NTRS)

Meade, Andrew J., Jr.

1992-01-01

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

Modeling delamination growth in composites

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reedy, E.D. Jr.; Mello, F.J.

1996-12-01

A method for modeling the initiation and growth of discrete delaminations in shell-like composite structures is presented. The laminate is divided into two or more sublaminates, with each sublaminate modeled with four-noded quadrilateral shell elements. A special, eight-noded hex constraint element connects opposing sublaminate shell elements. It supplies the nodal forces and moments needed to make the two opposing shell elements act as a single shell element until a prescribed failure criterion is satisfied. Once the failure criterion is attained, the connection is broken, creating or growing a discrete delamination. This approach has been implemented in a 3D finite elementmore » code. This code uses explicit time integration, and can analyze shell-like structures subjected to large deformations and complex contact conditions. The shell elements can use existing composite material models that include in-plane laminate failure modes. This analysis capability was developed to perform crashworthiness studies of composite structures, and is useful whenever there is a need to estimate peak loads, energy absorption, or the final shape of a highly deformed composite structure. This paper describes the eight-noded hex constraint element used to model the initiation and growth of a delamination, and discusses associated implementation issues. Particular attention is focused on the delamination growth criterion, and it is verified that calculated results do not depend on element size. In addition, results for double cantilever beam and end notched flexure specimens are presented and compared to measured data to assess the ability of the present approach to model a growing delamination.« less

Slip Continuity in Explicit Crystal Plasticity Simulations Using Nonlocal Continuum and Semi-discrete Approaches

DTIC Science & Technology

2013-01-01

Based Micropolar Single Crystal Plasticity: Comparison of Multi - and Single Criterion Theories. J. Mech. Phys. Solids 2011, 59, 398–422. ALE3D ...element boundaries in a multi -step constitutive evaluation (Becker, 2011). The results showed the desired effects of smoothing the deformation field...Implementation The model was implemented in the large-scale parallel, explicit finite element code ALE3D (2012). The crystal plasticity

A new approach for modeling composite materials

NASA Astrophysics Data System (ADS)

Alcaraz de la Osa, R.; Moreno, F.; Saiz, J. M.

2013-03-01

The increasing use of composite materials is due to their ability to tailor materials for special purposes, with applications evolving day by day. This is why predicting the properties of these systems from their constituents, or phases, has become so important. However, assigning macroscopical optical properties for these materials from the bulk properties of their constituents is not a straightforward task. In this research, we present a spectral analysis of three-dimensional random composite typical nanostructures using an Extension of the Discrete Dipole Approximation (E-DDA code), comparing different approaches and emphasizing the influences of optical properties of constituents and their concentration. In particular, we hypothesize a new approach that preserves the individual nature of the constituents introducing at the same time a variation in the optical properties of each discrete element that is driven by the surrounding medium. The results obtained with this new approach compare more favorably with the experiment than previous ones. We have also applied it to a non-conventional material composed of a metamaterial embedded in a dielectric matrix. Our version of the Discrete Dipole Approximation code, the EDDA code, has been formulated specifically to tackle this kind of problem, including materials with either magnetic and tensor properties.

Analysis of Discrete-Source Damage Progression in a Tensile Stiffened Composite Panel

NASA Technical Reports Server (NTRS)

Wang, John T.; Lotts, Christine G.; Sleight, David W.

1999-01-01

This paper demonstrates the progressive failure analysis capability in NASA Langley s COMET-AR finite element analysis code on a large-scale built-up composite structure. A large-scale five stringer composite panel with a 7-in. long discrete source damage was analyzed from initial loading to final failure including the geometric and material nonlinearities. Predictions using different mesh sizes, different saw cut modeling approaches, and different failure criteria were performed and assessed. All failure predictions have a reasonably good correlation with the test result.

Variational approach to probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1991-01-01

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Variational approach to probabilistic finite elements

NASA Astrophysics Data System (ADS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1991-08-01

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Variational approach to probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1987-01-01

Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

47 CFR 15.214 - Cordless telephones.

Code of Federal Regulations, 2010 CFR

2010-10-01

... discrete digital codes. Factory-set codes must be continuously varied over at least 256 possible codes as... readily select from among at least 256 possible discrete digital codes. The cordless telephone shall be... fixed code that is continuously varied among at least 256 discrete digital codes as each telephone is...

A finite element code for modelling tracer transport in a non-isothermal two-phase flow system for CO2 geological storage characterization

NASA Astrophysics Data System (ADS)

Tong, F.; Niemi, A. P.; Yang, Z.; Fagerlund, F.; Licha, T.; Sauter, M.

2011-12-01

This paper presents a new finite element method (FEM) code for modeling tracer transport in a non-isothermal two-phase flow system. The main intended application is simulation of the movement of so-called novel tracers for the purpose of characterization of geologically stored CO2 and its phase partitioning and migration in deep saline formations. The governing equations are based on the conservation of mass and energy. Among the phenomena accounted for are liquid-phase flow, gas flow, heat transport and the movement of the novel tracers. The movement of tracers includes diffusion and the advection associated with the gas and liquid flow. The temperature, gas pressure, suction, concentration of tracer in liquid phase and concentration of tracer in gas phase are chosen as the five primary variables. Parameters such as the density, viscosity, thermal expansion coefficient are expressed in terms of the primary variables. The governing equations are discretized in space using the Galerkin finite element formulation, and are discretized in time by one-dimensional finite difference scheme. This leads to an ill-conditioned FEM equation that has many small entries along the diagonal of the non-symmetric coefficient matrix. In order to deal with the problem of non-symmetric ill-conditioned matrix equation, special techniques are introduced . Firstly, only nonzero elements of the matrix need to be stored. Secondly, it is avoided to directly solve the whole large matrix. Thirdly, a strategy has been used to keep the diversity of solution methods in the calculation process. Additionally, an efficient adaptive mesh technique is included in the code in order to track the wetting front. The code has been validated against several classical analytical solutions, and will be applied for simulating the CO2 injection experiment to be carried out at the Heletz site, Israel, as part of the EU FP7 project MUSTANG.

Lagrangian continuum dynamics in ALEGRA.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, Michael K. W.; Love, Edward

Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.

The Programming Language Python In Earth System Simulations

NASA Astrophysics Data System (ADS)

Gross, L.; Imranullah, A.; Mora, P.; Saez, E.; Smillie, J.; Wang, C.

2004-12-01

Mathematical models in earth sciences base on the solution of systems of coupled, non-linear, time-dependent partial differential equations (PDEs). The spatial and time-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

Design criteria for small coded aperture masks in gamma-ray astronomy

NASA Technical Reports Server (NTRS)

Sembay, S.; Gehrels, Neil

1990-01-01

Most theoretical work on coded aperture masks in X-ray and low-energy gamma-ray astronomy has concentrated on masks with large numbers of elements. For gamma-ray spectrometers in the MeV range, the detector plane usually has only a few discrete elements, so that masks with small numbers of elements are called for. For this case it is feasible to analyze by computer all the possible mask patterns of given dimension to find the ones that best satisfy the desired performance criteria. A particular set of performance criteria for comparing the flux sensitivities, source positioning accuracies and transparencies of different mask patterns is developed. The results of such a computer analysis for masks up to dimension 5 x 5 unit cell are presented and it is concluded that there is a great deal of flexibility in the choice of mask pattern for each dimension.

Novel numerical techniques for magma dynamics

NASA Astrophysics Data System (ADS)

Rhebergen, S.; Katz, R. F.; Wathen, A.; Alisic, L.; Rudge, J. F.; Wells, G.

2013-12-01

We discuss the development of finite element techniques and solvers for magma dynamics computations. These are implemented within the FEniCS framework. This approach allows for user-friendly, expressive, high-level code development, but also provides access to powerful, scalable numerical solvers and a large family of finite element discretisations. With the recent addition of dolfin-adjoint, FeniCS supports automated adjoint and tangent-linear models, enabling the rapid development of Generalised Stability Analysis. The ability to easily scale codes to three dimensions with large meshes, and/or to apply intricate adjoint calculations means that efficiency of the numerical algorithms is vital. We therefore describe our development and analysis of preconditioners designed specifically for finite element discretizations of equations governing magma dynamics. The preconditioners are based on Elman-Silvester-Wathen methods for the Stokes equation, and we extend these to flows with compaction. Our simulations are validated by comparison of results with laboratory experiments on partially molten aggregates.

3D modelling of non-linear visco-elasto-plastic crustal and lithospheric processes using LaMEM

NASA Astrophysics Data System (ADS)

Popov, Anton; Kaus, Boris

2016-04-01

LaMEM (Lithosphere and Mantle Evolution Model) is a three-dimensional thermo-mechanical numerical code to simulate crustal and lithospheric deformation. The code is based on a staggered finite difference (FDSTAG) discretization in space, which is a stable and very efficient technique to solve the (nearly) incompressible Stokes equations that does not suffer from spurious pressure modes or artificial compressibility (a typical feature of low-order finite element techniques). Higher order finite element methods are more accurate than FDSTAG methods under idealized test cases where the jump in viscosity is exactly aligned with the boundaries of the elements. Yet, geodynamically more realistic cases involve evolving subduction zones, nonlinear rheologies or localized plastic shear bands. In these cases, the viscosity pattern evolves spontaneously during a simulation or even during nonlinear iterations, and the advantages of higher order methods disappear and they all converge with approximately first order accuracy, similar to that of FDSTAG [1]. Yet, since FDSTAG methods have considerably less degrees of freedom than quadratic finite element methods, they require about an order of magnitude less memory for the same number of nodes in 3D which also implies that every matrix-vector multiplication is significantly faster. LaMEM is build on top of the PETSc library and uses the particle-in-cell technique to track material properties, history variables which makes it straightforward to incorporate effects like phase changes or chemistry. An internal free surface is present, together with (simple) erosion and sedimentation processes, and a number of methods are available to import complex geometries into the code (e.g, http://geomio.bitbucket.org). Customized Galerkin coupled geometric multigrid preconditioners are implemented which resulted in a good parallel scalability of the code (we have tested LaMEM on 458'752 cores [2]). Yet, the drawback of using FDSTAG discretizations is that the Jacobian, which is a key component for fast and robust convergence of Newton-Raphson nonlinear iterative solvers, is more difficult to implement than in FE codes and actually results in a larger stencil. Rather than discretizing it explicitly, we therefore developed a matrix-free analytical Jacobian implementation for the coupled sets of momentum, mass, and energy conservation equations, combined with visco-elasto-plastic rheologies. Tests show that for simple nonlinear viscous rheologies there is little advantage of the MF approach over the standard MFFD PETSc approach, but that iterations converge slightly faster if plasticity is present. Results also show that the Newton solver usually converges in a quadratic manner even for pressure-dependent Drucker-Prager rheologies and without harmonic viscosity averaging of plastic and viscous rheologies. Yet, if the timestep is too large (and the model becomes effectively viscoplastic), or if the shear band pattern changes dramatically, stagnation of iterations might occur. This can be remedied with an appropriate regularization, which we discuss. LaMEM is available as open source software. [1] Thielmann, M., May, D.A., and Kaus, B., 2014, Discretization Errors in the Hybrid Finite Element Particle-in-cell Method: Pure and Applied Geophysics,, doi: 10.1007/s00024-014-0808-9. [2] Kaus B.J.P., Popov A.A., Baumann T.S., Püsök A.E., Bauville A., Fernandez N., Collignon M. (2015) Forward and inverse modelling of lithospheric deformation on geological timescales. NIC Symposium 2016 - Proceedings. NIC Series. Vol. 48.

TranAir: A full-potential, solution-adaptive, rectangular grid code for predicting subsonic, transonic, and supersonic flows about arbitrary configurations. Theory document

NASA Technical Reports Server (NTRS)

Johnson, F. T.; Samant, S. S.; Bieterman, M. B.; Melvin, R. G.; Young, D. P.; Bussoletti, J. E.; Hilmes, C. L.

1992-01-01

A new computer program, called TranAir, for analyzing complex configurations in transonic flow (with subsonic or supersonic freestream) was developed. This program provides accurate and efficient simulations of nonlinear aerodynamic flows about arbitrary geometries with the ease and flexibility of a typical panel method program. The numerical method implemented in TranAir is described. The method solves the full potential equation subject to a set of general boundary conditions and can handle regions with differing total pressure and temperature. The boundary value problem is discretized using the finite element method on a locally refined rectangular grid. The grid is automatically constructed by the code and is superimposed on the boundary described by networks of panels; thus no surface fitted grid generation is required. The nonlinear discrete system arising from the finite element method is solved using a preconditioned Krylov subspace method embedded in an inexact Newton method. The solution is obtained on a sequence of successively refined grids which are either constructed adaptively based on estimated solution errors or are predetermined based on user inputs. Many results obtained by using TranAir to analyze aerodynamic configurations are presented.

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

NASA Technical Reports Server (NTRS)

Day, Brad A.; Meade, Andrew J., Jr.

1993-01-01

A semi-discrete Galerkin (SDG) method is under development to model attached, turbulent, and compressible boundary layers for transonic airfoil analysis problems. For the boundary-layer formulation the method models the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby providing high resolution near the wall and permitting the use of a uniform finite element grid which automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past RAE 2822 and NACA 0012 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack.

BlazeDEM3D-GPU A Large Scale DEM simulation code for GPUs

NASA Astrophysics Data System (ADS)

Govender, Nicolin; Wilke, Daniel; Pizette, Patrick; Khinast, Johannes

2017-06-01

Accurately predicting the dynamics of particulate materials is of importance to numerous scientific and industrial areas with applications ranging across particle scales from powder flow to ore crushing. Computational discrete element simulations is a viable option to aid in the understanding of particulate dynamics and design of devices such as mixers, silos and ball mills, as laboratory scale tests comes at a significant cost. However, the computational time required to simulate an industrial scale simulation which consists of tens of millions of particles can take months to complete on large CPU clusters, making the Discrete Element Method (DEM) unfeasible for industrial applications. Simulations are therefore typically restricted to tens of thousands of particles with highly detailed particle shapes or a few million of particles with often oversimplified particle shapes. However, a number of applications require accurate representation of the particle shape to capture the macroscopic behaviour of the particulate system. In this paper we give an overview of the recent extensions to the open source GPU based DEM code, BlazeDEM3D-GPU, that can simulate millions of polyhedra and tens of millions of spheres on a desktop computer with a single or multiple GPUs.

Stencil computations for PDE-based applications with examples from DUNE and hypre

DOE Office of Scientific and Technical Information (OSTI.GOV)

Engwer, C.; Falgout, R. D.; Yang, U. M.

Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend themore » software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.« less

Stencil computations for PDE-based applications with examples from DUNE and hypre

DOE PAGES

Engwer, C.; Falgout, R. D.; Yang, U. M.

2017-02-24

Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend themore » software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.« less

EAC: A program for the error analysis of STAGS results for plates

NASA Technical Reports Server (NTRS)

Sistla, Rajaram; Thurston, Gaylen A.; Bains, Nancy Jane C.

1989-01-01

A computer code is now available for estimating the error in results from the STAGS finite element code for a shell unit consisting of a rectangular orthotropic plate. This memorandum contains basic information about the computer code EAC (Error Analysis and Correction) and describes the connection between the input data for the STAGS shell units and the input data necessary to run the error analysis code. The STAGS code returns a set of nodal displacements and a discrete set of stress resultants; the EAC code returns a continuous solution for displacements and stress resultants. The continuous solution is defined by a set of generalized coordinates computed in EAC. The theory and the assumptions that determine the continuous solution are also outlined in this memorandum. An example of application of the code is presented and instructions on its usage on the Cyber and the VAX machines have been provided.

Is a Genome a Codeword of an Error-Correcting Code?

PubMed Central

Kleinschmidt, João H.; Silva-Filho, Márcio C.; Bim, Edson; Herai, Roberto H.; Yamagishi, Michel E. B.; Palazzo, Reginaldo

2012-01-01

Since a genome is a discrete sequence, the elements of which belong to a set of four letters, the question as to whether or not there is an error-correcting code underlying DNA sequences is unavoidable. The most common approach to answering this question is to propose a methodology to verify the existence of such a code. However, none of the methodologies proposed so far, although quite clever, has achieved that goal. In a recent work, we showed that DNA sequences can be identified as codewords in a class of cyclic error-correcting codes known as Hamming codes. In this paper, we show that a complete intron-exon gene, and even a plasmid genome, can be identified as a Hamming code codeword as well. Although this does not constitute a definitive proof that there is an error-correcting code underlying DNA sequences, it is the first evidence in this direction. PMID:22649495

ATHENA 3D: A finite element code for ultrasonic wave propagation

NASA Astrophysics Data System (ADS)

Rose, C.; Rupin, F.; Fouquet, T.; Chassignole, B.

2014-04-01

The understanding of wave propagation phenomena requires use of robust numerical models. 3D finite element (FE) models are generally prohibitively time consuming. However, advances in computing processor speed and memory allow them to be more and more competitive. In this context, EDF R&D developed the 3D version of the well-validated FE code ATHENA2D. The code is dedicated to the simulation of wave propagation in all kinds of elastic media and in particular, heterogeneous and anisotropic materials like welds. It is based on solving elastodynamic equations in the calculation zone expressed in terms of stress and particle velocities. The particularity of the code relies on the fact that the discretization of the calculation domain uses a Cartesian regular 3D mesh while the defect of complex geometry can be described using a separate (2D) mesh using the fictitious domains method. This allows combining the rapidity of regular meshes computation with the capability of modelling arbitrary shaped defects. Furthermore, the calculation domain is discretized with a quasi-explicit time evolution scheme. Thereby only local linear systems of small size have to be solved. The final step to reduce the computation time relies on the fact that ATHENA3D has been parallelized and adapted to the use of HPC resources. In this paper, the validation of the 3D FE model is discussed. A cross-validation of ATHENA 3D and CIVA is proposed for several inspection configurations. The performances in terms of calculation time are also presented in the cases of both local computer and computation cluster use.

Accretional evolution of a planetesimal swarm. I - A new simulation

NASA Technical Reports Server (NTRS)

Spaute, Dominique; Weidenschilling, Stuart J.; Davis, Donald R.; Marzari, Francesco

1991-01-01

This novel simulation of planetary accretion simultaneously treats many interacting heliocentric distance zones and characterizes planetesimals via Keplerian elements. The numerical code employed, in addition to following the size distribution and the orbit-element distribution of a planetesimal swarm from arbitrary size and orbit distributions, treats a small number of the largest bodies as discrete objects with individual orbits. The accretion algorithm used yields good agreement with the analytic solutions; agreement is also obtained with the results of Weatherill and Stewart (1989) for gravitational accretion of planetesimals having equivalent initial conditions.

Advanced graphical user interface for multi-physics simulations using AMST

NASA Astrophysics Data System (ADS)

Hoffmann, Florian; Vogel, Frank

2017-07-01

Numerical modelling of particulate matter has gained much popularity in recent decades. Advanced Multi-physics Simulation Technology (AMST) is a state-of-the-art three dimensional numerical modelling technique combining the eX-tended Discrete Element Method (XDEM) with Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) [1]. One major limitation of this code is the lack of a graphical user interface (GUI) meaning that all pre-processing has to be made directly in a HDF5-file. This contribution presents the first graphical pre-processor developed for AMST.

Coupling of in-situ X-ray Microtomography Observations with Discrete Element Simulations-Application to Powder Sintering

NASA Astrophysics Data System (ADS)

Olmos, L.; Bouvard, D.; Martin, C. L.; Bellet, D.; Di Michiel, M.

2009-06-01

The sintering of both a powder with a wide particle size distribution (0-63 μm) and of a powder with artificially created pores is investigated by coupling in situ X-ray microtomography observations with Discrete Element simulations. The micro structure evolution of the copper particles is observed by microtomography all along a typical sintering cycle at 1050° C at the European Synchrotron Research Facilities (ESRF, Grenoble, France). A quantitative analysis of the 3D images provides original data on interparticle indentation, coordination and particle displacements throughout sintering. In parallel, the sintering of similar powder systems has been simulated with a discrete element code which incorporates appropriate sintering contact laws from the literature. The initial numerical packing is generated directly from the 3D microtomography images or alternatively from a random set of particles with the same size distribution. The comparison between the information drawn from the simulations and the one obtained by tomography leads to the conclusion that the first method is not satisfactory because real particles are not perfectly spherical as the numerical ones. On the opposite the packings built with the second method show sintering behaviors close to the behaviors of real materials, although particle rearrangement is underestimated by DEM simulations.

A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains

NASA Technical Reports Server (NTRS)

Kandil, Osama A.

1998-01-01

Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.

Error Correcting Codes and Related Designs

DTIC Science & Technology

1990-09-30

Theory, IT-37 (1991), 1222-1224. 6. Codes and designs, existence and uniqueness, Discrete Math ., to appear. 7. (with R. Brualdi and N. Cai), Orphan...structure of the first order Reed-Muller codes, Discrete Math ., to appear. 8. (with J. H. Conway and N.J.A. Sloane), The binary self-dual codes of length up...18, 1988. 4. "Codes and Designs," Mathematics Colloquium, Technion, Haifa, Israel, March 6, 1989. 5. "On the Covering Radius of Codes," Discrete Math . Group

Improved Subcell Model for the Prediction of Braided Composite Response

NASA Technical Reports Server (NTRS)

Cater, Christopher R.; Xinran, Xiao; Goldberg, Robert K.; Kohlman, Lee W.

2013-01-01

In this work, the modeling of triaxially braided composites was explored through a semi-analytical discretization. Four unique subcells, each approximated by a "mosaic" stacking of unidirectional composite plies, were modeled through the use of layered-shell elements within the explicit finite element code LS-DYNA. Two subcell discretizations were investigated: a model explicitly capturing pure matrix regions, and a novel model which absorbed pure matrix pockets into neighboring tow plies. The in-plane stiffness properties of both models, computed using bottom-up micromechanics, correlated well to experimental data. The absorbed matrix model, however, was found to best capture out-of- plane flexural properties by comparing numerical simulations of the out-of-plane displacements from single-ply tension tests to experimental full field data. This strong correlation of out-of-plane characteristics supports the current modeling approach as a viable candidate for future work involving impact simulations.

Engine structures modeling software system: Computer code. User's manual

NASA Technical Reports Server (NTRS)

1992-01-01

ESMOSS is a specialized software system for the construction of geometric descriptive and discrete analytical models of engine parts, components and substructures which can be transferred to finite element analysis programs such as NASTRAN. The software architecture of ESMOSS is designed in modular form with a central executive module through which the user controls and directs the development of the analytical model. Modules consist of a geometric shape generator, a library of discretization procedures, interfacing modules to join both geometric and discrete models, a deck generator to produce input for NASTRAN and a 'recipe' processor which generates geometric models from parametric definitions. ESMOSS can be executed both in interactive and batch modes. Interactive mode is considered to be the default mode and that mode will be assumed in the discussion in this document unless stated otherwise.

Finite Element Modeling of Coupled Flexible Multibody Dynamics and Liquid Sloshing

DTIC Science & Technology

2006-09-01

tanks is presented. The semi-discrete combined solid and fluid equations of motions are integrated using a time- accurate parallel explicit solver...Incompressible fluid flow in a moving/deforming container including accurate modeling of the free-surface, turbulence, and viscous effects ...paper, a single computational code which uses a time- accurate explicit solution procedure is used to solve both the solid and fluid equations of

14 CFR 93.339 - Requirements for operating in the DC SFRA, including the DC FRZ.

Code of Federal Regulations, 2010 CFR

2010-01-01

... aircraft in the DC SFRA, including the DC FRZ, the pilot obtains and transmits a discrete transponder code... flight plan by obtaining a discrete transponder code. The flight plan is closed upon landing at an... transmitting an Air Traffic Control-assigned discrete transponder code. (c) When operating an aircraft in the...

Numerical Simulations of Slow Stick Slip Events with PFC, a DEM Based Code

NASA Astrophysics Data System (ADS)

Ye, S. H.; Young, R. P.

2017-12-01

Nonvolcanic tremors around subduction zone have become a fascinating subject in seismology in recent years. Previous studies have shown that the nonvolcanic tremor beneath western Shikoku is composed of low frequency seismic waves overlapping each other. This finding provides direct link between tremor and slow earthquakes. Slow stick slip events are considered to be laboratory scaled slow earthquakes. Slow stick slip events are traditionally studied with direct shear or double direct shear experiment setup, in which the sliding velocity can be controlled to model a range of fast and slow stick slips. In this study, a PFC* model based on double direct shear is presented, with a central block clamped by two side blocks. The gauge layers between the central and side blocks are modelled as discrete fracture networks with smooth joint bonds between pairs of discrete elements. In addition, a second model is presented in this study. This model consists of a cylindrical sample subjected to triaxial stress. Similar to the previous model, a weak gauge layer at a 45 degrees is added into the sample, on which shear slipping is allowed. Several different simulations are conducted on this sample. While the confining stress is maintained at the same level in different simulations, the axial loading rate (displacement rate) varies. By varying the displacement rate, a range of slipping behaviour, from stick slip to slow stick slip are observed based on the stress-strain relationship. Currently, the stick slip and slow stick slip events are strictly observed based on the stress-strain relationship. In the future, we hope to monitor the displacement and velocity of the balls surrounding the gauge layer as a function of time, so as to generate a synthetic seismogram. This will allow us to extract seismic waveforms and potentially simulate the tremor-like waves found around subduction zones. *Particle flow code, a discrete element method based numerical simulation code developed by Itasca Inc.

Efficient and robust compositional two-phase reservoir simulation in fractured media

NASA Astrophysics Data System (ADS)

Zidane, A.; Firoozabadi, A.

2015-12-01

Compositional and compressible two-phase flow in fractured media has wide applications including CO2 injection. Accurate simulations are currently based on the discrete fracture approach using the cross-flow equilibrium model. In this approach the fractures and a small part of the matrix blocks are combined to form a grid cell. The major drawback is low computational efficiency. In this work we use the discrete-fracture approach to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross-flow equilibrium in the fractures (FCFE). This allows using large matrix elements in the neighborhood of the fractures. We solve the fracture transport equations implicitly to overcome the Courant-Freidricks-Levy (CFL) condition in the small fracture elements. Our implicit approach is based on calculation of the derivative of the molar concentration of component i in phase (cαi ) with respect to the total molar concentration (ci ) at constant volume V and temperature T. This contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix, and a finite volume (FV) discretization in the fractures. In large scale problems the proposed approach is orders of magnitude faster than the existing models.

Overview of the CHarring Ablator Response (CHAR) Code

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Oliver, A. Brandon; Kirk, Benjamin S.; Salazar, Giovanni; Droba, Justin

2016-01-01

An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation and contact interfaces, and example simulations are included. Finally, a discussion of ongoing development efforts is presented.

Overview of the CHarring Ablator Response (CHAR) Code

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Oliver, A. Brandon; Kirk, Benjamin S.; Salazar, Giovanni; Droba, Justin

2016-01-01

An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation, surface-to-surface radiation exchange, and flowfield coupling. Finally, a discussion of ongoing development efforts is presented.

The Overshoot Phenomenon in Geodynamics Codes

NASA Astrophysics Data System (ADS)

Kommu, R. K.; Heien, E. M.; Kellogg, L. H.; Bangerth, W.; Heister, T.; Studley, E. H.

2013-12-01

The overshoot phenomenon is a common occurrence in numerical software when a continuous function on a finite dimensional discretized space is used to approximate a discontinuous jump, in temperature and material concentration, for example. The resulting solution overshoots, and undershoots, the discontinuous jump. Numerical simulations play an extremely important role in mantle convection research. This is both due to the strong temperature and stress dependence of viscosity and also due to the inaccessibility of deep earth. Under these circumstances, it is essential that mantle convection simulations be extremely accurate and reliable. CitcomS and ASPECT are two finite element based mantle convection simulations developed and maintained by the Computational Infrastructure for Geodynamics. CitcomS is a finite element based mantle convection code that is designed to run on multiple high-performance computing platforms. ASPECT, an adaptive mesh refinement (AMR) code built on the Deal.II library, is also a finite element based mantle convection code that scales well on various HPC platforms. CitcomS and ASPECT both exhibit the overshoot phenomenon. One attempt at controlling the overshoot uses the Entropy Viscosity method, which introduces an artificial diffusion term in the energy equation of mantle convection. This artificial diffusion term is small where the temperature field is smooth. We present results from CitcomS and ASPECT that quantify the effect of the Entropy Viscosity method in reducing the overshoot phenomenon. In the discontinuous Galerkin (DG) finite element method, the test functions used in the method are continuous within each element but are discontinuous across inter-element boundaries. The solution space in the DG method is discontinuous. FEniCS is a collection of free software tools that automate the solution of differential equations using finite element methods. In this work we also present results from a finite element mantle convection simulation implemented in FEniCS that investigates the effect of using DG elements in reducing the overshoot problem.

Development of 3D electromagnetic modeling tools for airborne vehicles

NASA Technical Reports Server (NTRS)

Volakis, John L.

1992-01-01

The main goal of this project is to develop methodologies for scattering by airborne composite vehicles. Although our primary focus continues to be the development of a general purpose code for analyzing the entire structure as a single unit, a number of other tasks are also pursued in parallel with this effort. These tasks are important in testing the overall approach and in developing suitable models for materials coatings, junctions and, more generally, in assessing the effectiveness of the various parts comprising the final code. Here, we briefly discuss our progress on the five different tasks which were pursued during this period. Our progress on each of these tasks is described in the detailed reports (listed at the end of this report) and the memoranda included. The first task described below is, of course, the core of this project and deals with the development of the overall code. Undoubtedly, it is the outcome of the research which was funded by NASA-Ames and the Navy over the past three years. During this year we developed the first finite element code for scattering by structures of arbitrary shape and composition. The code employs a new absorbing boundary condition which allows termination of the finite element mesh only 0.3 lambda from the outer surface of the target. This leads to a remarkable reduction of the mesh size and is a unique feature of the code. Other unique features of this code include capabilities to model resistive sheets, impedance sheets and anisotropic materials. This last capability is the latest feature of the code and is still under development. The code has been extensively validated for a number of composite geometries and some examples are given. The validation of the code is still in progress for anisotropic and larger non-metallic geometries and cavities. The developed finite element code is based on a Galerkin's formulation and employs edge-based tetrahedral elements for discretizing the dielectric sections and the region between the target and the outer mesh termination boundary (ATB). This boundary is placed in conformity with the target's outer surface, thus resulting in additional reduction of the unknown count.

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

McGhee, J.M.; Roberts, R.M.; Morel, J.E.

1997-06-01

A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner formore » scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.« less

TADSim: Discrete Event-based Performance Prediction for Temperature Accelerated Dynamics

DOE PAGES

Mniszewski, Susan M.; Junghans, Christoph; Voter, Arthur F.; ...

2015-04-16

Next-generation high-performance computing will require more scalable and flexible performance prediction tools to evaluate software--hardware co-design choices relevant to scientific applications and hardware architectures. Here, we present a new class of tools called application simulators—parameterized fast-running proxies of large-scale scientific applications using parallel discrete event simulation. Parameterized choices for the algorithmic method and hardware options provide a rich space for design exploration and allow us to quickly find well-performing software--hardware combinations. We demonstrate our approach with a TADSim simulator that models the temperature-accelerated dynamics (TAD) method, an algorithmically complex and parameter-rich member of the accelerated molecular dynamics (AMD) family ofmore » molecular dynamics methods. The essence of the TAD application is captured without the computational expense and resource usage of the full code. We accomplish this by identifying the time-intensive elements, quantifying algorithm steps in terms of those elements, abstracting them out, and replacing them by the passage of time. We use TADSim to quickly characterize the runtime performance and algorithmic behavior for the otherwise long-running simulation code. We extend TADSim to model algorithm extensions, such as speculative spawning of the compute-bound stages, and predict performance improvements without having to implement such a method. Validation against the actual TAD code shows close agreement for the evolution of an example physical system, a silver surface. Finally, focused parameter scans have allowed us to study algorithm parameter choices over far more scenarios than would be possible with the actual simulation. This has led to interesting performance-related insights and suggested extensions.« less

Particles climbing along a vertically vibrating tube: numerical simulation using the Discrete Element Method (DEM)

DOE PAGES

Xu, Yupeng; Musser, Jordan; Li, Tingwen; ...

2017-07-22

It has been reported experimentally that granular particles can climb along a vertically vibrating tube partially inserted inside a granular silo. Here, we use the Discrete Element Method (DEM) available in the Multiphase Flow with Interphase eXchanges (MFIX) code to investigate this phenomenon. By tracking the movement of individual particles, the climbing mechanism was illustrated and analyzed. The numerical results show that a sufficiently high vibration strength is needed to form a low solids volume fraction region inside the lower end of the vibrating tube, a dense region in the middle of the tube, and to bring the particles outsidemore » from the top layers down to fill in the void. The results also show that particle compaction in the middle section of the tube is the main cause of the climbing. Consequently, varying parameters which influence the compacted region, such as the restitution coefficient, change the climbing height.« less

Particles climbing along a vertically vibrating tube: numerical simulation using the Discrete Element Method (DEM)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Yupeng; Musser, Jordan; Li, Tingwen

It has been reported experimentally that granular particles can climb along a vertically vibrating tube partially inserted inside a granular silo. Here, we use the Discrete Element Method (DEM) available in the Multiphase Flow with Interphase eXchanges (MFIX) code to investigate this phenomenon. By tracking the movement of individual particles, the climbing mechanism was illustrated and analyzed. The numerical results show that a sufficiently high vibration strength is needed to form a low solids volume fraction region inside the lower end of the vibrating tube, a dense region in the middle of the tube, and to bring the particles outsidemore » from the top layers down to fill in the void. The results also show that particle compaction in the middle section of the tube is the main cause of the climbing. Consequently, varying parameters which influence the compacted region, such as the restitution coefficient, change the climbing height.« less

A new 3D maser code applied to flaring events

NASA Astrophysics Data System (ADS)

Gray, M. D.; Mason, L.; Etoka, S.

2018-06-01

We set out the theory and discretization scheme for a new finite-element computer code, written specifically for the simulation of maser sources. The code was used to compute fractional inversions at each node of a 3D domain for a range of optical thicknesses. Saturation behaviour of the nodes with regard to location and optical depth was broadly as expected. We have demonstrated via formal solutions of the radiative transfer equation that the apparent size of the model maser cloud decreases as expected with optical depth as viewed by a distant observer. Simulations of rotation of the cloud allowed the construction of light curves for a number of observable quantities. Rotation of the model cloud may be a reasonable model for quasi-periodic variability, but cannot explain periodic flaring.

Fidelity of the Integrated Force Method Solution

NASA Technical Reports Server (NTRS)

Hopkins, Dale; Halford, Gary; Coroneos, Rula; Patnaik, Surya

2002-01-01

The theory of strain compatibility of the solid mechanics discipline was incomplete since St. Venant's 'strain formulation' in 1876. We have addressed the compatibility condition both in the continuum and the discrete system. This has lead to the formulation of the Integrated Force Method. A dual Integrated Force Method with displacement as the primal variable has also been formulated. A modest finite element code (IFM/Analyzers) based on the IFM theory has been developed. For a set of standard test problems the IFM results were compared with the stiffness method solutions and the MSC/Nastran code. For the problems IFM outperformed the existing methods. Superior IFM performance is attributed to simultaneous compliance of equilibrium equation and compatibility condition. MSC/Nastran organization expressed reluctance to accept the high fidelity IFM solutions. This report discusses the solutions to the examples. No inaccuracy was detected in the IFM solutions. A stiffness method code with a small programming effort can be improved to reap the many IFM benefits when implemented with the IFMD elements. Dr. Halford conducted a peer-review on the Integrated Force Method. Reviewers' response is included.

A comparison of the lattice discrete particle method to the finite-element method and the K&C material model for simulating the static and dynamic response of concrete.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Jovanca J.; Bishop, Joseph E.

2013-11-01

This report summarizes the work performed by the graduate student Jovanca Smith during a summer internship in the summer of 2012 with the aid of mentor Joe Bishop. The projects were a two-part endeavor that focused on the use of the numerical model called the Lattice Discrete Particle Model (LDPM). The LDPM is a discrete meso-scale model currently used at Northwestern University and the ERDC to model the heterogeneous quasi-brittle material, concrete. In the first part of the project, LDPM was compared to the Karagozian and Case Concrete Model (K&C) used in Presto, an explicit dynamics finite-element code, developed atmore » Sandia National Laboratories. In order to make this comparison, a series of quasi-static numerical experiments were performed, namely unconfined uniaxial compression tests on four varied cube specimen sizes, three-point bending notched experiments on three proportional specimen sizes, and six triaxial compression tests on a cylindrical specimen. The second part of this project focused on the application of LDPM to simulate projectile perforation on an ultra high performance concrete called CORTUF. This application illustrates the strengths of LDPM over traditional continuum models.« less

Grid Convergence for Turbulent Flows(Invited)

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Rumsey, Christopher L.; Schwoppe, Axel

2015-01-01

A detailed grid convergence study has been conducted to establish accurate reference solutions corresponding to the one-equation linear eddy-viscosity Spalart-Allmaras turbulence model for two dimensional turbulent flows around the NACA 0012 airfoil and a flat plate. The study involved three widely used codes, CFL3D (NASA), FUN3D (NASA), and TAU (DLR), and families of uniformly refined structured grids that differ in the grid density patterns. Solutions computed by different codes on different grid families appear to converge to the same continuous limit, but exhibit different convergence characteristics. The grid resolution in the vicinity of geometric singularities, such as a sharp trailing edge, is found to be the major factor affecting accuracy and convergence of discrete solutions, more prominent than differences in discretization schemes and/or grid elements. The results reported for these relatively simple turbulent flows demonstrate that CFL3D, FUN3D, and TAU solutions are very accurate on the finest grids used in the study, but even those grids are not sufficient to conclusively establish an asymptotic convergence order.

Which Chart Elements Accurately Identify Emergency Department Visits for Suicidal Ideation or Behavior?

PubMed

Arias, Sarah A; Boudreaux, Edwin D; Chen, Elizabeth; Miller, Ivan; Camargo, Carlos A; Jones, Richard N; Uebelacker, Lisa

2018-05-23

In an emergency department (ED) sample, we investigated the concordance between identification of suicide-related visits through standardized comprehensive chart review versus a subset of three specific chart elements: ICD-9-CM codes, free-text presenting complaints, and free-text physician discharge diagnoses. Review of medical records for adults (≥18 years) at eight EDs across the United States. A total of 3,776 charts were reviewed. A combination of the three chart elements (ICD-9-CM, presenting complaints, and discharge diagnoses) provided the most robust data with 85% sensitivity, 96% specificity, 92% PPV, and 92% NPV. These findings highlight the use of key discrete fields in the medical record that can be extracted to facilitate identification of whether an ED visit was suicide-related.

Probabilistic Structures Analysis Methods (PSAM) for select space propulsion system components

NASA Technical Reports Server (NTRS)

1991-01-01

The basic formulation for probabilistic finite element analysis is described and demonstrated on a few sample problems. This formulation is based on iterative perturbation that uses the factorized stiffness on the unperturbed system as the iteration preconditioner for obtaining the solution to the perturbed problem. This approach eliminates the need to compute, store and manipulate explicit partial derivatives of the element matrices and force vector, which not only reduces memory usage considerably, but also greatly simplifies the coding and validation tasks. All aspects for the proposed formulation were combined in a demonstration problem using a simplified model of a curved turbine blade discretized with 48 shell elements, and having random pressure and temperature fields with partial correlation, random uniform thickness, and random stiffness at the root.

A domain decomposition approach to implementing fault slip in finite-element models of quasi-static and dynamic crustal deformation

USGS Publications Warehouse

Aagaard, Brad T.; Knepley, M.G.; Williams, C.A.

2013-01-01

We employ a domain decomposition approach with Lagrange multipliers to implement fault slip in a finite-element code, PyLith, for use in both quasi-static and dynamic crustal deformation applications. This integrated approach to solving both quasi-static and dynamic simulations leverages common finite-element data structures and implementations of various boundary conditions, discretization schemes, and bulk and fault rheologies. We have developed a custom preconditioner for the Lagrange multiplier portion of the system of equations that provides excellent scalability with problem size compared to conventional additive Schwarz methods. We demonstrate application of this approach using benchmarks for both quasi-static viscoelastic deformation and dynamic spontaneous rupture propagation that verify the numerical implementation in PyLith.

Analysis and Calculation of the Fluid Flow and the Temperature Field by Finite Element Modeling

NASA Astrophysics Data System (ADS)

Dhamodaran, M.; Jegadeesan, S.; Kumar, R. Praveen

2018-04-01

This paper presents a fundamental and accurate approach to study numerical analysis of fluid flow and heat transfer inside a channel. In this study, the Finite Element Method is used to analyze the channel, which is divided into small subsections. The small subsections are discretized using higher number of domain elements and the corresponding number of nodes. MATLAB codes are developed to be used in the analysis. Simulation results showed that the analyses of fluid flow and temperature are influenced significantly by the changing entrance velocity. Also, there is an apparent effect on the temperature fields due to the presence of an energy source in the middle of the domain. In this paper, the characteristics of flow analysis and heat analysis in a channel have been investigated.

Hindcast Wave Information for the Great Lakes: Lake Huron. Wave Information Studies of US Coastlines

DTIC Science & Technology

1991-12-01

model used in this study, DWAVE , was developed by Dr. Donald T. Resio of Offshore and Coastal Technologies, Inc. It is described in Resio and Perrie...1989) and in an unpublished contractor’s report* available from the Wave Information Study (WIS) Project Office. 17. DWAVE is a FORTRAN computer code...discrete elements. Figure 4 shows how energy is partitioned in a directional spectrum within DWAVE . As seen there, each frequency-direction increment

Fast non-overlapping Schwarz domain decomposition methods for solving the neutron diffusion equation

NASA Astrophysics Data System (ADS)

Jamelot, Erell; Ciarlet, Patrick

2013-05-01

Studying numerically the steady state of a nuclear core reactor is expensive, in terms of memory storage and computational time. In order to address both requirements, one can use a domain decomposition method, implemented on a parallel computer. We present here such a method for the mixed neutron diffusion equations, discretized with Raviart-Thomas-Nédélec finite elements. This method is based on the Schwarz iterative algorithm with Robin interface conditions to handle communications. We analyse this method from the continuous point of view to the discrete point of view, and we give some numerical results in a realistic highly heterogeneous 3D configuration. Computations are carried out with the MINOS solver of the APOLLO3® neutronics code. APOLLO3 is a registered trademark in France.

ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

NASA Technical Reports Server (NTRS)

Fleury, C.; Schmit, L. A., Jr.

1980-01-01

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.

A novel encoding scheme for effective biometric discretization: Linearly Separable Subcode.

PubMed

Lim, Meng-Hui; Teoh, Andrew Beng Jin

2013-02-01

Separability in a code is crucial in guaranteeing a decent Hamming-distance separation among the codewords. In multibit biometric discretization where a code is used for quantization-intervals labeling, separability is necessary for preserving distance dissimilarity when feature components are mapped from a discrete space to a Hamming space. In this paper, we examine separability of Binary Reflected Gray Code (BRGC) encoding and reveal its inadequacy in tackling interclass variation during the discrete-to-binary mapping, leading to a tradeoff between classification performance and entropy of binary output. To overcome this drawback, we put forward two encoding schemes exhibiting full-ideal and near-ideal separability capabilities, known as Linearly Separable Subcode (LSSC) and Partially Linearly Separable Subcode (PLSSC), respectively. These encoding schemes convert the conventional entropy-performance tradeoff into an entropy-redundancy tradeoff in the increase of code length. Extensive experimental results vindicate the superiority of our schemes over the existing encoding schemes in discretization performance. This opens up possibilities of achieving much greater classification performance with high output entropy.

Sensitivity of Particle Size in Discrete Element Method to Particle Gas Method (DEM_PGM) Coupling in Underbody Blast Simulations

DTIC Science & Technology

2016-06-12

Particle Size in Discrete Element Method to Particle Gas Method (DEM_PGM) Coupling in Underbody Blast Simulations Venkatesh Babu, Kumar Kulkarni, Sanjay...buried in soil viz., (1) coupled discrete element & particle gas methods (DEM-PGM) and (2) Arbitrary Lagrangian-Eulerian (ALE), are investigated. The...DEM_PGM and identify the limitations/strengths compared to the ALE method. Discrete Element Method (DEM) can model individual particle directly, and

14 CFR 93.341 - Aircraft operations in the DC FRZ.

Code of Federal Regulations, 2010 CFR

2010-01-01

...-assigned discrete transponder code. The pilot must monitor VHF frequency 121.5 or UHF frequency 243.0. (d... authorization must file and activate an IFR or a DC FRZ or a DC SFRA flight plan and transmit a discrete transponder code assigned by an Air Traffic Control facility. Aircraft must transmit the discrete transponder...

Development of an hp-version finite element method for computational optimal control

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Warner, Michael S.

1993-01-01

The purpose of this research effort was to begin the study of the application of hp-version finite elements to the numerical solution of optimal control problems. Under NAG-939, the hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element. One possible drawback is the increased computational effort within each element required in implementing hp-version finite elements. We are trying to determine whether this computational effort is sufficiently offset by the reduction in the number of time elements used and improved Newton-Raphson convergence so as to be useful in solving optimal control problems in real time. Because certain of the element interior unknowns can be eliminated at the element level by solving a small set of nonlinear algebraic equations in which the nodal values are taken as given, the scheme may turn out to be especially powerful in a parallel computing environment. A different processor could be assigned to each element. The number of processors, strictly speaking, is not required to be any larger than the number of sub-regions which are free of discontinuities of any kind.

FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

NASA Astrophysics Data System (ADS)

Regnier, D.; Verrière, M.; Dubray, N.; Schunck, N.

2016-03-01

We describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in N-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank-Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle a realistic calculation of fission dynamics.

Setting up virgin stress conditions in discrete element models.

PubMed

Rojek, J; Karlis, G F; Malinowski, L J; Beer, G

2013-03-01

In the present work, a methodology for setting up virgin stress conditions in discrete element models is proposed. The developed algorithm is applicable to discrete or coupled discrete/continuum modeling of underground excavation employing the discrete element method (DEM). Since the DEM works with contact forces rather than stresses there is a need for the conversion of pre-excavation stresses to contact forces for the DEM model. Different possibilities of setting up virgin stress conditions in the DEM model are reviewed and critically assessed. Finally, a new method to obtain a discrete element model with contact forces equivalent to given macroscopic virgin stresses is proposed. The test examples presented show that good results may be obtained regardless of the shape of the DEM domain.

Setting up virgin stress conditions in discrete element models

PubMed Central

Rojek, J.; Karlis, G.F.; Malinowski, L.J.; Beer, G.

2013-01-01

In the present work, a methodology for setting up virgin stress conditions in discrete element models is proposed. The developed algorithm is applicable to discrete or coupled discrete/continuum modeling of underground excavation employing the discrete element method (DEM). Since the DEM works with contact forces rather than stresses there is a need for the conversion of pre-excavation stresses to contact forces for the DEM model. Different possibilities of setting up virgin stress conditions in the DEM model are reviewed and critically assessed. Finally, a new method to obtain a discrete element model with contact forces equivalent to given macroscopic virgin stresses is proposed. The test examples presented show that good results may be obtained regardless of the shape of the DEM domain. PMID:27087731

Final report for''FOSPACK''

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ruge, J W; Dean, D

2000-11-20

The goal of this subcontract was to modify the FOSPACK code, developed by John Ruge, to call the BoomerAMG solver developed at LLNL through the HYPRE interface. FOSPACK is a package developed for the automatic discretization and solution of First-Order System Least-Squares (FOSLS) formulations of 2D partial differential equations (c.f [3-9]). FOSPACK takes a user-specified mesh (which can be an unstructured combination of triangular and quadrilateral elements) and specification of the first-order system, and produces the discretizations needed for solution. Generally, all specifications are contained in data files, so no re-compilation is necessary when changing domains, mesh sizes, problems, etc.more » Much of the work in FOSPACK has gone into an interpreter that allows for simple, intuitive specification of the equations. The interpreter reads the equations, processes them, and stores them as instruction lists needed to apply the operators involved to finite element basis functions, allowing assembly of the discrete system. Quite complex equations may be specified, including variable coefficients, user defined functions, and vector notation. The first-order systems may be nonlinear, with linearizations either performed automatically, or specified in a convenient way by the user. The program also includes global/local refinement capability. FOSLS formulations are very well suited for solution by algebraic multigrid (AMG) (c.f. [10-13]). The original version uses a version of algebraic multigrid written by John Ruge in FORTRAN 77, and modified somewhat for use with FOSPACK. BoomerAMG, a version of AMG developed at CASC, has a number of advantages over the FORTRAN version, including dynamic memory allocation and parallel capability. This project was to benefit both FRSC and CASC, giving FOSPACK the advantages of BoomerAMG, while giving CASC a tool for testing FOSLS as a discretization method for problems of interest there. The major parts of this work were implementation and testing of the HYPRE package on our computers, writing a C wrapper/driver for the FOSPACK code, and modifying the wrapper to call BoomerAMG through the HYPRE interface.« less

Automatic programming of simulation models

NASA Technical Reports Server (NTRS)

Schroer, Bernard J.; Tseng, Fan T.; Zhang, Shou X.; Dwan, Wen S.

1990-01-01

The concepts of software engineering were used to improve the simulation modeling environment. Emphasis was placed on the application of an element of rapid prototyping, or automatic programming, to assist the modeler define the problem specification. Then, once the problem specification has been defined, an automatic code generator is used to write the simulation code. The following two domains were selected for evaluating the concepts of software engineering for discrete event simulation: manufacturing domain and a spacecraft countdown network sequence. The specific tasks were to: (1) define the software requirements for a graphical user interface to the Automatic Manufacturing Programming System (AMPS) system; (2) develop a graphical user interface for AMPS; and (3) compare the AMPS graphical interface with the AMPS interactive user interface.

Calibrating the stress-time curve of a combined finite-discrete element method to a Split Hopkinson Pressure Bar experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osthus, Dave; Godinez, Humberto C.; Rougier, Esteban

We presenmore » t a generic method for automatically calibrating a computer code to an experiment, with uncertainty, for a given “training” set of computer code runs. The calibration technique is general and probabilistic, meaning the calibration uncertainty is represented in the form of a probability distribution. We demonstrate the calibration method by calibrating a combined Finite-Discrete Element Method (FDEM) to a Split Hopkinson Pressure Bar (SHPB) experiment with a granite sample. The probabilistic calibration method combines runs of a FDEM computer simulation for a range of “training” settings and experimental uncertainty to develop a statistical emulator. The process allows for calibration of input parameters and produces output quantities with uncertainty estimates for settings where simulation results are desired. Input calibration and FDEM fitted results are presented. We find that the maximum shear strength σ t max and to a lesser extent maximum tensile strength σ n max govern the behavior of the stress-time curve before and around the peak, while the specific energy in Mode II (shear) E t largely governs the post-peak behavior of the stress-time curve. Good agreement is found between the calibrated FDEM and the SHPB experiment. Interestingly, we find the SHPB experiment to be rather uninformative for calibrating the softening-curve shape parameters (a, b, and c). This work stands as a successful demonstration of how a general probabilistic calibration framework can automatically calibrate FDEM parameters to an experiment.« less

Calibrating the stress-time curve of a combined finite-discrete element method to a Split Hopkinson Pressure Bar experiment

DOE PAGES

Osthus, Dave; Godinez, Humberto C.; Rougier, Esteban; ...

2018-05-01

We presenmore » t a generic method for automatically calibrating a computer code to an experiment, with uncertainty, for a given “training” set of computer code runs. The calibration technique is general and probabilistic, meaning the calibration uncertainty is represented in the form of a probability distribution. We demonstrate the calibration method by calibrating a combined Finite-Discrete Element Method (FDEM) to a Split Hopkinson Pressure Bar (SHPB) experiment with a granite sample. The probabilistic calibration method combines runs of a FDEM computer simulation for a range of “training” settings and experimental uncertainty to develop a statistical emulator. The process allows for calibration of input parameters and produces output quantities with uncertainty estimates for settings where simulation results are desired. Input calibration and FDEM fitted results are presented. We find that the maximum shear strength σ t max and to a lesser extent maximum tensile strength σ n max govern the behavior of the stress-time curve before and around the peak, while the specific energy in Mode II (shear) E t largely governs the post-peak behavior of the stress-time curve. Good agreement is found between the calibrated FDEM and the SHPB experiment. Interestingly, we find the SHPB experiment to be rather uninformative for calibrating the softening-curve shape parameters (a, b, and c). This work stands as a successful demonstration of how a general probabilistic calibration framework can automatically calibrate FDEM parameters to an experiment.« less

Finite element code development for modeling detonation of HMX composites

NASA Astrophysics Data System (ADS)

Duran, Adam V.; Sundararaghavan, Veera

2017-01-01

In this work, we present a hydrodynamics code for modeling shock and detonation waves in HMX. A stable efficient solution strategy based on a Taylor-Galerkin finite element (FE) discretization was developed to solve the reactive Euler equations. In our code, well calibrated equations of state for the solid unreacted material and gaseous reaction products have been implemented, along with a chemical reaction scheme and a mixing rule to define the properties of partially reacted states. A linear Gruneisen equation of state was employed for the unreacted HMX calibrated from experiments. The JWL form was used to model the EOS of gaseous reaction products. It is assumed that the unreacted explosive and reaction products are in both pressure and temperature equilibrium. The overall specific volume and internal energy was computed using the rule of mixtures. Arrhenius kinetics scheme was integrated to model the chemical reactions. A locally controlled dissipation was introduced that induces a non-oscillatory stabilized scheme for the shock front. The FE model was validated using analytical solutions for SOD shock and ZND strong detonation models. Benchmark problems are presented for geometries in which a single HMX crystal is subjected to a shock condition.

A Fast Optimization Method for General Binary Code Learning.

PubMed

Shen, Fumin; Zhou, Xiang; Yang, Yang; Song, Jingkuan; Shen, Heng; Tao, Dacheng

2016-09-22

Hashing or binary code learning has been recognized to accomplish efficient near neighbor search, and has thus attracted broad interests in recent retrieval, vision and learning studies. One main challenge of learning to hash arises from the involvement of discrete variables in binary code optimization. While the widely-used continuous relaxation may achieve high learning efficiency, the pursued codes are typically less effective due to accumulated quantization error. In this work, we propose a novel binary code optimization method, dubbed Discrete Proximal Linearized Minimization (DPLM), which directly handles the discrete constraints during the learning process. Specifically, the discrete (thus nonsmooth nonconvex) problem is reformulated as minimizing the sum of a smooth loss term with a nonsmooth indicator function. The obtained problem is then efficiently solved by an iterative procedure with each iteration admitting an analytical discrete solution, which is thus shown to converge very fast. In addition, the proposed method supports a large family of empirical loss functions, which is particularly instantiated in this work by both a supervised and an unsupervised hashing losses, together with the bits uncorrelation and balance constraints. In particular, the proposed DPLM with a supervised `2 loss encodes the whole NUS-WIDE database into 64-bit binary codes within 10 seconds on a standard desktop computer. The proposed approach is extensively evaluated on several large-scale datasets and the generated binary codes are shown to achieve very promising results on both retrieval and classification tasks.

Investigation into discretization methods of the six-parameter Iwan model

NASA Astrophysics Data System (ADS)

Li, Yikun; Hao, Zhiming; Feng, Jiaquan; Zhang, Dingguo

2017-02-01

Iwan model is widely applied for the purpose of describing nonlinear mechanisms of jointed structures. In this paper, parameter identification procedures of the six-parameter Iwan model based on joint experiments with different preload techniques are performed. Four kinds of discretization methods deduced from stiffness equation of the six-parameter Iwan model are provided, which can be used to discretize the integral-form Iwan model into a sum of finite Jenkins elements. In finite element simulation, the influences of discretization methods and numbers of Jenkins elements on computing accuracy are discussed. Simulation results indicate that a higher accuracy can be obtained with larger numbers of Jenkins elements. It is also shown that compared with other three kinds of discretization methods, the geometric series discretization based on stiffness provides the highest computing accuracy.

Modeling interfacial fracture in Sierra.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Arthur A.; Ohashi, Yuki; Lu, Wei-Yang

2013-09-01

This report summarizes computational efforts to model interfacial fracture using cohesive zone models in the SIERRA/SolidMechanics (SIERRA/SM) finite element code. Cohesive surface elements were used to model crack initiation and propagation along predefined paths. Mesh convergence was observed with SIERRA/SM for numerous geometries. As the funding for this project came from the Advanced Simulation and Computing Verification and Validation (ASC V&V) focus area, considerable effort was spent performing verification and validation. Code verification was performed to compare code predictions to analytical solutions for simple three-element simulations as well as a higher-fidelity simulation of a double-cantilever beam. Parameter identification was conductedmore » with Dakota using experimental results on asymmetric double-cantilever beam (ADCB) and end-notched-flexure (ENF) experiments conducted under Campaign-6 funding. Discretization convergence studies were also performed with respect to mesh size and time step and an optimization study was completed for mode II delamination using the ENF geometry. Throughout this verification process, numerous SIERRA/SM bugs were found and reported, all of which have been fixed, leading to over a 10-fold increase in convergence rates. Finally, mixed-mode flexure experiments were performed for validation. One of the unexplained issues encountered was material property variability for ostensibly the same composite material. Since the variability is not fully understood, it is difficult to accurately assess uncertainty when performing predictions.« less

Discrete Ramanujan transform for distinguishing the protein coding regions from other regions.

PubMed

Hua, Wei; Wang, Jiasong; Zhao, Jian

2014-01-01

Based on the study of Ramanujan sum and Ramanujan coefficient, this paper suggests the concepts of discrete Ramanujan transform and spectrum. Using Voss numerical representation, one maps a symbolic DNA strand as a numerical DNA sequence, and deduces the discrete Ramanujan spectrum of the numerical DNA sequence. It is well known that of discrete Fourier power spectrum of protein coding sequence has an important feature of 3-base periodicity, which is widely used for DNA sequence analysis by the technique of discrete Fourier transform. It is performed by testing the signal-to-noise ratio at frequency N/3 as a criterion for the analysis, where N is the length of the sequence. The results presented in this paper show that the property of 3-base periodicity can be only identified as a prominent spike of the discrete Ramanujan spectrum at period 3 for the protein coding regions. The signal-to-noise ratio for discrete Ramanujan spectrum is defined for numerical measurement. Therefore, the discrete Ramanujan spectrum and the signal-to-noise ratio of a DNA sequence can be used for distinguishing the protein coding regions from the noncoding regions. All the exon and intron sequences in whole chromosomes 1, 2, 3 and 4 of Caenorhabditis elegans have been tested and the histograms and tables from the computational results illustrate the reliability of our method. In addition, we have analyzed theoretically and gotten the conclusion that the algorithm for calculating discrete Ramanujan spectrum owns the lower computational complexity and higher computational accuracy. The computational experiments show that the technique by using discrete Ramanujan spectrum for classifying different DNA sequences is a fast and effective method. Copyright © 2014 Elsevier Ltd. All rights reserved.

Blasim: A computational tool to assess ice impact damage on engine blades

NASA Astrophysics Data System (ADS)

Reddy, E. S.; Abumeri, G. H.; Chamis, C. C.

1993-04-01

A portable computer called BLASIM was developed at NASA LeRC to assess ice impact damage on aircraft engine blades. In addition to ice impact analyses, the code also contains static, dynamic, resonance margin, and supersonic flutter analysis capabilities. Solid, hollow, superhybrid, and composite blades are supported. An optional preprocessor (input generator) was also developed to interactively generate input for BLASIM. The blade geometry can be defined using a series of airfoils at discrete input stations or by a finite element grid. The code employs a coarse, fixed finite element mesh containing triangular plate finite elements to minimize program execution time. Ice piece is modeled using an equivalent spherical objective that has a high velocity opposite that of the aircraft and parallel to the engine axis. For local impact damage assessment, the impact load is considered as a distributed force acting over a region around the impact point. The average radial strain of the finite elements along the leading edge is used as a measure of the local damage. To estimate damage at the blade root, the impact is treated as an impulse and a combined stress failure criteria is employed. Parametric studies of local and root ice impact damage, and post-impact dynamics are discussed for solid and composite blades.

Development of an integrated BEM approach for hot fluid structure interaction

NASA Technical Reports Server (NTRS)

Dargush, Gary F.; Banerjee, Prasanta K.; Dunn, Michael G.

1988-01-01

Significant progress was made toward the goal of developing a general purpose boundary element method for hot fluid-structure interaction. For the solid phase, a boundary-only formulation was developed and implemented for uncoupled transient thermoelasticity in two dimensions. The elimination of volume discretization not only drastically reduces required modeling effort, but also permits unconstrained variation of the through-the-thickness temperature distribution. Meanwhile, for the fluids, fundamental solutions were derived for transient incompressible and compressible flow in the absence of the convective terms. Boundary element formulations were developed and described. For the incompressible case, the necessary kernal functions, under transient and steady-state conditions, were derived and fully implemented into a general purpose, multi-region boundary element code. Several examples were examined to study the suitability and convergence characteristics of the various algorithms.

Development of an adaptive hp-version finite element method for computational optimal control

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Warner, Michael S.

1994-01-01

In this research effort, the usefulness of hp-version finite elements and adaptive solution-refinement techniques in generating numerical solutions to optimal control problems has been investigated. Under NAG-939, a general FORTRAN code was developed which approximated solutions to optimal control problems with control constraints and state constraints. Within that methodology, to get high-order accuracy in solutions, the finite element mesh would have to be refined repeatedly through bisection of the entire mesh in a given phase. In the current research effort, the order of the shape functions in each element has been made a variable, giving more flexibility in error reduction and smoothing. Similarly, individual elements can each be subdivided into many pieces, depending on the local error indicator, while other parts of the mesh remain coarsely discretized. The problem remains to reduce and smooth the error while still keeping computational effort reasonable enough to calculate time histories in a short enough time for on-board applications.

Higher-order adaptive finite-element methods for Kohn–Sham density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Motamarri, P.; Nowak, M.R.; Leiter, K.

2013-11-15

We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposedmore » solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using modest computational resources, and good scalability of the present implementation up to 192 processors.« less

Stabilization and discontinuity-capturing parameters for space-time flow computations with finite element and isogeometric discretizations

NASA Astrophysics Data System (ADS)

Takizawa, Kenji; Tezduyar, Tayfun E.; Otoguro, Yuto

2018-04-01

Stabilized methods, which have been very common in flow computations for many years, typically involve stabilization parameters, and discontinuity-capturing (DC) parameters if the method is supplemented with a DC term. Various well-performing stabilization and DC parameters have been introduced for stabilized space-time (ST) computational methods in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible and compressible flows. These parameters were all originally intended for finite element discretization but quite often used also for isogeometric discretization. The stabilization and DC parameters we present here for ST computations are in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible flows, target isogeometric discretization, and are also applicable to finite element discretization. The parameters are based on a direction-dependent element length expression. The expression is outcome of an easy to understand derivation. The key components of the derivation are mapping the direction vector from the physical ST element to the parent ST element, accounting for the discretization spacing along each of the parametric coordinates, and mapping what we have in the parent element back to the physical element. The test computations we present for pure-advection cases show that the parameters proposed result in good solution profiles.

Learning Discriminative Binary Codes for Large-scale Cross-modal Retrieval.

PubMed

Xu, Xing; Shen, Fumin; Yang, Yang; Shen, Heng Tao; Li, Xuelong

2017-05-01

Hashing based methods have attracted considerable attention for efficient cross-modal retrieval on large-scale multimedia data. The core problem of cross-modal hashing is how to learn compact binary codes that construct the underlying correlations between heterogeneous features from different modalities. A majority of recent approaches aim at learning hash functions to preserve the pairwise similarities defined by given class labels. However, these methods fail to explicitly explore the discriminative property of class labels during hash function learning. In addition, they usually discard the discrete constraints imposed on the to-be-learned binary codes, and compromise to solve a relaxed problem with quantization to obtain the approximate binary solution. Therefore, the binary codes generated by these methods are suboptimal and less discriminative to different classes. To overcome these drawbacks, we propose a novel cross-modal hashing method, termed discrete cross-modal hashing (DCH), which directly learns discriminative binary codes while retaining the discrete constraints. Specifically, DCH learns modality-specific hash functions for generating unified binary codes, and these binary codes are viewed as representative features for discriminative classification with class labels. An effective discrete optimization algorithm is developed for DCH to jointly learn the modality-specific hash function and the unified binary codes. Extensive experiments on three benchmark data sets highlight the superiority of DCH under various cross-modal scenarios and show its state-of-the-art performance.

Full Wave Analysis of RF Signal Attenuation in a Lossy Cave using a High Order Time Domain Vector Finite Element Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pingenot, J; Rieben, R; White, D

2004-12-06

We present a computational study of signal propagation and attenuation of a 200 MHz dipole antenna in a cave environment. The cave is modeled as a straight and lossy random rough wall. To simulate a broad frequency band, the full wave Maxwell equations are solved directly in the time domain via a high order vector finite element discretization using the massively parallel CEM code EMSolve. The simulation is performed for a series of random meshes in order to generate statistical data for the propagation and attenuation properties of the cave environment. Results for the power spectral density and phase ofmore » the electric field vector components are presented and discussed.« less

FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

DOE PAGES

Regnier, D.; Verriere, M.; Dubray, N.; ...

2015-11-30

In this study, we describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in NN-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank–Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle amore » realistic calculation of fission dynamics.« less

NASTRAN as a resource in code development

NASA Technical Reports Server (NTRS)

Stanton, E. L.; Crain, L. M.; Neu, T. F.

1975-01-01

A case history is presented in which the NASTRAN system provided both guidelines and working software for use in the development of a discrete element program, PATCHES-111. To avoid duplication and to take advantage of the wide spread user familiarity with NASTRAN, the PATCHES-111 system uses NASTRAN bulk data syntax, NASTRAN matrix utilities, and the NASTRAN linkage editor. Problems in developing the program are discussed along with details on the architecture of the PATCHES-111 parametric cubic modeling system. The system includes model construction procedures, checkpoint/restart strategies, and other features.

Discrete Sparse Coding.

PubMed

Exarchakis, Georgios; Lücke, Jörg

2017-11-01

Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.

An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA

NASA Technical Reports Server (NTRS)

Djomehri, M. Jahed; Erickson, Larry L.

1994-01-01

A three-dimensional solution-adaptive Euler flow solver for unstructured tetrahedral meshes is assessed, and the accuracy and efficiency of the method for predicting sonic boom pressure signatures about simple generic models are demonstrated. Comparison of computational and wind tunnel data and enhancement of numerical solutions by means of grid adaptivity are discussed. The mesh generation is based on the advancing front technique. The FELISA code consists of two solvers, the Taylor-Galerkin and the Runge-Kutta-Galerkin schemes, both of which are spacially discretized by the usual Galerkin weighted residual finite-element methods but with different explicit time-marching schemes to steady state. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry adaptive procedure is also incorporated.

Vectorial finite elements for solving the radiative transfer equation

NASA Astrophysics Data System (ADS)

Badri, M. A.; Jolivet, P.; Rousseau, B.; Le Corre, S.; Digonnet, H.; Favennec, Y.

2018-06-01

The discrete ordinate method coupled with the finite element method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard finite elements, we reformulate the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial finite element discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.

Meshfree Modeling of Munitions Penetration in Soils

DTIC Science & Technology

2017-04-01

discretization ...................... 8 Figure 2. Nodal smoothing domain for the modified stabilized nonconforming nodal integration...projectile ............................................................................................... 36 Figure 17. Discretization for the...List of Acronyms DEM: discrete element methods FEM: finite element methods MSNNI: modified stabilized nonconforming nodal integration RK

A refined finite element method for bending analysis of laminated plates integrated with piezoelectric fiber-reinforced composite actuators

NASA Astrophysics Data System (ADS)

Rouzegar, J.; Abbasi, A.

2018-03-01

This research presents a finite element formulation based on four-variable refined plate theory for bending analysis of cross-ply and angle-ply laminated composite plates integrated with a piezoelectric fiber-reinforced composite actuator under electromechanical loading. The four-variable refined plate theory is a simple and efficient higher-order shear deformation theory, which predicts parabolic variation of transverse shear stresses across the plate thickness and satisfies zero traction conditions on the plate free surfaces. The weak form of governing equations is derived using the principle of minimum potential energy, and a 4-node non-conforming rectangular plate element with 8 degrees of freedom per node is introduced for discretizing the domain. Several benchmark problems are solved by the developed MATLAB code and the obtained results are compared with those from exact and other numerical solutions, showing good agreement.

Stochastic-Strength-Based Damage Simulation of Ceramic Matrix Composite Laminates

NASA Technical Reports Server (NTRS)

Nemeth, Noel N.; Mital, Subodh K.; Murthy, Pappu L. N.; Bednarcyk, Brett A.; Pineda, Evan J.; Bhatt, Ramakrishna T.; Arnold, Steven M.

2016-01-01

The Finite Element Analysis-Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program was used to characterize and predict the progressive damage response of silicon-carbide-fiber-reinforced reaction-bonded silicon nitride matrix (SiC/RBSN) composite laminate tensile specimens. Studied were unidirectional laminates [0] (sub 8), [10] (sub 8), [45] (sub 8), and [90] (sub 8); cross-ply laminates [0 (sub 2) divided by 90 (sub 2),]s; angled-ply laminates [plus 45 (sub 2) divided by -45 (sub 2), ]s; doubled-edge-notched [0] (sub 8), laminates; and central-hole laminates. Results correlated well with the experimental data. This work was performed as a validation and benchmarking exercise of the FEAMAC/CARES program. FEAMAC/CARES simulates stochastic-based discrete-event progressive damage of ceramic matrix composite and polymer matrix composite material structures. It couples three software programs: (1) the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), (2) the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program (CARES/Life), and (3) the Abaqus finite element analysis program. MAC/GMC contributes multiscale modeling capabilities and micromechanics relations to determine stresses and deformations at the microscale of the composite material repeating-unit-cell (RUC). CARES/Life contributes statistical multiaxial failure criteria that can be applied to the individual brittle-material constituents of the RUC, and Abaqus is used to model the overall composite structure. For each FEAMAC/CARES simulation trial, the stochastic nature of brittle material strength results in random, discrete damage events that incrementally progress until ultimate structural failure.

Albany/FELIX: A parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

DOE PAGES

Tezaur, I. K.; Perego, M.; Salinger, A. G.; ...

2015-04-27

This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, alongmore » with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.« less

A parallel Discrete Element Method to model collisions between non-convex particles

NASA Astrophysics Data System (ADS)

Rakotonirina, Andriarimina Daniel; Delenne, Jean-Yves; Wachs, Anthony

2017-06-01

In many dry granular and suspension flow configurations, particles can be highly non-spherical. It is now well established in the literature that particle shape affects the flow dynamics or the microstructure of the particles assembly in assorted ways as e.g. compacity of packed bed or heap, dilation under shear, resistance to shear, momentum transfer between translational and angular motions, ability to form arches and block the flow. In this talk, we suggest an accurate and efficient way to model collisions between particles of (almost) arbitrary shape. For that purpose, we develop a Discrete Element Method (DEM) combined with a soft particle contact model. The collision detection algorithm handles contacts between bodies of various shape and size. For nonconvex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones. Therefore, our novel method can be called "glued-convex method" (in the sense clumping convex bodies together), as an extension of the popular "glued-spheres" method, and is implemented in our own granular dynamics code Grains3D. Since the whole problem is solved explicitly, our fully-MPI parallelized code Grains3D exhibits a very high scalability when dynamic load balancing is not required. In particular, simulations on up to a few thousands cores in configurations involving up to a few tens of millions of particles can readily be performed. We apply our enhanced numerical model to (i) the collapse of a granular column made of convex particles and (i) the microstructure of a heap of non-convex particles in a cylindrical reactor.

PowderSim: Lagrangian Discrete and Mesh-Free Continuum Simulation Code for Cohesive Soils

NASA Technical Reports Server (NTRS)

Johnson, Scott; Walton, Otis; Settgast, Randolph

2013-01-01

PowderSim is a calculation tool that combines a discrete-element method (DEM) module, including calibrated interparticle-interaction relationships, with a mesh-free, continuum, SPH (smoothed-particle hydrodynamics) based module that utilizes enhanced, calibrated, constitutive models capable of mimicking both large deformations and the flow behavior of regolith simulants and lunar regolith under conditions anticipated during in situ resource utilization (ISRU) operations. The major innovation introduced in PowderSim is to use a mesh-free method (SPH-based) with a calibrated and slightly modified critical-state soil mechanics constitutive model to extend the ability of the simulation tool to also address full-scale engineering systems in the continuum sense. The PowderSim software maintains the ability to address particle-scale problems, like size segregation, in selected regions with a traditional DEM module, which has improved contact physics and electrostatic interaction models.

Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces.

PubMed

Bardhan, Jaydeep P; Altman, Michael D; Willis, David J; Lippow, Shaun M; Tidor, Bruce; White, Jacob K

2007-07-07

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.

An Application of Discrete Mathematics to Coding Theory.

ERIC Educational Resources Information Center

Donohoe, L. Joyce

1992-01-01

Presents a public-key cryptosystem application to introduce students to several topics in discrete mathematics. A computer algorithms using recursive methods is presented to solve a problem in which one person wants to send a coded message to a second person while keeping the message secret from a third person. (MDH)

Hypersonic Viscous Flow Over Large Roughness Elements

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Choudhari, Meelan M.

2009-01-01

Viscous flow over discrete or distributed surface roughness has great implications for hypersonic flight due to aerothermodynamic considerations related to laminar-turbulent transition. Current prediction capability is greatly hampered by the limited knowledge base for such flows. To help fill that gap, numerical computations are used to investigate the intricate flow physics involved. An unstructured mesh, compressible Navier-Stokes code based on the space-time conservation element, solution element (CESE) method is used to perform time-accurate Navier-Stokes calculations for two roughness shapes investigated in wind tunnel experiments at NASA Langley Research Center. It was found through 2D parametric study that at subcritical Reynolds numbers of the boundary layers, absolute instability resulting in vortex shedding downstream, is likely to weaken at supersonic free-stream conditions. On the other hand, convective instability may be the dominant mechanism for supersonic boundary layers. Three-dimensional calculations for a rectangular or cylindrical roughness element at post-shock Mach numbers of 4.1 and 6.5 also confirm that no self-sustained vortex generation is present.

Inversion of potential field data using the finite element method on parallel computers

NASA Astrophysics Data System (ADS)

Gross, L.; Altinay, C.; Shaw, S.

2015-11-01

In this paper we present a formulation of the joint inversion of potential field anomaly data as an optimization problem with partial differential equation (PDE) constraints. The problem is solved using the iterative Broyden-Fletcher-Goldfarb-Shanno (BFGS) method with the Hessian operator of the regularization and cross-gradient component of the cost function as preconditioner. We will show that each iterative step requires the solution of several PDEs namely for the potential fields, for the adjoint defects and for the application of the preconditioner. In extension to the traditional discrete formulation the BFGS method is applied to continuous descriptions of the unknown physical properties in combination with an appropriate integral form of the dot product. The PDEs can easily be solved using standard conforming finite element methods (FEMs) with potentially different resolutions. For two examples we demonstrate that the number of PDE solutions required to reach a given tolerance in the BFGS iteration is controlled by weighting regularization and cross-gradient but is independent of the resolution of PDE discretization and that as a consequence the method is weakly scalable with the number of cells on parallel computers. We also show a comparison with the UBC-GIF GRAV3D code.

Preliminary user's manuals for DYNA3D and DYNAP. [In FORTRAN IV for CDC 7600 and Cray-1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hallquist, J. O.

1979-10-01

This report provides a user's manual for DYNA3D, an explicit three-dimensional finite-element code for analyzing the large deformation dynamic response of inelastic solids. A contact-impact algorithm permits gaps and sliding along material interfaces. By a specialization of this algorithm, such interfaces can be rigidly tied to admit variable zoning without the need of transition regions. Spatial discretization is achieved by the use of 8-node solid elements, and the equations of motion are integrated by the central difference method. Post-processors for DYNA3D include GRAPE for plotting deformed shapes and stress contours and DYNAP for plotting time histories. A user's manual formore » DYNAP is also provided. 23 figures.« less

The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions.

PubMed

Arridge, S R; Dehghani, H; Schweiger, M; Okada, E

2000-01-01

We present a method for handling nonscattering regions within diffusing domains. The method develops from an iterative radiosity-diffusion approach using Green's functions that was computationally slow. Here we present an improved implementation using a finite element method (FEM) that is direct. The fundamental idea is to introduce extra equations into the standard diffusion FEM to represent nondiffusive light propagation across a nonscattering region. By appropriate mesh node ordering the computational time is not much greater than for diffusion alone. We compare results from this method with those from a discrete ordinate transport code, and with Monte Carlo calculations. The agreement is very good, and, in addition, our scheme allows us to easily model time-dependent and frequency domain problems.

DEM code-based modeling of energy accumulation and release in structurally heterogeneous rock masses

NASA Astrophysics Data System (ADS)

Lavrikov, S. V.; Revuzhenko, A. F.

2015-10-01

Based on discrete element method, the authors model loading of a physical specimen to describe its capacity to accumulate and release elastic energy. The specimen is modeled as a packing of particles with viscoelastic coupling and friction. The external elastic boundary of the packing is represented by particles connected by elastic springs. The latter means introduction of an additional special potential of interaction between the boundary particles, that exercises effect even when there is no direct contact between the particles. On the whole, the model specimen represents an element of a medium capable of accumulation of deformation energy in the form of internal stresses. The data of the numerical modeling of the physical specimen compression and the laboratory testing results show good qualitative consistency.

Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements

NASA Astrophysics Data System (ADS)

Crean, Jared; Hicken, Jason E.; Del Rey Fernández, David C.; Zingg, David W.; Carpenter, Mark H.

2018-03-01

We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor-product discretizations. In the absence of dissipation, we prove that the semi-discrete scheme conserves entropy; significantly, this proof of nonlinear L2 stability does not rely on integral exactness. Furthermore, interior penalties can be incorporated into the discretization to ensure that the total (mathematical) entropy decreases monotonically, producing an entropy-stable scheme. SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions. In three-dimensions, we describe an elementwise optimization that leads to suitable Jacobians in the case of polynomial mappings. The properties of the semi-discrete scheme are verified and investigated using numerical experiments.

Numerical simulation of inductive method for determining spatial distribution of critical current density

NASA Astrophysics Data System (ADS)

Kamitani, A.; Takayama, T.; Tanaka, A.; Ikuno, S.

2010-11-01

The inductive method for measuring the critical current density jC in a high-temperature superconducting (HTS) thin film has been investigated numerically. In order to simulate the method, a non-axisymmetric numerical code has been developed for analyzing the time evolution of the shielding current density. In the code, the governing equation of the shielding current density is spatially discretized with the finite element method and the resulting first-order ordinary differential system is solved by using the 5th-order Runge-Kutta method with an adaptive step-size control algorithm. By using the code, the threshold current IT is evaluated for various positions of a coil. The results of computations show that, near a film edge, the accuracy of the estimating formula for jC is remarkably degraded. Moreover, even the proportional relationship between jC and IT will be lost there. Hence, the critical current density near a film edge cannot be estimated by using the inductive method.

A Deep Penetration Problem Calculation Using AETIUS:An Easy Modeling Discrete Ordinates Transport Code UsIng Unstructured Tetrahedral Mesh, Shared Memory Parallel

NASA Astrophysics Data System (ADS)

KIM, Jong Woon; LEE, Young-Ouk

2017-09-01

As computing power gets better and better, computer codes that use a deterministic method seem to be less useful than those using the Monte Carlo method. In addition, users do not like to think about space, angles, and energy discretization for deterministic codes. However, a deterministic method is still powerful in that we can obtain a solution of the flux throughout the problem, particularly as when particles can barely penetrate, such as in a deep penetration problem with small detection volumes. Recently, a new state-of-the-art discrete-ordinates code, ATTILA, was developed and has been widely used in several applications. ATTILA provides the capabilities to solve geometrically complex 3-D transport problems by using an unstructured tetrahedral mesh. Since 2009, we have been developing our own code by benchmarking ATTILA. AETIUS is a discrete ordinates code that uses an unstructured tetrahedral mesh such as ATTILA. For pre- and post- processing, Gmsh is used to generate an unstructured tetrahedral mesh by importing a CAD file (*.step) and visualizing the calculation results of AETIUS. Using a CAD tool, the geometry can be modeled very easily. In this paper, we describe a brief overview of AETIUS and provide numerical results from both AETIUS and a Monte Carlo code, MCNP5, in a deep penetration problem with small detection volumes. The results demonstrate the effectiveness and efficiency of AETIUS for such calculations.

Simple Common Plane contact algorithm for explicit FE/FD methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vorobiev, O

2006-12-18

Common-plane (CP) algorithm is widely used in Discrete Element Method (DEM) to model contact forces between interacting particles or blocks. A new simple contact algorithm is proposed to model contacts in FE/FD methods which is similar to the CP algorithm. The CP is defined as a plane separating interacting faces of FE/FD mesh instead of blocks or particles used in the original CP method. The new method does not require iterations even for very stiff contacts. It is very robust and easy to implement both in 2D and 3D parallel codes.

Wheat mill stream properties for discrete element method modeling

USDA-ARS?s Scientific Manuscript database

A discrete phase approach based on individual wheat kernel characteristics is needed to overcome the limitations of previous statistical models and accurately predict the milling behavior of wheat. As a first step to develop a discrete element method (DEM) model for the wheat milling process, this s...

Numerical Simulations of Free Surface Magnetohydrodynamic Flows

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Glimm, James; Oh, Wonho; Prykarpatskyy, Yarema

2003-11-01

We have developed a numerical algorithm and performed simulations of magnetohydrodynamic (MHD) free surface flows. The corresponding system of MHD equations is a system of strongly coupled hyperbolic and parabolic/elliptic equations in moving and geometrically complex domains. The hyperbolic system is solved using the front tracking technique for the free fluid interface. Parallel algorithms for solving elliptic and parabolic equations are based on a finite element discretization on moving grids dynamically conforming to fluid interfaces. The method has been implemented as an MHD extension of the FronTier code. The code has been applied for modeling the behavior of lithium and mercury jets in magnetic fields, laser ablation plumes, and the Richtmyer-Meshkov instability of a liquid mercury jet interacting with a high energy proton pulse in a strong magnetic field. Such an instability occurs in the target for the Muon Collider.

Infant differential behavioral responding to discrete emotions.

PubMed

Walle, Eric A; Reschke, Peter J; Camras, Linda A; Campos, Joseph J

2017-10-01

Emotional communication regulates the behaviors of social partners. Research on individuals' responding to others' emotions typically compares responses to a single negative emotion compared with responses to a neutral or positive emotion. Furthermore, coding of such responses routinely measure surface level features of the behavior (e.g., approach vs. avoidance) rather than its underlying function (e.g., the goal of the approach or avoidant behavior). This investigation examined infants' responding to others' emotional displays across 5 discrete emotions: joy, sadness, fear, anger, and disgust. Specifically, 16-, 19-, and 24-month-old infants observed an adult communicate a discrete emotion toward a stimulus during a naturalistic interaction. Infants' responses were coded to capture the function of their behaviors (e.g., exploration, prosocial behavior, and security seeking). The results revealed a number of instances indicating that infants use different functional behaviors in response to discrete emotions. Differences in behaviors across emotions were clearest in the 24-month-old infants, though younger infants also demonstrated some differential use of behaviors in response to discrete emotions. This is the first comprehensive study to identify differences in how infants respond with goal-directed behaviors to discrete emotions. Additionally, the inclusion of a function-based coding scheme and interpersonal paradigms may be informative for future emotion research with children and adults. Possible developmental accounts for the observed behaviors and the benefits of coding techniques emphasizing the function of social behavior over their form are discussed. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields. I - An extended DKT element for thick-plate bending analysis. II - An extended DKQ element for thick-plate bending analysis

NASA Astrophysics Data System (ADS)

Katili, Irwan

1993-06-01

A new three-node nine-degree-of-freedom triangular plate bending element is proposed which is valid for the analysis of both thick and thin plates. The element, called the discrete Kirchhoff-Mindlin triangle (DKMT), has a proper rank, passes the patch test for thin and thick plates in an arbitrary mesh, and is free of shear locking. As an extension of the DKMT element, a four-node element with 3 degrees of freedom per node is developed. The element, referred to as DKMQ (discrete Kirchhoff-Mindlin quadrilateral) is found to provide good results for both thin and thick plates without any compatibility problems.

Cortical Neural Computation by Discrete Results Hypothesis

PubMed Central

Castejon, Carlos; Nuñez, Angel

2016-01-01

One of the most challenging problems we face in neuroscience is to understand how the cortex performs computations. There is increasing evidence that the power of the cortical processing is produced by populations of neurons forming dynamic neuronal ensembles. Theoretical proposals and multineuronal experimental studies have revealed that ensembles of neurons can form emergent functional units. However, how these ensembles are implicated in cortical computations is still a mystery. Although cell ensembles have been associated with brain rhythms, the functional interaction remains largely unclear. It is still unknown how spatially distributed neuronal activity can be temporally integrated to contribute to cortical computations. A theoretical explanation integrating spatial and temporal aspects of cortical processing is still lacking. In this Hypothesis and Theory article, we propose a new functional theoretical framework to explain the computational roles of these ensembles in cortical processing. We suggest that complex neural computations underlying cortical processing could be temporally discrete and that sensory information would need to be quantized to be computed by the cerebral cortex. Accordingly, we propose that cortical processing is produced by the computation of discrete spatio-temporal functional units that we have called “Discrete Results” (Discrete Results Hypothesis). This hypothesis represents a novel functional mechanism by which information processing is computed in the cortex. Furthermore, we propose that precise dynamic sequences of “Discrete Results” is the mechanism used by the cortex to extract, code, memorize and transmit neural information. The novel “Discrete Results” concept has the ability to match the spatial and temporal aspects of cortical processing. We discuss the possible neural underpinnings of these functional computational units and describe the empirical evidence supporting our hypothesis. We propose that fast-spiking (FS) interneuron may be a key element in our hypothesis providing the basis for this computation. PMID:27807408

Cortical Neural Computation by Discrete Results Hypothesis.

PubMed

Castejon, Carlos; Nuñez, Angel

2016-01-01

One of the most challenging problems we face in neuroscience is to understand how the cortex performs computations. There is increasing evidence that the power of the cortical processing is produced by populations of neurons forming dynamic neuronal ensembles. Theoretical proposals and multineuronal experimental studies have revealed that ensembles of neurons can form emergent functional units. However, how these ensembles are implicated in cortical computations is still a mystery. Although cell ensembles have been associated with brain rhythms, the functional interaction remains largely unclear. It is still unknown how spatially distributed neuronal activity can be temporally integrated to contribute to cortical computations. A theoretical explanation integrating spatial and temporal aspects of cortical processing is still lacking. In this Hypothesis and Theory article, we propose a new functional theoretical framework to explain the computational roles of these ensembles in cortical processing. We suggest that complex neural computations underlying cortical processing could be temporally discrete and that sensory information would need to be quantized to be computed by the cerebral cortex. Accordingly, we propose that cortical processing is produced by the computation of discrete spatio-temporal functional units that we have called "Discrete Results" (Discrete Results Hypothesis). This hypothesis represents a novel functional mechanism by which information processing is computed in the cortex. Furthermore, we propose that precise dynamic sequences of "Discrete Results" is the mechanism used by the cortex to extract, code, memorize and transmit neural information. The novel "Discrete Results" concept has the ability to match the spatial and temporal aspects of cortical processing. We discuss the possible neural underpinnings of these functional computational units and describe the empirical evidence supporting our hypothesis. We propose that fast-spiking (FS) interneuron may be a key element in our hypothesis providing the basis for this computation.

Semidiscrete Galerkin modelling of compressible viscous flow past a circular cone at incidence. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Meade, Andrew James, Jr.

1989-01-01

A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.

Original data preprocessor for Femap/Nastran

NASA Astrophysics Data System (ADS)

Oanta, Emil M.; Panait, Cornel; Raicu, Alexandra

2016-12-01

Automatic data processing and visualization in the finite elements analysis of the structural problems is a long run concern in mechanical engineering. The paper presents the `common database' concept according to which the same information may be accessed from an analytical model, as well as from a numerical one. In this way, input data expressed as comma-separated-value (CSV) files are loaded into the Femap/Nastran environment using original API codes, being automatically generated: the geometry of the model, the loads and the constraints. The original API computer codes are general, being possible to generate the input data of any model. In the next stages, the user may create the discretization of the model, set the boundary conditions and perform a given analysis. If additional accuracy is needed, the analyst may delete the previous discretizations and using the same information automatically loaded, other discretizations and analyses may be done. Moreover, if new more accurate information regarding the loads or constraints is acquired, they may be modelled and then implemented in the data generating program which creates the `common database'. This means that new more accurate models may be easily generated. Other facility consists of the opportunity to control the CSV input files, several loading scenarios being possible to be generated in Femap/Nastran. In this way, using original intelligent API instruments the analyst is focused to accurately model the phenomena and on creative aspects, the repetitive and time-consuming activities being performed by the original computer-based instruments. Using this data processing technique we apply to the best Asimov's principle `minimum change required / maximum desired response'.

Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces

PubMed Central

Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.

2012-01-01

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that our methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online at http://web.mit.edu/tidor. PMID:17627358

ONERA-NASA Cooperative Effort on Liner Impedance Eduction

NASA Technical Reports Server (NTRS)

Primus, Julien; Piot, Estelle; Simon, Frank; Jones, Michael G.; Watson, Willie R

2013-01-01

As part of a cooperation between ONERA and NASA, the liner impedance eduction methods developed by the two research centers are compared. The NASA technique relies on an objective function built on acoustic pressure measurements located on the wall opposite the test liner, and the propagation code solves the convected Helmholtz equation in uniform ow using a finite element method that implements a continuous Galerkin discretization. The ONERA method uses an objective function based either on wall acoustic pressure or on acoustic velocity acquired above the liner by Laser Doppler Anemometry, and the propagation code solves the linearized Euler equations by a discontinuous Galerkin discretization. Two acoustic liners are tested in both ONERA and NASA ow ducts and the measured data are treated with the corresponding impedance eduction method. The first liner is a wire mesh facesheet mounted onto a honeycomb core, designed to be linear with respect to incident sound pressure level and to grazing ow velocity. The second one is a conventional, nonlinear, perforate-over-honeycomb single layer liner. Configurations without and with ow are considered. For the nonlinear liner, the comparison of liner impedance educed by NASA and ONERA shows a sensitivity to the experimental conditions, namely to the nature of the source and to the sample width.

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Barth, Timothy; Chancellor, Marisa K. (Technical Monitor)

1997-01-01

Several stabilized discretization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin discretization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobian linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. These variants have been implemented in the "ELF" library for which example calculations will be shown. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Some prevalent limiting strategies will be reviewed. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc. will be addressed as needed.

A design study for the addition of higher order parametric discrete elements to NASTRAN

NASA Technical Reports Server (NTRS)

Stanton, E. L.

1972-01-01

The addition of discrete elements to NASTRAN poses significant interface problems with the level 15.1 assembly modules and geometry modules. Potential problems in designing new modules for higher-order parametric discrete elements are reviewed in both areas. An assembly procedure is suggested that separates grid point degrees of freedom on the basis of admissibility. New geometric input data are described that facilitate the definition of surfaces in parametric space.

Vertical discretization with finite elements for a global hydrostatic model on the cubed sphere

NASA Astrophysics Data System (ADS)

Yi, Tae-Hyeong; Park, Ja-Rin

2017-06-01

A formulation of Galerkin finite element with basis-spline functions on a hybrid sigma-pressure coordinate is presented to discretize the vertical terms of global Eulerian hydrostatic equations employed in a numerical weather prediction system, which is horizontally discretized with high-order spectral elements on a cubed sphere grid. This replaces the vertical discretization of conventional central finite difference that is first-order accurate in non-uniform grids and causes numerical instability in advection-dominant flows. Therefore, a model remains in the framework of Galerkin finite elements for both the horizontal and vertical spatial terms. The basis-spline functions, obtained from the de-Boor algorithm, are employed to derive both the vertical derivative and integral operators, since Eulerian advection terms are involved. These operators are used to discretize the vertical terms of the prognostic and diagnostic equations. To verify the vertical discretization schemes and compare their performance, various two- and three-dimensional idealized cases and a hindcast case with full physics are performed in terms of accuracy and stability. It was shown that the vertical finite element with the cubic basis-spline function is more accurate and stable than that of the vertical finite difference, as indicated by faster residual convergence, fewer statistical errors, and reduction in computational mode. This leads to the general conclusion that the overall performance of a global hydrostatic model might be significantly improved with the vertical finite element.

TIME-DEPENDENT MULTI-GROUP MULTI-DIMENSIONAL RELATIVISTIC RADIATIVE TRANSFER CODE BASED ON SPHERICAL HARMONIC DISCRETE ORDINATE METHOD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tominaga, Nozomu; Shibata, Sanshiro; Blinnikov, Sergei I., E-mail: tominaga@konan-u.ac.jp, E-mail: sshibata@post.kek.jp, E-mail: Sergei.Blinnikov@itep.ru

We develop a time-dependent, multi-group, multi-dimensional relativistic radiative transfer code, which is required to numerically investigate radiation from relativistic fluids that are involved in, e.g., gamma-ray bursts and active galactic nuclei. The code is based on the spherical harmonic discrete ordinate method (SHDOM) which evaluates a source function including anisotropic scattering in spherical harmonics and implicitly solves the static radiative transfer equation with ray tracing in discrete ordinates. We implement treatments of time dependence, multi-frequency bins, Lorentz transformation, and elastic Thomson and inelastic Compton scattering to the publicly available SHDOM code. Our code adopts a mixed-frame approach; the source functionmore » is evaluated in the comoving frame, whereas the radiative transfer equation is solved in the laboratory frame. This implementation is validated using various test problems and comparisons with the results from a relativistic Monte Carlo code. These validations confirm that the code correctly calculates the intensity and its evolution in the computational domain. The code enables us to obtain an Eddington tensor that relates the first and third moments of intensity (energy density and radiation pressure) and is frequently used as a closure relation in radiation hydrodynamics calculations.« less

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

Reconstruction of finite-valued sparse signals

NASA Astrophysics Data System (ADS)

Keiper, Sandra; Kutyniok, Gitta; Lee, Dae Gwan; Pfander, Götz

2017-08-01

The need of reconstructing discrete-valued sparse signals from few measurements, that is solving an undetermined system of linear equations, appears frequently in science and engineering. Those signals appear, for example, in error correcting codes as well as massive Multiple-Input Multiple-Output (MIMO) channel and wideband spectrum sensing. A particular example is given by wireless communications, where the transmitted signals are sequences of bits, i.e., with entries in f0; 1g. Whereas classical compressed sensing algorithms do not incorporate the additional knowledge of the discrete nature of the signal, classical lattice decoding approaches do not utilize sparsity constraints. In this talk, we present an approach that incorporates a discrete values prior into basis pursuit. In particular, we address finite-valued sparse signals, i.e., sparse signals with entries in a finite alphabet. We will introduce an equivalent null space characterization and show that phase transition takes place earlier than when using the classical basis pursuit approach. We will further discuss robustness of the algorithm and show that the nonnegative case is very different from the bipolar one. One of our findings is that the positioning of the zero in the alphabet - i.e., whether it is a boundary element or not - is crucial.

Large deflection elastic-plastic dynamic response of stiffened shells of revolution

NASA Technical Reports Server (NTRS)

Stricklin, J. A.; Haisler, W. E.; Vonriesemann, W. A.; Leick, R. D.; Hunsaker, B.; Saczalski, K. J.

1972-01-01

The formulation and check out porblems for a computer code DYNAPLAS, which analyzes the large deflection elastic-plastic dynamic response of stiffened shells of revolution, are presented. The formulation for special discretization is by the finite element method with finite differences being used for the evaluation of the pseudo forces due to material and geometric nonlinearities. Time integration is by the Houbolt method. The stiffeners may be due to concentrated or distributed eccentric rings and spring supports at arbitrary angles around the circumference of the elements. Check out porblems include the comparison of solutions from DYNAPLAS with experimental and other computer solutions for rings, conical and cylindrical shells and a curved panel. A hypothetical submarine including stiffeners and missile tube is studied under a combination of hydrostatic and dynamically applied asymmetrical pressure loadings.

Conservative discretization of the Landau collision integral

DOE PAGES

Hirvijoki, E.; Adams, M. F.

2017-03-28

Here we describe a density, momentum-, and energy-conserving discretization of the nonlinear Landau collision integral. The method is suitable for both the finite-element and discontinuous Galerkin methods and does not require structured meshes. The conservation laws for the discretization are proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation problem using a finite-element implementation.

Geometric Nonlinear Computation of Thin Rods and Shells

NASA Astrophysics Data System (ADS)

Grinspun, Eitan

2011-03-01

We develop simple, fast numerical codes for the dynamics of thin elastic rods and shells, by exploiting the connection between physics, geometry, and computation. By building a discrete mechanical picture from the ground up, mimicking the axioms, structures, and symmetries of the smooth setting, we produce numerical codes that not only are consistent in a classical sense, but also reproduce qualitative, characteristic behavior of a physical system----such as exact preservation of conservation laws----even for very coarse discretizations. As two recent examples, we present discrete computational models of elastic rods and shells, with straightforward extensions to the viscous setting. Even at coarse discretizations, the resulting simulations capture characteristic geometric instabilities. The numerical codes we describe are used in experimental mechanics, cinema, and consumer software products. This is joint work with Miklós Bergou, Basile Audoly, Max Wardetzky, and Etienne Vouga. This research is supported in part by the Sloan Foundation, the NSF, Adobe, Autodesk, Intel, the Walt Disney Company, and Weta Digital.

GEMPIC: geometric electromagnetic particle-in-cell methods

NASA Astrophysics Data System (ADS)

Kraus, Michael; Kormann, Katharina; Morrison, Philip J.; Sonnendrücker, Eric

2017-08-01

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

RELAP-7 Development Updates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hongbin; Zhao, Haihua; Gleicher, Frederick Nathan

RELAP-7 is a nuclear systems safety analysis code being developed at the Idaho National Laboratory, and is the next generation tool in the RELAP reactor safety/systems analysis application series. RELAP-7 development began in 2011 to support the Risk Informed Safety Margins Characterization (RISMC) Pathway of the Light Water Reactor Sustainability (LWRS) program. The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical methods, and physical models in order to provide capabilities needed for the RISMC methodology and to support nuclear power safety analysis. The code is beingmore » developed based on Idaho National Laboratory’s modern scientific software development framework – MOOSE (the Multi-Physics Object-Oriented Simulation Environment). The initial development goal of the RELAP-7 approach focused primarily on the development of an implicit algorithm capable of strong (nonlinear) coupling of the dependent hydrodynamic variables contained in the 1-D/2-D flow models with the various 0-D system reactor components that compose various boiling water reactor (BWR) and pressurized water reactor nuclear power plants (NPPs). During Fiscal Year (FY) 2015, the RELAP-7 code has been further improved with expanded capability to support boiling water reactor (BWR) and pressurized water reactor NPPs analysis. The accumulator model has been developed. The code has also been coupled with other MOOSE-based applications such as neutronics code RattleSnake and fuel performance code BISON to perform multiphysics analysis. A major design requirement for the implicit algorithm in RELAP-7 is that it is capable of second-order discretization accuracy in both space and time, which eliminates the traditional first-order approximation errors. The second-order temporal is achieved by a second-order backward temporal difference, and the one-dimensional second-order accurate spatial discretization is achieved with the Galerkin approximation of Lagrange finite elements. During FY-2015, we have done numerical verification work to verify that the RELAP-7 code indeed achieves 2nd-order accuracy in both time and space for single phase models at the system level.« less

Convection equation modeling: A non-iterative direct matrix solution algorithm for use with SINDA

NASA Technical Reports Server (NTRS)

Schrage, Dean S.

1993-01-01

The determination of the boundary conditions for a component-level analysis, applying discrete finite element and finite difference modeling techniques often requires an analysis of complex coupled phenomenon that cannot be described algebraically. For example, an analysis of the temperature field of a coldplate surface with an integral fluid loop requires a solution to the parabolic heat equation and also requires the boundary conditions that describe the local fluid temperature. However, the local fluid temperature is described by a convection equation that can only be solved with the knowledge of the locally-coupled coldplate temperatures. Generally speaking, it is not computationally efficient, and sometimes, not even possible to perform a direct, coupled phenomenon analysis of the component-level and boundary condition models within a single analysis code. An alternative is to perform a disjoint analysis, but transmit the necessary information between models during the simulation to provide an indirect coupling. For this approach to be effective, the component-level model retains full detail while the boundary condition model is simplified to provide a fast, first-order prediction of the phenomenon in question. Specifically for the present study, the coldplate structure is analyzed with a discrete, numerical model (SINDA) while the fluid loop convection equation is analyzed with a discrete, analytical model (direct matrix solution). This indirect coupling allows a satisfactory prediction of the boundary condition, while not subjugating the overall computational efficiency of the component-level analysis. In the present study a discussion of the complete analysis of the derivation and direct matrix solution algorithm of the convection equation is presented. Discretization is analyzed and discussed to extend of solution accuracy, stability and computation speed. Case studies considering a pulsed and harmonic inlet disturbance to the fluid loop are analyzed to assist in the discussion of numerical dissipation and accuracy. In addition, the issues of code melding or integration with standard class solvers such as SINDA are discussed to advise the user of the potential problems to be encountered.

Reduced discretization error in HZETRN

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slaba, Tony C., E-mail: Tony.C.Slaba@nasa.gov; Blattnig, Steve R., E-mail: Steve.R.Blattnig@nasa.gov; Tweed, John, E-mail: jtweed@odu.edu

2013-02-01

The deterministic particle transport code HZETRN is an efficient analysis tool for studying the effects of space radiation on humans, electronics, and shielding materials. In a previous work, numerical methods in the code were reviewed, and new methods were developed that further improved efficiency and reduced overall discretization error. It was also shown that the remaining discretization error could be attributed to low energy light ions (A < 4) with residual ranges smaller than the physical step-size taken by the code. Accurately resolving the spectrum of low energy light particles is important in assessing risk associated with astronaut radiation exposure.more » In this work, modifications to the light particle transport formalism are presented that accurately resolve the spectrum of low energy light ion target fragments. The modified formalism is shown to significantly reduce overall discretization error and allows a physical approximation to be removed. For typical step-sizes and energy grids used in HZETRN, discretization errors for the revised light particle transport algorithms are shown to be less than 4% for aluminum and water shielding thicknesses as large as 100 g/cm{sup 2} exposed to both solar particle event and galactic cosmic ray environments.« less

Parallel Numerical Simulations of Water Reservoirs

NASA Astrophysics Data System (ADS)

Torres, Pedro; Mangiavacchi, Norberto

2010-11-01

The study of the water flow and scalar transport in water reservoirs is important for the determination of the water quality during the initial stages of the reservoir filling and during the life of the reservoir. For this scope, a parallel 2D finite element code for solving the incompressible Navier-Stokes equations coupled with scalar transport was implemented using the message-passing programming model, in order to perform simulations of hidropower water reservoirs in a computer cluster environment. The spatial discretization is based on the MINI element that satisfies the Babuska-Brezzi (BB) condition, which provides sufficient conditions for a stable mixed formulation. All the distributed data structures needed in the different stages of the code, such as preprocessing, solving and post processing, were implemented using the PETSc library. The resulting linear systems for the velocity and the pressure fields were solved using the projection method, implemented by an approximate block LU factorization. In order to increase the parallel performance in the solution of the linear systems, we employ the static condensation method for solving the intermediate velocity at vertex and centroid nodes separately. We compare performance results of the static condensation method with the approach of solving the complete system. In our tests the static condensation method shows better performance for large problems, at the cost of an increased memory usage. Performance results for other intensive parts of the code in a computer cluster are also presented.

Finite element code development for modeling detonation of HMX composites

NASA Astrophysics Data System (ADS)

Duran, Adam; Sundararaghavan, Veera

2015-06-01

In this talk, we present a hydrodynamics code for modeling shock and detonation waves in HMX. A stable efficient solution strategy based on a Taylor-Galerkin finite element (FE) discretization was developed to solve the reactive Euler equations. In our code, well calibrated equations of state for the solid unreacted material and gaseous reaction products have been implemented, along with a chemical reaction scheme and a mixing rule to define the properties of partially reacted states. A linear Gruneisen equation of state was employed for the unreacted HMX calibrated from experiments. The JWL form was used to model the EOS of gaseous reaction products. It is assumed that the unreacted explosive and reaction products are in both pressure and temperature equilibrium. The overall specific volume and internal energy was computed using the rule of mixtures. Arrhenius kinetics scheme was integrated to model the chemical reactions. A locally controlled dissipation was introduced that induces a non-oscillatory stabilized scheme for the shock front. The FE model was validated using analytical solutions for sod shock and ZND strong detonation models and then used to perform 2D and 3D shock simulations. We will present benchmark problems for geometries in which a single HMX crystal is subjected to a shock condition. Our current progress towards developing microstructural models of HMX/binder composite will also be discussed.

Development and Application of Compatible Discretizations of Maxwell's Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, D; Koning, J; Rieben, R

We present the development and application of compatible finite element discretizations of electromagnetics problems derived from the time dependent, full wave Maxwell equations. We review the H(curl)-conforming finite element method, using the concepts and notations of differential forms as a theoretical framework. We chose this approach because it can handle complex geometries, it is free of spurious modes, it is numerically stable without the need for filtering or artificial diffusion, it correctly models the discontinuity of fields across material boundaries, and it can be very high order. Higher-order H(curl) and H(div) conforming basis functions are not unique and we havemore » designed an extensible C++ framework that supports a variety of specific instantiations of these such as standard interpolatory bases, spectral bases, hierarchical bases, and semi-orthogonal bases. Virtually any electromagnetics problem that can be cast in the language of differential forms can be solved using our framework. For time dependent problems a method-of-lines scheme is used where the Galerkin method reduces the PDE to a semi-discrete system of ODE's, which are then integrated in time using finite difference methods. For time integration of wave equations we employ the unconditionally stable implicit Newmark-Beta method, as well as the high order energy conserving explicit Maxwell Symplectic method; for diffusion equations, we employ a generalized Crank-Nicholson method. We conclude with computational examples from resonant cavity problems, time-dependent wave propagation problems, and transient eddy current problems, all obtained using the authors massively parallel computational electromagnetics code EMSolve.« less

Discrete-Roughness-Element-Enhanced Swept-Wing Natural Laminar Flow at High Reynolds Numbers

NASA Technical Reports Server (NTRS)

Malik, Mujeeb; Liao, Wei; Li, Fei; Choudhari, Meelan

2015-01-01

Nonlinear parabolized stability equations and secondary-instability analyses are used to provide a computational assessment of the potential use of the discrete-roughness-element technology for extending swept-wing natural laminar flow at chord Reynolds numbers relevant to transport aircraft. Computations performed for the boundary layer on a natural-laminar-flow airfoil with a leading-edge sweep angle of 34.6 deg, freestream Mach number of 0.75, and chord Reynolds numbers of 17 × 10(exp 6), 24 × 10(exp 6), and 30 × 10(exp 6) suggest that discrete roughness elements could delay laminar-turbulent transition by about 20% when transition is caused by stationary crossflow disturbances. Computations show that the introduction of small-wavelength stationary crossflow disturbances (i.e., discrete roughness element) also suppresses the growth of most amplified traveling crossflow disturbances.

A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Mortensen, Mikael; Langtangen, Hans Petter; Wells, Garth N.

2011-09-01

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier-Stokes model.

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

DOE PAGES

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.; ...

2016-09-22

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

Evaluation of Transverse Thermal Stresses in Composite Plates Based on First-Order Shear Deformation Theory

NASA Technical Reports Server (NTRS)

Rolfes, R.; Noor, A. K.; Sparr, H.

1998-01-01

A postprocessing procedure is presented for the evaluation of the transverse thermal stresses in laminated plates. The analytical formulation is based on the first-order shear deformation theory and the plate is discretized by using a single-field displacement finite element model. The procedure is based on neglecting the derivatives of the in-plane forces and the twisting moments, as well as the mixed derivatives of the bending moments, with respect to the in-plane coordinates. The calculated transverse shear stiffnesses reflect the actual stacking sequence of the composite plate. The distributions of the transverse stresses through-the-thickness are evaluated by using only the transverse shear forces and the thermal effects resulting from the finite element analysis. The procedure is implemented into a postprocessing routine which can be easily incorporated into existing commercial finite element codes. Numerical results are presented for four- and ten-layer cross-ply laminates subjected to mechanical and thermal loads.

Discrete-Element bonded-particle Sea Ice model DESIgn, version 1.3a - model description and implementation

NASA Astrophysics Data System (ADS)

Herman, Agnieszka

2016-04-01

This paper presents theoretical foundations, numerical implementation and examples of application of the two-dimensional Discrete-Element bonded-particle Sea Ice model - DESIgn. In the model, sea ice is represented as an assemblage of objects of two types: disk-shaped "grains" and semi-elastic bonds connecting them. Grains move on the sea surface under the influence of forces from the atmosphere and the ocean, as well as interactions with surrounding grains through direct contact (Hertzian contact mechanics) and/or through bonds. The model has an experimental option of taking into account quasi-three-dimensional effects related to the space- and time-varying curvature of the sea surface, thus enabling simulation of ice breaking due to stresses resulting from bending moments associated with surface waves. Examples of the model's application to simple sea ice deformation and breaking problems are presented, with an analysis of the influence of the basic model parameters ("microscopic" properties of grains and bonds) on the large-scale response of the modeled material. The model is written as a toolbox suitable for usage with the open-source numerical library LIGGGHTS. The code, together with full technical documentation and example input files, is freely available with this paper and on the Internet.

Three-dimensional discrete element method simulation of core disking

NASA Astrophysics Data System (ADS)

Wu, Shunchuan; Wu, Haoyan; Kemeny, John

2018-04-01

The phenomenon of core disking is commonly seen in deep drilling of highly stressed regions in the Earth's crust. Given its close relationship with the in situ stress state, the presence and features of core disking can be used to interpret the stresses when traditional in situ stress measuring techniques are not available. The core disking process was simulated in this paper using the three-dimensional discrete element method software PFC3D (particle flow code). In particular, PFC3D is used to examine the evolution of fracture initiation, propagation and coalescence associated with core disking under various stress states. In this paper, four unresolved problems concerning core disking are investigated with a series of numerical simulations. These simulations also provide some verification of existing results by other researchers: (1) Core disking occurs when the maximum principal stress is about 6.5 times the tensile strength. (2) For most stress situations, core disking occurs from the outer surface, except for the thrust faulting stress regime, where the fractures were found to initiate from the inner part. (3) The anisotropy of the two horizontal principal stresses has an effect on the core disking morphology. (4) The thickness of core disk has a positive relationship with radial stress and a negative relationship with axial stresses.

Simulation of Powder Layer Deposition in Additive Manufacturing Processes Using the Discrete Element Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herbold, E. B.; Walton, O.; Homel, M. A.

2015-10-26

This document serves as a final report to a small effort where several improvements were added to a LLNL code GEODYN-­L to develop Discrete Element Method (DEM) algorithms coupled to Lagrangian Finite Element (FE) solvers to investigate powder-­bed formation problems for additive manufacturing. The results from these simulations will be assessed for inclusion as the initial conditions for Direct Metal Laser Sintering (DMLS) simulations performed with ALE3D. The algorithms were written and performed on parallel computing platforms at LLNL. The total funding level was 3-­4 weeks of an FTE split amongst two staff scientists and one post-­doc. The DEM simulationsmore » emulated, as much as was feasible, the physical process of depositing a new layer of powder over a bed of existing powder. The DEM simulations utilized truncated size distributions spanning realistic size ranges with a size distribution profile consistent with realistic sample set. A minimum simulation sample size on the order of 40-­particles square by 10-­particles deep was utilized in these scoping studies in order to evaluate the potential effects of size segregation variation with distance displaced in front of a screed blade. A reasonable method for evaluating the problem was developed and validated. Several simulations were performed to show the viability of the approach. Future investigations will focus on running various simulations investigating powder particle sizing and screen geometries.« less

Center for Efficient Exascale Discretizations Software Suite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolev, Tzanio; Dobrev, Veselin; Tomov, Vladimir

The CEED Software suite is a collection of generally applicable software tools focusing on the following computational motives: PDE discretizations on unstructured meshes, high-order finite element and spectral element methods and unstructured adaptive mesh refinement. All of this software is being developed as part of CEED, a co-design Center for Efficient Exascale Discretizations, within DOE's Exascale Computing Project (ECP) program.

Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

NASA Technical Reports Server (NTRS)

Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.

1977-01-01

An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.

How does a three-dimensional continuum muscle model affect the kinematics and muscle strains of a finite element neck model compared to a discrete muscle model in rear-end, frontal, and lateral impacts.

PubMed

Hedenstierna, Sofia; Halldin, Peter

2008-04-15

A finite element (FE) model of the human neck with incorporated continuum or discrete muscles was used to simulate experimental impacts in rear, frontal, and lateral directions. The aim of this study was to determine how a continuum muscle model influences the impact behavior of a FE human neck model compared with a discrete muscle model. Most FE neck models used for impact analysis today include a spring element musculature and are limited to discrete geometries and nodal output results. A solid-element muscle model was thought to improve the behavior of the model by adding properties such as tissue inertia and compressive stiffness and by improving the geometry. It would also predict the strain distribution within the continuum elements. A passive continuum muscle model with nonlinear viscoelastic materials was incorporated into the KTH neck model together with active spring muscles and used in impact simulations. The resulting head and vertebral kinematics was compared with the results from a discrete muscle model as well as volunteer corridors. The muscle strain prediction was compared between the 2 muscle models. The head and vertebral kinematics were within the volunteer corridors for both models when activated. The continuum model behaved more stiffly than the discrete model and needed less active force to fit the experimental results. The largest difference was seen in the rear impact. The strain predicted by the continuum model was lower than for the discrete model. The continuum muscle model stiffened the response of the KTH neck model compared with a discrete model, and the strain prediction in the muscles was improved.

Aeroelastic-Acoustics Simulation of Flight Systems

NASA Technical Reports Server (NTRS)

Gupta, kajal K.; Choi, S.; Ibrahim, A.

2009-01-01

This paper describes the details of a numerical finite element (FE) based analysis procedure and a resulting code for the simulation of the acoustics phenomenon arising from aeroelastic interactions. Both CFD and structural simulations are based on FE discretization employing unstructured grids. The sound pressure level (SPL) on structural surfaces is calculated from the root mean square (RMS) of the unsteady pressure and the acoustic wave frequencies are computed from a fast Fourier transform (FFT) of the unsteady pressure distribution as a function of time. The resulting tool proves to be unique as it is designed to analyze complex practical problems, involving large scale computations, in a routine fashion.

Configuration-interaction relativistic-many-body-perturbation-theory calculations of photoionization cross sections from quasicontinuum oscillator strengths

DOE PAGES

Savukov, I. M.; Filin, D. V.

2014-12-29

Many applications are in need of accurate photoionization cross sections, especially in the case of complex atoms. Configuration-interaction relativistic-many-body-perturbation theory (CI-RMBPT) has been successful in predicting atomic energies, matrix elements between discrete states, and other properties, which is quite promising, but it has not been applied to photoionization problems owing to extra complications arising from continuum states. In this paper a method that will allow the conversion of discrete CI-(R)MPBT oscillator strengths (OS) to photoionization cross sections with minimal modifications of the codes is introduced and CI-RMBPT cross sections of Ne, Ar, Kr, and Xe are calculated. A consistent agreementmore » with experiment is found. RMBPT corrections are particularly significant for Ar, Kr, and Xe and improve agreement with experimental results compared to the particle-hole CI method. As a result, the demonstrated conversion method can be applied to CI-RMBPT photoionization calculations for a large number of multivalence atoms and ions.« less

A generalized vortex lattice method for subsonic and supersonic flow applications

NASA Technical Reports Server (NTRS)

Miranda, L. R.; Elliot, R. D.; Baker, W. M.

1977-01-01

If the discrete vortex lattice is considered as an approximation to the surface-distributed vorticity, then the concept of the generalized principal part of an integral yields a residual term to the vorticity-induced velocity field. The proper incorporation of this term to the velocity field generated by the discrete vortex lines renders the present vortex lattice method valid for supersonic flow. Special techniques for simulating nonzero thickness lifting surfaces and fusiform bodies with vortex lattice elements are included. Thickness effects of wing-like components are simulated by a double (biplanar) vortex lattice layer, and fusiform bodies are represented by a vortex grid arranged on a series of concentrical cylindrical surfaces. The analysis of sideslip effects by the subject method is described. Numerical considerations peculiar to the application of these techniques are also discussed. The method has been implemented in a digital computer code. A users manual is included along with a complete FORTRAN compilation, an executed case, and conversion programs for transforming input for the NASA wave drag program.

Discontinuous finite element method for vector radiative transfer

NASA Astrophysics Data System (ADS)

Wang, Cun-Hai; Yi, Hong-Liang; Tan, He-Ping

2017-03-01

The discontinuous finite element method (DFEM) is applied to solve the vector radiative transfer in participating media. The derivation in a discrete form of the vector radiation governing equations is presented, in which the angular space is discretized by the discrete-ordinates approach with a local refined modification, and the spatial domain is discretized into finite non-overlapped discontinuous elements. The elements in the whole solution domain are connected by modelling the boundary numerical flux between adjacent elements, which makes the DFEM numerically stable for solving radiative transfer equations. Several various problems of vector radiative transfer are tested to verify the performance of the developed DFEM, including vector radiative transfer in a one-dimensional parallel slab containing a Mie/Rayleigh/strong forward scattering medium and a two-dimensional square medium. The fact that DFEM results agree very well with the benchmark solutions in published references shows that the developed DFEM in this paper is accurate and effective for solving vector radiative transfer problems.

CTViz: A tool for the visualization of transport in nanocomposites.

PubMed

Beach, Benjamin; Brown, Joshua; Tarlton, Taylor; Derosa, Pedro A

2016-05-01

A visualization tool (CTViz) for charge transport processes in 3-D hybrid materials (nanocomposites) was developed, inspired by the need for a graphical application to assist in code debugging and data presentation of an existing in-house code. As the simulation code grew, troubleshooting problems grew increasingly difficult without an effective way to visualize 3-D samples and charge transport in those samples. CTViz is able to produce publication and presentation quality visuals of the simulation box, as well as static and animated visuals of the paths of individual carriers through the sample. CTViz was designed to provide a high degree of flexibility in the visualization of the data. A feature that characterizes this tool is the use of shade and transparency levels to highlight important details in the morphology or in the transport paths by hiding or dimming elements of little relevance to the current view. This is fundamental for the visualization of 3-D systems with complex structures. The code presented here provides these required capabilities, but has gone beyond the original design and could be used as is or easily adapted for the visualization of other particulate transport where transport occurs on discrete paths. Copyright © 2016 Elsevier Inc. All rights reserved.

Contrasting Five Different Theories of Letter Position Coding: Evidence from Orthographic Similarity Effects

ERIC Educational Resources Information Center

Davis, Colin J.; Bowers, Jeffrey S.

2006-01-01

Five theories of how letter position is coded are contrasted: position-specific slot-coding, Wickelcoding, open-bigram coding (discrete and continuous), and spatial coding. These theories make different predictions regarding the relative similarity of three different types of pairs of letter strings: substitution neighbors,…

Verification of Three Dimensional Triangular Prismatic Discrete Ordinates Transport Code ENSEMBLE-TRIZ by Comparison with Monte Carlo Code GMVP

NASA Astrophysics Data System (ADS)

Homma, Yuto; Moriwaki, Hiroyuki; Ohki, Shigeo; Ikeda, Kazumi

2014-06-01

This paper deals with verification of three dimensional triangular prismatic discrete ordinates transport calculation code ENSEMBLE-TRIZ by comparison with multi-group Monte Carlo calculation code GMVP in a large fast breeder reactor. The reactor is a 750 MWe electric power sodium cooled reactor. Nuclear characteristics are calculated at beginning of cycle of an initial core and at beginning and end of cycle of equilibrium core. According to the calculations, the differences between the two methodologies are smaller than 0.0002 Δk in the multi-plication factor, relatively about 1% in the control rod reactivity, and 1% in the sodium void reactivity.

Nonconforming mortar element methods: Application to spectral discretizations

NASA Technical Reports Server (NTRS)

Maday, Yvon; Mavriplis, Cathy; Patera, Anthony

1988-01-01

Spectral element methods are p-type weighted residual techniques for partial differential equations that combine the generality of finite element methods with the accuracy of spectral methods. Presented here is a new nonconforming discretization which greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement. The method is based on the introduction of an auxiliary mortar trace space, and constitutes a new approach to discretization-driven domain decomposition characterized by a clean decoupling of the local, structure-preserving residual evaluations and the transmission of boundary and continuity conditions. The flexibility of the mortar method is illustrated by several nonconforming adaptive Navier-Stokes calculations in complex geometry.

Variations in the non-coding transcriptome as a driver of inter-strain divergence and physiological adaptation in bacteria.

PubMed

Kopf, Matthias; Klähn, Stephan; Scholz, Ingeborg; Hess, Wolfgang R; Voß, Björn

2015-04-22

In all studied organisms, a substantial portion of the transcriptome consists of non-coding RNAs that frequently execute regulatory functions. Here, we have compared the primary transcriptomes of the cyanobacteria Synechocystis sp. PCC 6714 and PCC 6803 under 10 different conditions. These strains share 2854 protein-coding genes and a 16S rRNA identity of 99.4%, indicating their close relatedness. Conserved major transcriptional start sites (TSSs) give rise to non-coding transcripts within the sigB gene, from the 5'UTRs of cmpA and isiA, and 168 loci in antisense orientation. Distinct differences include single nucleotide polymorphisms rendering promoters inactive in one of the strains, e.g., for cmpR and for the asRNA PsbA2R. Based on the genome-wide mapped location, regulation and classification of TSSs, non-coding transcripts were identified as the most dynamic component of the transcriptome. We identified a class of mRNAs that originate by read-through from an sRNA that accumulates as a discrete and abundant transcript while also serving as the 5'UTR. Such an sRNA/mRNA structure, which we name 'actuaton', represents another way for bacteria to remodel their transcriptional network. Our findings support the hypothesis that variations in the non-coding transcriptome constitute a major evolutionary element of inter-strain divergence and capability for physiological adaptation.

Finite element method for viscoelastic medium with damage and the application to structural analysis of solid rocket motor grain

NASA Astrophysics Data System (ADS)

Deng, Bin; Shen, ZhiBin; Duan, JingBo; Tang, GuoJin

2014-05-01

This paper studies the damage-viscoelastic behavior of composite solid propellants of solid rocket motors (SRM). Based on viscoelastic theories and strain equivalent hypothesis in damage mechanics, a three-dimensional (3-D) nonlinear viscoelastic constitutive model incorporating with damage is developed. The resulting viscoelastic constitutive equations are numerically discretized by integration algorithm, and a stress-updating method is presented by solving nonlinear equations according to the Newton-Raphson method. A material subroutine of stress-updating is made up and embedded into commercial code of Abaqus. The material subroutine is validated through typical examples. Our results indicate that the finite element results are in good agreement with the analytical ones and have high accuracy, and the suggested method and designed subroutine are efficient and can be further applied to damage-coupling structural analysis of practical SRM grain.

Full Wave Analysis of RF Signal Attenuation in a Lossy Rough Surface Cave using a High Order Time Domain Vector Finite Element Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pingenot, J; Rieben, R; White, D

2005-10-31

We present a computational study of signal propagation and attenuation of a 200 MHz planar loop antenna in a cave environment. The cave is modeled as a straight and lossy random rough wall. To simulate a broad frequency band, the full wave Maxwell equations are solved directly in the time domain via a high order vector finite element discretization using the massively parallel CEM code EMSolve. The numerical technique is first verified against theoretical results for a planar loop antenna in a smooth lossy cave. The simulation is then performed for a series of random rough surface meshes in ordermore » to generate statistical data for the propagation and attenuation properties of the antenna in a cave environment. Results for the mean and variance of the power spectral density of the electric field are presented and discussed.« less

Optical signal processing of spatially distributed sensor data in smart structures

NASA Technical Reports Server (NTRS)

Bennett, K. D.; Claus, R. O.; Murphy, K. A.; Goette, A. M.

1989-01-01

Smart structures which contain dense two- or three-dimensional arrays of attached or embedded sensor elements inherently require signal multiplexing and processing capabilities to permit good spatial data resolution as well as the adequately short calculation times demanded by real time active feedback actuator drive circuitry. This paper reports the implementation of an in-line optical signal processor and its application in a structural sensing system which incorporates multiple discrete optical fiber sensor elements. The signal processor consists of an array of optical fiber couplers having tailored s-parameters and arranged to allow gray code amplitude scaling of sensor inputs. The use of this signal processor in systems designed to indicate the location of distributed strain and damage in composite materials, as well as to quantitatively characterize that damage, is described. Extension of similar signal processing methods to more complicated smart materials and structures applications are discussed.

A novel method of the image processing on irregular triangular meshes

NASA Astrophysics Data System (ADS)

Vishnyakov, Sergey; Pekhterev, Vitaliy; Sokolova, Elizaveta

2018-04-01

The paper describes a novel method of the image processing based on irregular triangular meshes implementation. The triangular mesh is adaptive to the image content, least mean square linear approximation is proposed for the basic interpolation within the triangle. It is proposed to use triangular numbers to simplify using of the local (barycentric) coordinates for the further analysis - triangular element of the initial irregular mesh is to be represented through the set of the four equilateral triangles. This allows to use fast and simple pixels indexing in local coordinates, e.g. "for" or "while" loops for access to the pixels. Moreover, representation proposed allows to use discrete cosine transform of the simple "rectangular" symmetric form without additional pixels reordering (as it is used for shape-adaptive DCT forms). Furthermore, this approach leads to the simple form of the wavelet transform on triangular mesh. The results of the method application are presented. It is shown that advantage of the method proposed is a combination of the flexibility of the image-adaptive irregular meshes with the simple form of the pixel indexing in local triangular coordinates and the using of the common forms of the discrete transforms for triangular meshes. Method described is proposed for the image compression, pattern recognition, image quality improvement, image search and indexing. It also may be used as a part of video coding (intra-frame or inter-frame coding, motion detection).

Toward Optimal Manifold Hashing via Discrete Locally Linear Embedding.

PubMed

Rongrong Ji; Hong Liu; Liujuan Cao; Di Liu; Yongjian Wu; Feiyue Huang

2017-11-01

Binary code learning, also known as hashing, has received increasing attention in large-scale visual search. By transforming high-dimensional features to binary codes, the original Euclidean distance is approximated via Hamming distance. More recently, it is advocated that it is the manifold distance, rather than the Euclidean distance, that should be preserved in the Hamming space. However, it retains as an open problem to directly preserve the manifold structure by hashing. In particular, it first needs to build the local linear embedding in the original feature space, and then quantize such embedding to binary codes. Such a two-step coding is problematic and less optimized. Besides, the off-line learning is extremely time and memory consuming, which needs to calculate the similarity matrix of the original data. In this paper, we propose a novel hashing algorithm, termed discrete locality linear embedding hashing (DLLH), which well addresses the above challenges. The DLLH directly reconstructs the manifold structure in the Hamming space, which learns optimal hash codes to maintain the local linear relationship of data points. To learn discrete locally linear embeddingcodes, we further propose a discrete optimization algorithm with an iterative parameters updating scheme. Moreover, an anchor-based acceleration scheme, termed Anchor-DLLH, is further introduced, which approximates the large similarity matrix by the product of two low-rank matrices. Experimental results on three widely used benchmark data sets, i.e., CIFAR10, NUS-WIDE, and YouTube Face, have shown superior performance of the proposed DLLH over the state-of-the-art approaches.

Finite element solution for energy conservation using a highly stable explicit integration algorithm

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1972-01-01

Theoretical derivation of a finite element solution algorithm for the transient energy conservation equation in multidimensional, stationary multi-media continua with irregular solution domain closure is considered. The complete finite element matrix forms for arbitrarily irregular discretizations are established, using natural coordinate function representations. The algorithm is embodied into a user-oriented computer program (COMOC) which obtains transient temperature distributions at the node points of the finite element discretization using a highly stable explicit integration procedure with automatic error control features. The finite element algorithm is shown to posses convergence with discretization for a transient sample problem. The condensed form for the specific heat element matrix is shown to be preferable to the consistent form. Computed results for diverse problems illustrate the versatility of COMOC, and easily prepared output subroutines are shown to allow quick engineering assessment of solution behavior.

Coding for Single-Line Transmission

NASA Technical Reports Server (NTRS)

Madison, L. G.

1983-01-01

Digital transmission code combines data and clock signals into single waveform. MADCODE needs four standard integrated circuits in generator and converter plus five small discrete components. MADCODE allows simple coding and decoding for transmission of digital signals over single line.

An Efficient Variable Length Coding Scheme for an IID Source

NASA Technical Reports Server (NTRS)

Cheung, K. -M.

1995-01-01

A scheme is examined for using two alternating Huffman codes to encode a discrete independent and identically distributed source with a dominant symbol. This combined strategy, or alternating runlength Huffman (ARH) coding, was found to be more efficient than ordinary coding in certain circumstances.

Discrete Element Method (DEM) Simulations using PFC3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matt Evans

Contains input scripts, background information, reduced data, and results associated with the discrete element method (DEM) simulations of interface shear tests, plate anchor pullout tests, and torpedo anchor installation and pullout tests, using the software PFC3D (v4.0).

Utilization of the Discrete Differential Evolution for Optimization in Multidimensional Point Clouds.

PubMed

Uher, Vojtěch; Gajdoš, Petr; Radecký, Michal; Snášel, Václav

2016-01-01

The Differential Evolution (DE) is a widely used bioinspired optimization algorithm developed by Storn and Price. It is popular for its simplicity and robustness. This algorithm was primarily designed for real-valued problems and continuous functions, but several modified versions optimizing both integer and discrete-valued problems have been developed. The discrete-coded DE has been mostly used for combinatorial problems in a set of enumerative variants. However, the DE has a great potential in the spatial data analysis and pattern recognition. This paper formulates the problem as a search of a combination of distinct vertices which meet the specified conditions. It proposes a novel approach called the Multidimensional Discrete Differential Evolution (MDDE) applying the principle of the discrete-coded DE in discrete point clouds (PCs). The paper examines the local searching abilities of the MDDE and its convergence to the global optimum in the PCs. The multidimensional discrete vertices cannot be simply ordered to get a convenient course of the discrete data, which is crucial for good convergence of a population. A novel mutation operator utilizing linear ordering of spatial data based on the space filling curves is introduced. The algorithm is tested on several spatial datasets and optimization problems. The experiments show that the MDDE is an efficient and fast method for discrete optimizations in the multidimensional point clouds.

Utilization of the Discrete Differential Evolution for Optimization in Multidimensional Point Clouds

PubMed Central

Radecký, Michal; Snášel, Václav

2016-01-01

The Differential Evolution (DE) is a widely used bioinspired optimization algorithm developed by Storn and Price. It is popular for its simplicity and robustness. This algorithm was primarily designed for real-valued problems and continuous functions, but several modified versions optimizing both integer and discrete-valued problems have been developed. The discrete-coded DE has been mostly used for combinatorial problems in a set of enumerative variants. However, the DE has a great potential in the spatial data analysis and pattern recognition. This paper formulates the problem as a search of a combination of distinct vertices which meet the specified conditions. It proposes a novel approach called the Multidimensional Discrete Differential Evolution (MDDE) applying the principle of the discrete-coded DE in discrete point clouds (PCs). The paper examines the local searching abilities of the MDDE and its convergence to the global optimum in the PCs. The multidimensional discrete vertices cannot be simply ordered to get a convenient course of the discrete data, which is crucial for good convergence of a population. A novel mutation operator utilizing linear ordering of spatial data based on the space filling curves is introduced. The algorithm is tested on several spatial datasets and optimization problems. The experiments show that the MDDE is an efficient and fast method for discrete optimizations in the multidimensional point clouds. PMID:27974884

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Kutler, Paul (Technical Monitor)

1998-01-01

Several stabilized demoralization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin demoralization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS, and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobean linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Discrete maximum principle theory will be presented for general finite volume approximations on unstructured meshes. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc, will. be addressed as needed.

Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations

NASA Astrophysics Data System (ADS)

Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran

2018-06-01

This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.

Discrete Cosine Transform Image Coding With Sliding Block Codes

NASA Astrophysics Data System (ADS)

Divakaran, Ajay; Pearlman, William A.

1989-11-01

A transform trellis coding scheme for images is presented. A two dimensional discrete cosine transform is applied to the image followed by a search on a trellis structured code. This code is a sliding block code that utilizes a constrained size reproduction alphabet. The image is divided into blocks by the transform coding. The non-stationarity of the image is counteracted by grouping these blocks in clusters through a clustering algorithm, and then encoding the clusters separately. Mandela ordered sequences are formed from each cluster i.e identically indexed coefficients from each block are grouped together to form one dimensional sequences. A separate search ensues on each of these Mandela ordered sequences. Padding sequences are used to improve the trellis search fidelity. The padding sequences absorb the error caused by the building up of the trellis to full size. The simulations were carried out on a 256x256 image ('LENA'). The results are comparable to any existing scheme. The visual quality of the image is enhanced considerably by the padding and clustering.

Methods of parallel computation applied on granular simulations

NASA Astrophysics Data System (ADS)

Martins, Gustavo H. B.; Atman, Allbens P. F.

2017-06-01

Every year, parallel computing has becoming cheaper and more accessible. As consequence, applications were spreading over all research areas. Granular materials is a promising area for parallel computing. To prove this statement we study the impact of parallel computing in simulations of the BNE (Brazil Nut Effect). This property is due the remarkable arising of an intruder confined to a granular media when vertically shaken against gravity. By means of DEM (Discrete Element Methods) simulations, we study the code performance testing different methods to improve clock time. A comparison between serial and parallel algorithms, using OpenMP® is also shown. The best improvement was obtained by optimizing the function that find contacts using Verlet's cells.

Original analytic solution of a half-bridge modelled as a statically indeterminate system

NASA Astrophysics Data System (ADS)

Oanta, Emil M.; Panait, Cornel; Raicu, Alexandra; Barhalescu, Mihaela

2016-12-01

The paper presents an original computer based analytical model of a half-bridge belonging to a circular settling tank. The primary unknown is computed using the force method, the coefficients of the canonical equation being calculated using either the discretization of the bending moment diagram in trapezoids, or using the relations specific to the polygons. A second algorithm based on the method of initial parameters is also presented. Analyzing the new solution we came to the conclusion that most of the computer code developed for other model may be reused. The results are useful to evaluate the behavior of the structure and to compare with the results of the finite element models.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zardecki, A.

The effect of multiple scattering on the validity of the Beer-Lambert law is discussed for a wide range of particle-size parameters and optical depths. To predict the amount of received radiant power, appropriate correction terms are introduced. For particles larger than or comparable to the wavelength of radiation, the small-angle approximation is adequate; whereas for small densely packed particles, the diffusion theory is advantageously employed. These two approaches are used in the context of the problem of laser-beam propagation in a dense aerosol medium. In addition, preliminary results obtained by using a two-dimensional finite-element discrete-ordinates transport code are described. Multiple-scatteringmore » effects for laser propagation in fog, cloud, rain, and aerosol cloud are modeled.« less

The X chromosome in space.

PubMed

Jégu, Teddy; Aeby, Eric; Lee, Jeannie T

2017-06-01

Extensive 3D folding is required to package a genome into the tiny nuclear space, and this packaging must be compatible with proper gene expression. Thus, in the well-hierarchized nucleus, chromosomes occupy discrete territories and adopt specific 3D organizational structures that facilitate interactions between regulatory elements for gene expression. The mammalian X chromosome exemplifies this structure-function relationship. Recent studies have shown that, upon X-chromosome inactivation, active and inactive X chromosomes localize to different subnuclear positions and adopt distinct chromosomal architectures that reflect their activity states. Here, we review the roles of long non-coding RNAs, chromosomal organizational structures and the subnuclear localization of chromosomes as they relate to X-linked gene expression.

Test functions for three-dimensional control-volume mixed finite-element methods on irregular grids

USGS Publications Warehouse

Naff, R.L.; Russell, T.F.; Wilson, J.D.; ,; ,; ,; ,; ,

2000-01-01

Numerical methods based on unstructured grids, with irregular cells, usually require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element methods, vector shape functions are used to approximate the distribution of velocities across cells and vector test functions are used to minimize the error associated with the numerical approximation scheme. For a logically cubic mesh, the lowest-order shape functions are chosen in a natural way to conserve intercell fluxes that vary linearly in logical space. Vector test functions, while somewhat restricted by the mapping into the logical reference cube, admit a wider class of possibilities. Ideally, an error minimization procedure to select the test function from an acceptable class of candidates would be the best procedure. Lacking such a procedure, we first investigate the effect of possible test functions on the pressure distribution over the control volume; specifically, we look for test functions that allow for the elimination of intermediate pressures on cell faces. From these results, we select three forms for the test function for use in a control-volume mixed method code and subject them to an error analysis for different forms of grid irregularity; errors are reported in terms of the discrete L2 norm of the velocity error. Of these three forms, one appears to produce optimal results for most forms of grid irregularity.

A finite element boundary integral formulation for radiation and scattering by cavity antennas using tetrahedral elements

NASA Technical Reports Server (NTRS)

Gong, J.; Volakis, J. L.; Chatterjee, A.; Jin, J. M.

1992-01-01

A hybrid finite element boundary integral formulation is developed using tetrahedral and/or triangular elements for discretizing the cavity and/or aperture of microstrip antenna arrays. The tetrahedral elements with edge based linear expansion functions are chosen for modeling the volume region and triangular elements are used for discretizing the aperture. The edge based expansion functions are divergenceless thus removing the requirement to introduce a penalty term and the tetrahedral elements permit greater geometrical adaptability than the rectangular bricks. The underlying theory and resulting expressions are discussed in detail together with some numerical scattering examples for comparison and demonstration.

Metriplectic integrators for the Landau collision operator

DOE PAGES

Kraus, Michael; Hirvijoki, Eero

2017-10-02

Here, we present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and, using a Galerkin discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonicmore » behavior of entropy are guaranteed for finite element discretizations, in general, independently of the mesh configuration.« less

Applications of discrete element method in modeling of grain postharvest operations

USDA-ARS?s Scientific Manuscript database

Grain kernels are finite and discrete materials. Although flowing grain can behave like a continuum fluid at times, the discontinuous behavior exhibited by grain kernels cannot be simulated solely with conventional continuum-based computer modeling such as finite-element or finite-difference methods...

Numerical uncertainty in computational engineering and physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hemez, Francois M

2009-01-01

Obtaining a solution that approximates ordinary or partial differential equations on a computational mesh or grid does not necessarily mean that the solution is accurate or even 'correct'. Unfortunately assessing the quality of discrete solutions by questioning the role played by spatial and temporal discretizations generally comes as a distant third to test-analysis comparison and model calibration. This publication is contributed to raise awareness of the fact that discrete solutions introduce numerical uncertainty. This uncertainty may, in some cases, overwhelm in complexity and magnitude other sources of uncertainty that include experimental variability, parametric uncertainty and modeling assumptions. The concepts ofmore » consistency, convergence and truncation error are overviewed to explain the articulation between the exact solution of continuous equations, the solution of modified equations and discrete solutions computed by a code. The current state-of-the-practice of code and solution verification activities is discussed. An example in the discipline of hydro-dynamics illustrates the significant effect that meshing can have on the quality of code predictions. A simple method is proposed to derive bounds of solution uncertainty in cases where the exact solution of the continuous equations, or its modified equations, is unknown. It is argued that numerical uncertainty originating from mesh discretization should always be quantified and accounted for in the overall uncertainty 'budget' that supports decision-making for applications in computational physics and engineering.« less

Hypersonic Viscous Flow Over Large Roughness Elements

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Choudhari, Meelan M.

2009-01-01

Viscous flow over discrete or distributed surface roughness has great implications for hypersonic flight due to aerothermodynamic considerations related to laminar-turbulent transition. Current prediction capability is greatly hampered by the limited knowledge base for such flows. To help fill that gap, numerical computations are used to investigate the intricate flow physics involved. An unstructured mesh, compressible Navier-Stokes code based on the space-time conservation element, solution element (CESE) method is used to perform time-accurate Navier-Stokes calculations for two roughness shapes investigated in wind tunnel experiments at NASA Langley Research Center. It was found through 2D parametric study that at subcritical Reynolds numbers, spontaneous absolute instability accompanying by sustained vortex shedding downstream of the roughness is likely to take place at subsonic free-stream conditions. On the other hand, convective instability may be the dominant mechanism for supersonic boundary layers. Three-dimensional calculations for both a rectangular and a cylindrical roughness element at post-shock Mach numbers of 4.1 and 6.5 also confirm that no self-sustained vortex generation from the top face of the roughness is observed, despite the presence of flow unsteadiness for the smaller post-shock Mach number case.

Exponential convergence through linear finite element discretization of stratified subdomains

NASA Astrophysics Data System (ADS)

Guddati, Murthy N.; Druskin, Vladimir; Vaziri Astaneh, Ali

2016-10-01

Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The key features of the discretization are (a) use of midpoint integration to evaluate the contribution matrices, and (b) an unconventional mapping of the mesh into complex space. Named complex-length finite element method (CFEM), the technique is linked to Padé approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified points in the domain. Exponential convergence facilitates drastic reduction in the number of elements. This, combined with sparse computation associated with linear finite elements, results in significant reduction in the computational cost. The paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving Laplace, Helmholtz and elastodynamics equations.

Finite elements of nonlinear continua.

NASA Technical Reports Server (NTRS)

Oden, J. T.

1972-01-01

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Simulation of prompt gamma-ray emission during proton radiotherapy.

PubMed

Verburg, Joost M; Shih, Helen A; Seco, Joao

2012-09-07

The measurement of prompt gamma rays emitted from proton-induced nuclear reactions has been proposed as a method to verify in vivo the range of a clinical proton radiotherapy beam. A good understanding of the prompt gamma-ray emission during proton therapy is key to develop a clinically feasible technique, as it can facilitate accurate simulations and uncertainty analysis of gamma detector designs. Also, the gamma production cross-sections may be incorporated as prior knowledge in the reconstruction of the proton range from the measurements. In this work, we performed simulations of proton-induced nuclear reactions with the main elements of human tissue, carbon-12, oxygen-16 and nitrogen-14, using the nuclear reaction models of the GEANT4 and MCNP6 Monte Carlo codes and the dedicated nuclear reaction codes TALYS and EMPIRE. For each code, we made an effort to optimize the input parameters and model selection. The results of the models were compared to available experimental data of discrete gamma line cross-sections. Overall, the dedicated nuclear reaction codes reproduced the experimental data more consistently, while the Monte Carlo codes showed larger discrepancies for a number of gamma lines. The model differences lead to a variation of the total gamma production near the end of the proton range by a factor of about 2. These results indicate a need for additional theoretical and experimental study of proton-induced gamma emission in human tissue.

Particle models for discrete element modeling of bulk grain properties of wheat kernels

USDA-ARS?s Scientific Manuscript database

Recent research has shown the potential of discrete element method (DEM) in simulating grain flow in bulk handling systems. Research has also revealed that simulation of grain flow with DEM requires establishment of appropriate particle models for each grain type. This research completes the three-p...

Quadratic Finite Element Method for 1D Deterministic Transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tolar, Jr., D R; Ferguson, J M

2004-01-06

In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.

Dual Formulations of Mixed Finite Element Methods with Applications

PubMed Central

Gillette, Andrew; Bajaj, Chandrajit

2011-01-01

Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail. PMID:21984841

SPAMCART: a code for smoothed particle Monte Carlo radiative transfer

NASA Astrophysics Data System (ADS)

Lomax, O.; Whitworth, A. P.

2016-10-01

We present a code for generating synthetic spectral energy distributions and intensity maps from smoothed particle hydrodynamics simulation snapshots. The code is based on the Lucy Monte Carlo radiative transfer method, I.e. it follows discrete luminosity packets as they propagate through a density field, and then uses their trajectories to compute the radiative equilibrium temperature of the ambient dust. The sources can be extended and/or embedded, and discrete and/or diffuse. The density is not mapped on to a grid, and therefore the calculation is performed at exactly the same resolution as the hydrodynamics. We present two example calculations using this method. First, we demonstrate that the code strictly adheres to Kirchhoff's law of radiation. Secondly, we present synthetic intensity maps and spectra of an embedded protostellar multiple system. The algorithm uses data structures that are already constructed for other purposes in modern particle codes. It is therefore relatively simple to implement.

From Physics Model to Results: An Optimizing Framework for Cross-Architecture Code Generation

DOE PAGES

Blazewicz, Marek; Hinder, Ian; Koppelman, David M.; ...

2013-01-01

Starting from a high-level problem description in terms of partial differential equations using abstract tensor notation, the Chemora framework discretizes, optimizes, and generates complete high performance codes for a wide range of compute architectures. Chemora extends the capabilities of Cactus, facilitating the usage of large-scale CPU/GPU systems in an efficient manner for complex applications, without low-level code tuning. Chemora achieves parallelism through MPI and multi-threading, combining OpenMP and CUDA. Optimizations include high-level code transformations, efficient loop traversal strategies, dynamically selected data and instruction cache usage strategies, and JIT compilation of GPU code tailored to the problem characteristics. The discretization ismore » based on higher-order finite differences on multi-block domains. Chemora's capabilities are demonstrated by simulations of black hole collisions. This problem provides an acid test of the framework, as the Einstein equations contain hundreds of variables and thousands of terms.« less

Fast transient digitizer

DOEpatents

Villa, Francesco

1982-01-01

Method and apparatus for sequentially scanning a plurality of target elements with an electron scanning beam modulated in accordance with variations in a high-frequency analog signal to provide discrete analog signal samples representative of successive portions of the analog signal; coupling the discrete analog signal samples from each of the target elements to a different one of a plurality of high speed storage devices; converting the discrete analog signal samples to equivalent digital signals; and storing the digital signals in a digital memory unit for subsequent measurement or display.

A constrained Delaunay discretization method for adaptively meshing highly discontinuous geological media

NASA Astrophysics Data System (ADS)

Wang, Yang; Ma, Guowei; Ren, Feng; Li, Tuo

2017-12-01

A constrained Delaunay discretization method is developed to generate high-quality doubly adaptive meshes of highly discontinuous geological media. Complex features such as three-dimensional discrete fracture networks (DFNs), tunnels, shafts, slopes, boreholes, water curtains, and drainage systems are taken into account in the mesh generation. The constrained Delaunay triangulation method is used to create adaptive triangular elements on planar fractures. Persson's algorithm (Persson, 2005), based on an analogy between triangular elements and spring networks, is enriched to automatically discretize a planar fracture into mesh points with varying density and smooth-quality gradient. The triangulated planar fractures are treated as planar straight-line graphs (PSLGs) to construct piecewise-linear complex (PLC) for constrained Delaunay tetrahedralization. This guarantees the doubly adaptive characteristic of the resulted mesh: the mesh is adaptive not only along fractures but also in space. The quality of elements is compared with the results from an existing method. It is verified that the present method can generate smoother elements and a better distribution of element aspect ratios. Two numerical simulations are implemented to demonstrate that the present method can be applied to various simulations of complex geological media that contain a large number of discontinuities.

Multidimensional Modeling of Atmospheric Effects and Surface Heterogeneities on Remote Sensing

NASA Technical Reports Server (NTRS)

Gerstl, S. A. W.; Simmer, C.; Zardecki, A. (Principal Investigator)

1985-01-01

The overall goal of this project is to establish a modeling capability that allows a quantitative determination of atmospheric effects on remote sensing including the effects of surface heterogeneities. This includes an improved understanding of aerosol and haze effects in connection with structural, angular, and spatial surface heterogeneities. One important objective of the research is the possible identification of intrinsic surface or canopy characteristics that might be invariant to atmospheric perturbations so that they could be used for scene identification. Conversely, an equally important objective is to find a correction algorithm for atmospheric effects in satellite-sensed surface reflectances. The technical approach is centered around a systematic model and code development effort based on existing, highly advanced computer codes that were originally developed for nuclear radiation shielding applications. Computational techniques for the numerical solution of the radiative transfer equation are adapted on the basis of the discrete-ordinates finite-element method which proved highly successful for one and two-dimensional radiative transfer problems with fully resolved angular representation of the radiation field.

A Three-Dimensional Finite-Element Model for Simulating Water Flow in Variably Saturated Porous Media

NASA Astrophysics Data System (ADS)

Huyakorn, Peter S.; Springer, Everett P.; Guvanasen, Varut; Wadsworth, Terry D.

1986-12-01

A three-dimensional finite-element model for simulating water flow in variably saturated porous media is presented. The model formulation is general and capable of accommodating complex boundary conditions associated with seepage faces and infiltration or evaporation on the soil surface. Included in this formulation is an improved Picard algorithm designed to cope with severely nonlinear soil moisture relations. The algorithm is formulated for both rectangular and triangular prism elements. The element matrices are evaluated using an "influence coefficient" technique that avoids costly numerical integration. Spatial discretization of a three-dimensional region is performed using a vertical slicing approach designed to accommodate complex geometry with irregular boundaries, layering, and/or lateral discontinuities. Matrix solution is achieved using a slice successive overrelaxation scheme that permits a fairly large number of nodal unknowns (on the order of several thousand) to be handled efficiently on small minicomputers. Six examples are presented to verify and demonstrate the utility of the proposed finite-element model. The first four examples concern one- and two-dimensional flow problems used as sample problems to benchmark the code. The remaining examples concern three-dimensional problems. These problems are used to illustrate the performance of the proposed algorithm in three-dimensional situations involving seepage faces and anisotropic soil media.

Variations in the non-coding transcriptome as a driver of inter-strain divergence and physiological adaptation in bacteria

PubMed Central

Kopf, Matthias; Klähn, Stephan; Scholz, Ingeborg; Hess, Wolfgang R.; Voß, Björn

2015-01-01

In all studied organisms, a substantial portion of the transcriptome consists of non-coding RNAs that frequently execute regulatory functions. Here, we have compared the primary transcriptomes of the cyanobacteria Synechocystis sp. PCC 6714 and PCC 6803 under 10 different conditions. These strains share 2854 protein-coding genes and a 16S rRNA identity of 99.4%, indicating their close relatedness. Conserved major transcriptional start sites (TSSs) give rise to non-coding transcripts within the sigB gene, from the 5′UTRs of cmpA and isiA, and 168 loci in antisense orientation. Distinct differences include single nucleotide polymorphisms rendering promoters inactive in one of the strains, e.g., for cmpR and for the asRNA PsbA2R. Based on the genome-wide mapped location, regulation and classification of TSSs, non-coding transcripts were identified as the most dynamic component of the transcriptome. We identified a class of mRNAs that originate by read-through from an sRNA that accumulates as a discrete and abundant transcript while also serving as the 5′UTR. Such an sRNA/mRNA structure, which we name ‘actuaton’, represents another way for bacteria to remodel their transcriptional network. Our findings support the hypothesis that variations in the non-coding transcriptome constitute a major evolutionary element of inter-strain divergence and capability for physiological adaptation. PMID:25902393

Partitioned fluid-solid coupling for cardiovascular blood flow: left-ventricular fluid mechanics.

PubMed

Krittian, Sebastian; Janoske, Uwe; Oertel, Herbert; Böhlke, Thomas

2010-04-01

We present a 3D code-coupling approach which has been specialized towards cardiovascular blood flow. For the first time, the prescribed geometry movement of the cardiovascular flow model KaHMo (Karlsruhe Heart Model) has been replaced by a myocardial composite model. Deformation is driven by fluid forces and myocardial response, i.e., both its contractile and constitutive behavior. Whereas the arbitrary Lagrangian-Eulerian formulation (ALE) of the Navier-Stokes equations is discretized by finite volumes (FVM), the solid mechanical finite elasticity equations are discretized by a finite element (FEM) approach. Taking advantage of specialized numerical solution strategies for non-matching fluid and solid domain meshes, an iterative data-exchange guarantees the interface equilibrium of the underlying governing equations. The focus of this work is on left-ventricular fluid-structure interaction based on patient-specific magnetic resonance imaging datasets. Multi-physical phenomena are described by temporal visualization and characteristic FSI numbers. The results gained show flow patterns that are in good agreement with previous observations. A deeper understanding of cavity deformation, blood flow, and their vital interaction can help to improve surgical treatment and clinical therapy planning.

The domain interface method: a general-purpose non-intrusive technique for non-conforming domain decomposition problems

NASA Astrophysics Data System (ADS)

Cafiero, M.; Lloberas-Valls, O.; Cante, J.; Oliver, J.

2016-04-01

A domain decomposition technique is proposed which is capable of properly connecting arbitrary non-conforming interfaces. The strategy essentially consists in considering a fictitious zero-width interface between the non-matching meshes which is discretized using a Delaunay triangulation. Continuity is satisfied across domains through normal and tangential stresses provided by the discretized interface and inserted in the formulation in the form of Lagrange multipliers. The final structure of the global system of equations resembles the dual assembly of substructures where the Lagrange multipliers are employed to nullify the gap between domains. A new approach to handle floating subdomains is outlined which can be implemented without significantly altering the structure of standard industrial finite element codes. The effectiveness of the developed algorithm is demonstrated through a patch test example and a number of tests that highlight the accuracy of the methodology and independence of the results with respect to the framework parameters. Considering its high degree of flexibility and non-intrusive character, the proposed domain decomposition framework is regarded as an attractive alternative to other established techniques such as the mortar approach.

LinAir: A multi-element discrete vortex Weissinger aerodynamic prediction method

NASA Technical Reports Server (NTRS)

Durston, Donald A.

1993-01-01

LinAir is a vortex lattice aerodynamic prediction method similar to Weissinger's extended lifting-line theory, except that the circulation around a wing is represented by discrete horseshoe vortices, not a continuous distribution of vorticity. The program calculates subsonic longitudinal and lateral/directional aerodynamic forces and moments for arbitrary aircraft geometries. It was originally written by Dr. Ilan Kroo of Stanford University, and subsequently modified by the author to simplify modeling of complex configurations. The Polhamus leading-edge suction analogy was added by the author to extend the range of applicability of LinAir to low aspect ratio (i.e., fighter-type) configurations. A brief discussion of the theory of LinAir is presented, and details on how to run the program are given along with some comparisons with experimental data to validate the code. Example input and output files are given in the appendices to aid in understanding the program and its use. This version of LinAir runs in the VAX/VMS, Cray UNICOS, and Silicon Graphics Iris workstation environments at the time of this writing.

Using a simulation assistant in modeling manufacturing systems

NASA Technical Reports Server (NTRS)

Schroer, Bernard J.; Tseng, Fan T.; Zhang, S. X.; Wolfsberger, John W.

1988-01-01

Numerous simulation languages exist for modeling discrete event processes, and are now ported to microcomputers. Graphic and animation capabilities were added to many of these languages to assist the users build models and evaluate the simulation results. With all these languages and added features, the user is still plagued with learning the simulation language. Futhermore, the time to construct and then to validate the simulation model is always greater than originally anticipated. One approach to minimize the time requirement is to use pre-defined macros that describe various common processes or operations in a system. The development of a simulation assistant for modeling discrete event manufacturing processes is presented. A simulation assistant is defined as an interactive intelligent software tool that assists the modeler in writing a simulation program by translating the modeler's symbolic description of the problem and then automatically generating the corresponding simulation code. The simulation assistant is discussed with emphasis on an overview of the simulation assistant, the elements of the assistant, and the five manufacturing simulation generators. A typical manufacturing system will be modeled using the simulation assistant and the advantages and disadvantages discussed.

What counts as a health service? Weight loss companies through the looking glass of New Zealand's Code of Patients' Rights.

PubMed

Neill, Megan J

2013-03-01

In New Zealand, the Code of Health and Disability Services Consumer's Rights is a key innovative piece of legislation for the protection of health and disability service users. It provides rights to consumers and imposes duties on the providers of such services, complemented by a cost-free statutory complaints process for the resolution of breakdowns in the relationship between the two. The Code has a potentially liberal application and is theoretically capable of applying to all manner of services through the generalised definitions of the Health and Disability Commissioner Act 1994 (NZ). As the facilitator of the Code, the Health and Disability Commissioner has a correspondingly wide discretion in determining whether to further investigate complaints of Code breaches. This article considers the extent to which the Code's apparent breadth of application could incorporate commercial weight loss companies as providers and the likelihood of the Commissioner using the discretion to investigate complaints against such companies.

3D Discrete element approach to the problem on abutment pressure in a gently dipping coal seam

NASA Astrophysics Data System (ADS)

Klishin, S. V.; Revuzhenko, A. F.

2017-09-01

Using the discrete element method, the authors have carried out 3D implementation of the problem on strength loss in surrounding rock mass in the vicinity of a production heading and on abutment pressure in a gently dripping coal seam. The calculation of forces at the contacts between particles accounts for friction, rolling resistance and viscosity. Between discrete particles modeling coal seam, surrounding rock mass and broken rocks, an elastic connecting element is introduced to allow simulating coherent materials. The paper presents the kinematic patterns of rock mass deformation, stresses in particles and the graph of the abutment pressure behavior in the coal seam.

Stochastic-Strength-Based Damage Simulation Tool for Ceramic Matrix and Polymer Matrix Composite Structures

NASA Technical Reports Server (NTRS)

Nemeth, Noel N.; Bednarcyk, Brett A.; Pineda, Evan J.; Walton, Owen J.; Arnold, Steven M.

2016-01-01

Stochastic-based, discrete-event progressive damage simulations of ceramic-matrix composite and polymer matrix composite material structures have been enabled through the development of a unique multiscale modeling tool. This effort involves coupling three independently developed software programs: (1) the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), (2) the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program (CARES/ Life), and (3) the Abaqus finite element analysis (FEA) program. MAC/GMC contributes multiscale modeling capabilities and micromechanics relations to determine stresses and deformations at the microscale of the composite material repeating unit cell (RUC). CARES/Life contributes statistical multiaxial failure criteria that can be applied to the individual brittle-material constituents of the RUC. Abaqus is used at the global scale to model the overall composite structure. An Abaqus user-defined material (UMAT) interface, referred to here as "FEAMAC/CARES," was developed that enables MAC/GMC and CARES/Life to operate seamlessly with the Abaqus FEA code. For each FEAMAC/CARES simulation trial, the stochastic nature of brittle material strength results in random, discrete damage events, which incrementally progress and lead to ultimate structural failure. This report describes the FEAMAC/CARES methodology and discusses examples that illustrate the performance of the tool. A comprehensive example problem, simulating the progressive damage of laminated ceramic matrix composites under various off-axis loading conditions and including a double notched tensile specimen geometry, is described in a separate report.

SUPG Finite Element Simulations of Compressible Flows for Aerothermodynamic Applications

NASA Technical Reports Server (NTRS)

Kirk, Benjamin S.

2007-01-01

This viewgraph presentation reviews the Streamline-Upwind Petrov-Galerkin (SUPG) Finite Element Simulation. It covers the background, governing equations, weak formulation, shock capturing, inviscid flux discretization, time discretization, linearization, and implicit solution strategies. It also reviews some applications such as Type IV Shock Interaction, Forward-Facing Cavity and AEDC Sharp Double Cone.

Automated quadrilateral surface discretization method and apparatus usable to generate mesh in a finite element analysis system

DOEpatents

Blacker, Teddy D.

1994-01-01

An automatic quadrilateral surface discretization method and apparatus is provided for automatically discretizing a geometric region without decomposing the region. The automated quadrilateral surface discretization method and apparatus automatically generates a mesh of all quadrilateral elements which is particularly useful in finite element analysis. The generated mesh of all quadrilateral elements is boundary sensitive, orientation insensitive and has few irregular nodes on the boundary. A permanent boundary of the geometric region is input and rows are iteratively layered toward the interior of the geometric region. Also, an exterior permanent boundary and an interior permanent boundary for a geometric region may be input and the rows are iteratively layered inward from the exterior boundary in a first counter clockwise direction while the rows are iteratively layered from the interior permanent boundary toward the exterior of the region in a second clockwise direction. As a result, a high quality mesh for an arbitrary geometry may be generated with a technique that is robust and fast for complex geometric regions and extreme mesh gradations.

A note on the R sub 0-parameter for discrete memoryless channels

NASA Technical Reports Server (NTRS)

Mceliece, R. J.

1980-01-01

An explicit class of discrete memoryless channels (q-ary erasure channels) is exhibited. Practical and explicit coded systems of rate R with R/R sub o as large as desired can be designed for this class.

Modulation and coding for a compatible Discrete Address Beacon System.

DOT National Transportation Integrated Search

1972-02-01

One of several possible candidate configurations for the Discrete Address System is described. The configuration presented is compatible with the Air Traffic Control Radar Beacon System, and it provides for gradual transition from one system to the o...

A High-Resolution Capability for Large-Eddy Simulation of Jet Flows

NASA Technical Reports Server (NTRS)

DeBonis, James R.

2011-01-01

A large-eddy simulation (LES) code that utilizes high-resolution numerical schemes is described and applied to a compressible jet flow. The code is written in a general manner such that the accuracy/resolution of the simulation can be selected by the user. Time discretization is performed using a family of low-dispersion Runge-Kutta schemes, selectable from first- to fourth-order. Spatial discretization is performed using central differencing schemes. Both standard schemes, second- to twelfth-order (3 to 13 point stencils) and Dispersion Relation Preserving schemes from 7 to 13 point stencils are available. The code is written in Fortran 90 and uses hybrid MPI/OpenMP parallelization. The code is applied to the simulation of a Mach 0.9 jet flow. Four-stage third-order Runge-Kutta time stepping and the 13 point DRP spatial discretization scheme of Bogey and Bailly are used. The high resolution numerics used allows for the use of relatively sparse grids. Three levels of grid resolution are examined, 3.5, 6.5, and 9.2 million points. Mean flow, first-order turbulent statistics and turbulent spectra are reported. Good agreement with experimental data for mean flow and first-order turbulent statistics is shown.

Crack Turning and Arrest Mechanisms for Integral Structure

NASA Technical Reports Server (NTRS)

Pettit, Richard; Ingraffea, Anthony

1999-01-01

In the course of several years of research efforts to predict crack turning and flapping in aircraft fuselage structures and other problems related to crack turning, the 2nd order maximum tangential stress theory has been identified as the theory most capable of predicting the observed test results. This theory requires knowledge of a material specific characteristic length, and also a computation of the stress intensity factors and the T-stress, or second order term in the asymptotic stress field in the vicinity of the crack tip. A characteristic length, r(sub c), is proposed for ductile materials pertaining to the onset of plastic instability, as opposed to the void spacing theories espoused by previous investigators. For the plane stress case, an approximate estimate of r(sub c), is obtained from the asymptotic field for strain hardening materials given by Hutchinson, Rice and Rosengren (HRR). A previous study using of high order finite element methods to calculate T-stresses by contour integrals resulted in extremely high accuracy values obtained for selected test specimen geometries, and a theoretical error estimation parameter was defined. In the present study, it is shown that a large portion of the error in finite element computations of both K and T are systematic, and can be corrected after the initial solution if the finite element implementation utilizes a similar crack tip discretization scheme for all problems. This scheme is applied for two-dimensional problems to a both a p-version finite element code, showing that sufficiently accurate values of both K(sub I) and T can be obtained with fairly low order elements if correction is used. T-stress correction coefficients are also developed for the singular crack tip rosette utilized in the adaptive mesh finite element code FRANC2D, and shown to reduce the error in the computed T-stress significantly. Stress intensity factor correction was not attempted for FRANC2D because it employs a highly accurate quarter-point scheme to obtain stress intensity factors.

High Productivity Computing Systems Analysis and Performance

DTIC Science & Technology

2005-07-01

cubic grid Discrete Math Global Updates per second (GUP/S) RandomAccess Paper & Pencil Contact Bob Lucas (ISI) Multiple Precision none...can be found at the web site. One of the HPCchallenge codes, RandomAccess, is derived from the HPCS discrete math benchmarks that we released, and...Kernels Discrete Math … Graph Analysis … Linear Solvers … Signal Processi ng Execution Bounds Execution Indicators 6 Scalable Compact

Viewing hybrid systems as products of control systems and automata

NASA Technical Reports Server (NTRS)

Grossman, R. L.; Larson, R. G.

1992-01-01

The purpose of this note is to show how hybrid systems may be modeled as products of nonlinear control systems and finite state automata. By a hybrid system, we mean a network of consisting of continuous, nonlinear control system connected to discrete, finite state automata. Our point of view is that the automata switches between the control systems, and that this switching is a function of the discrete input symbols or letters that it receives. We show how a nonlinear control system may be viewed as a pair consisting of a bialgebra of operators coding the dynamics, and an algebra of observations coding the state space. We also show that a finite automata has a similar representation. A hybrid system is then modeled by taking suitable products of the bialgebras coding the dynamics and the observation algebras coding the state spaces.

Nonlinear initial-boundary value solutions by the finite element method. [for Navier-Stokes equations of two dimensional flow

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.

Domain decomposition methods for nonconforming finite element spaces of Lagrange-type

NASA Technical Reports Server (NTRS)

Cowsar, Lawrence C.

1993-01-01

In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.

A Numerical Investigation of the Extinction of Low Strain Rate Diffusion Flames by an Agent in Microgravity

NASA Technical Reports Server (NTRS)

Puri, Ishwar K.

2004-01-01

Our goal has been to investigate the influence of both dilution and radiation on the extinction process of nonpremixed flames at low strain rates. Simulations have been performed by using a counterflow code and three radiation models have been included in it, namely, the optically thin, the narrowband, and discrete ordinate models. The counterflow flame code OPPDIFF was modified to account for heat transfer losses by radiation from the hot gases. The discrete ordinate method (DOM) approximation was first suggested by Chandrasekhar for solving problems in interstellar atmospheres. Carlson and Lathrop developed the method for solving multi-dimensional problem in neutron transport. Only recently has the method received attention in the field of heat transfer. Due to the applicability of the discrete ordinate method for thermal radiation problems involving flames, the narrowband code RADCAL was modified to calculate the radiative properties of the gases. A non-premixed counterflow flame was simulated with the discrete ordinate method for radiative emissions. In comparison with two other models, it was found that the heat losses were comparable with the optically thin and simple narrowband model. The optically thin model had the highest heat losses followed by the DOM model and the narrow-band model.

Space-time adaptive solution of inverse problems with the discrete adjoint method

NASA Astrophysics Data System (ADS)

Alexe, Mihai; Sandu, Adrian

2014-08-01

This paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent, adaptive grid, adaptive step models. Discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation. However, this approach brings several important challenges. The space-time adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations. A reduction in accuracy of the discrete adjoint sensitivities may appear due to the inter-grid transfer operators. Moreover, the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations. This work shows that several of these potential issues can be avoided through a multi-level optimization strategy using discontinuous Galerkin (DG) hp-adaptive discretizations paired with Runge-Kutta (RK) time integration. We extend the concept of dual (adjoint) consistency to space-time RK-DG discretizations, which are then shown to be well suited for the adaptive solution of time-dependent inverse problems. Furthermore, we prove that DG mesh transfer operators on general meshes are also dual consistent. This allows the simultaneous derivation of the discrete adjoint for both the numerical solver and the mesh transfer logic with an automatic code generation mechanism such as algorithmic differentiation (AD), potentially speeding up development of large-scale simulation codes. The theoretical analysis is supported by numerical results reported for a two-dimensional non-stationary inverse problem.

The ADER-DG method for seismic wave propagation and earthquake rupture dynamics

NASA Astrophysics Data System (ADS)

Pelties, Christian; Gabriel, Alice; Ampuero, Jean-Paul; de la Puente, Josep; Käser, Martin

2013-04-01

We will present the Arbitrary high-order DERivatives Discontinuous Galerkin (ADER-DG) method for solving the combined elastodynamic wave propagation and dynamic rupture problem. The ADER-DG method enables high-order accuracy in space and time while being implemented on unstructured tetrahedral meshes. A tetrahedral element discretization provides rapid and automatized mesh generation as well as geometrical flexibility. Features as mesh coarsening and local time stepping schemes can be applied to reduce computational efforts without introducing numerical artifacts. The method is well suited for parallelization and large scale high-performance computing since only directly neighboring elements exchange information via numerical fluxes. The concept of fluxes is a key ingredient of the numerical scheme as it governs the numerical dispersion and diffusion properties and allows to accommodate for boundary conditions, empirical friction laws of dynamic rupture processes, or the combination of different element types and non-conforming mesh transitions. After introducing fault dynamics into the ADER-DG framework, we will demonstrate its specific advantages in benchmarking test scenarios provided by the SCEC/USGS Spontaneous Rupture Code Verification Exercise. An important result of the benchmark is that the ADER-DG method avoids spurious high-frequency contributions in the slip rate spectra and therefore does not require artificial Kelvin-Voigt damping, filtering or other modifications of the produced synthetic seismograms. To demonstrate the capabilities of the proposed scheme we simulate an earthquake scenario, inspired by the 1992 Landers earthquake, that includes branching and curved fault segments. Furthermore, topography is respected in the discretized model to capture the surface waves correctly. The advanced geometrical flexibility combined with an enhanced accuracy will make the ADER-DG method a useful tool to study earthquake dynamics on complex fault systems in realistic rheologies.

A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

PubMed Central

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L 2(Ω))2 space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term w = −Δu and a priori error estimates in (L 2)2-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes. PMID:23864831

A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.

PubMed

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L²(Ω))² space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.

Prediction of Vehicle Mobility on Large-Scale Soft-Soil Terrain Maps Using Physics-Based Simulation

DTIC Science & Technology

2016-08-04

soil type. The modeling approach is based on (i) a seamless integration of multibody dynamics and discrete element method (DEM) solvers, and (ii...ensure that the vehicle follows a desired path. The soil is modeled as a Discrete Element Model (DEM) with a general cohesive material model that is

Unified viscoelasticity: Applying discrete element models to soft tissues with two characteristic times.

PubMed

Anssari-Benam, Afshin; Bucchi, Andrea; Bader, Dan L

2015-09-18

Discrete element models have often been the primary tool in investigating and characterising the viscoelastic behaviour of soft tissues. However, studies have employed varied configurations of these models, based on the choice of the number of elements and the utilised formation, for different subject tissues. This approach has yielded a diverse array of viscoelastic models in the literature, each seemingly resulting in different descriptions of viscoelastic constitutive behaviour and/or stress-relaxation and creep functions. Moreover, most studies do not apply a single discrete element model to characterise both stress-relaxation and creep behaviours of tissues. The underlying assumption for this disparity is the implicit perception that the viscoelasticity of soft tissues cannot be described by a universal behaviour or law, resulting in the lack of a unified approach in the literature based on discrete element representations. This paper derives the constitutive equation for different viscoelastic models applicable to soft tissues with two characteristic times. It demonstrates that all possible configurations exhibit a unified and universal behaviour, captured by a single constitutive relationship between stress, strain and time as: σ+Aσ̇+Bσ¨=Pε̇+Qε¨. The ensuing stress-relaxation G(t) and creep J(t) functions are also unified and universal, derived as [Formula: see text] and J(t)=c2+(ε0-c2)e(-PQt)+σ0Pt, respectively. Application of these relationships to experimental data is illustrated for various tissues including the aortic valve, ligament and cerebral artery. The unified model presented in this paper may be applied to all tissues with two characteristic times, obviating the need for employing varied configurations of discrete element models in preliminary investigation of the viscoelastic behaviour of soft tissues. Copyright © 2015 Elsevier Ltd. All rights reserved.

76 FR 37034 - Certain Employee Remuneration in Excess of $1,000,000 Under Internal Revenue Code Section 162(m)

Federal Register 2010, 2011, 2012, 2013, 2014

2011-06-24

... Certain Employee Remuneration in Excess of $1,000,000 Under Internal Revenue Code Section 162(m) AGENCY... remuneration in excess of $1,000,000 under the Internal Revenue Code (Code). The proposed regulations clarify... stock options, it is intended that the directors may retain discretion as to the exact number of options...

Peridynamics with LAMMPS : a user guide.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehoucq, Richard B.; Silling, Stewart Andrew; Plimpton, Steven James

2008-01-01

Peridynamics is a nonlocal formulation of continuum mechanics. The discrete peridynamic model has the same computational structure as a molecular dynamic model. This document details the implementation of a discrete peridynamic model within the LAMMPS molecular dynamic code. This document provides a brief overview of the peridynamic model of a continuum, then discusses how the peridynamic model is discretized, and overviews the LAMMPS implementation. A nontrivial example problem is also included.

Multi-Aperture Digital Coherent Combining for Free-Space Optical Communication Receivers

DTIC Science & Technology

2016-04-21

Distribution A: Public Release; unlimited distribution 2016 Optical Society of America OCIS codes: (060.1660) Coherent communications; (070.2025) Discrete ...Coherent combining algorithm Multi-aperture coherent combining enables using many discrete apertures together to create a large effective aperture. A

Pellet Cladding Mechanical Interaction Modeling Using the Extended Finite Element Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spencer, Benjamin W.; Jiang, Wen; Dolbow, John E.

As a brittle material, the ceramic UO2 used as light water reactor fuel experiences significant fracturing throughout its life, beginning with the first rise to power of fresh fuel. This has multiple effects on the thermal and mechanical response of the fuel/cladding system. One such effect that is particularly important is that when there is mechanical contact between the fuel and cladding, cracks that extending from the outer surface of the fuel into the volume of the fuel cause elevated stresses in the adjacent cladding, which can potentially lead to cladding failure. Modeling the thermal and mechanical response of themore » cladding in the vicinity of these surface-breaking cracks in the fuel can provide important insights into this behavior to help avoid operating conditions that could lead to cladding failure. Such modeling has traditionally been done in the context of finite-element-based fuel performance analysis by modifying the fuel mesh to introduce discrete cracks. While this approach is effective in capturing the important behavior at the fuel/cladding interface, there are multiple drawbacks to explicitly incorporating the cracks in the finite element mesh. Because the cracks are incorporated in the original mesh, the mesh must be modified for cracks of specified location and depth, so it is difficult to account for crack propagation and the formation of new cracks at other locations. The extended finite element method (XFEM) has emerged in recent years as a powerful method to represent arbitrary, evolving, discrete discontinuities within the context of the finite element method. Development work is underway by the authors to implement XFEM in the BISON fuel performance code, and this capability has previously been demonstrated in simulations of fracture propagation in ceramic nuclear fuel. These preliminary demonstrations have included only the fuel, and excluded the cladding for simplicity. This paper presents initial results of efforts to apply XFEM to model stress concentrations induced by fuel fractures at the fuel/cladding interface during pellet cladding mechanical interaction (PCMI). This is accomplished by enhancing the thermal and mechanical contact enforcement algorithms employed by BISON to permit their use in conjunction with XFEM. The results from this methodology are demonstrated to be equivalent to those from using meshed discrete cracks. While the results of the two methods are equivalent for the case of a stationary crack, it is demonstrated that XFEM provides the additional flexibility of allowing arbitrary crack initiation and propagation during the analysis, and minimizes model setup effort for cases with stationary cracks.« less

Network Science Research Laboratory (NSRL) Discrete Event Toolkit

DTIC Science & Technology

2016-01-01

ARL-TR-7579 ● JAN 2016 US Army Research Laboratory Network Science Research Laboratory (NSRL) Discrete Event Toolkit by...Laboratory (NSRL) Discrete Event Toolkit by Theron Trout and Andrew J Toth Computational and Information Sciences Directorate, ARL...Research Laboratory (NSRL) Discrete Event Toolkit 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Theron Trout

The Clemson University, University Research Initiative Program in Discrete Mathematics and Computational Analysis

DTIC Science & Technology

1990-03-01

Assmus, E. F., and J. D. Key, "Affine and projective planes", to appear in Discrete Math (Special Coding Theory Issue). 5. Assumus, E. F. and J. D...S. Locke, ’The subchromatic number of a graph", Discrete Math . 74 (1989)33-49. 24. Hedetniemi, S. T., and T. V. Wimer, "K-terminal recursive families...34Designs and geometries with Cayley", submitted to Journal of Symbolic Computation. 34. Key, J. D., "Regular sets in geometries", Annals of Discrete Math . 37

General phase spaces: from discrete variables to rotor and continuum limits

NASA Astrophysics Data System (ADS)

Albert, Victor V.; Pascazio, Saverio; Devoret, Michel H.

2017-12-01

We provide a basic introduction to discrete-variable, rotor, and continuous-variable quantum phase spaces, explaining how the latter two can be understood as limiting cases of the first. We extend the limit-taking procedures used to travel between phase spaces to a general class of Hamiltonians (including many local stabilizer codes) and provide six examples: the Harper equation, the Baxter parafermionic spin chain, the Rabi model, the Kitaev toric code, the Haah cubic code (which we generalize to qudits), and the Kitaev honeycomb model. We obtain continuous-variable generalizations of all models, some of which are novel. The Baxter model is mapped to a chain of coupled oscillators and the Rabi model to the optomechanical radiation pressure Hamiltonian. The procedures also yield rotor versions of all models, five of which are novel many-body extensions of the almost Mathieu equation. The toric and cubic codes are mapped to lattice models of rotors, with the toric code case related to U(1) lattice gauge theory.

Groundwater flow and heat transport for systems undergoing freeze-thaw: Intercomparison of numerical simulators for 2D test cases

NASA Astrophysics Data System (ADS)

Grenier, Christophe; Anbergen, Hauke; Bense, Victor; Chanzy, Quentin; Coon, Ethan; Collier, Nathaniel; Costard, François; Ferry, Michel; Frampton, Andrew; Frederick, Jennifer; Gonçalvès, Julio; Holmén, Johann; Jost, Anne; Kokh, Samuel; Kurylyk, Barret; McKenzie, Jeffrey; Molson, John; Mouche, Emmanuel; Orgogozo, Laurent; Pannetier, Romain; Rivière, Agnès; Roux, Nicolas; Rühaak, Wolfram; Scheidegger, Johanna; Selroos, Jan-Olof; Therrien, René; Vidstrand, Patrik; Voss, Clifford

2018-04-01

In high-elevation, boreal and arctic regions, hydrological processes and associated water bodies can be strongly influenced by the distribution of permafrost. Recent field and modeling studies indicate that a fully-coupled multidimensional thermo-hydraulic approach is required to accurately model the evolution of these permafrost-impacted landscapes and groundwater systems. However, the relatively new and complex numerical codes being developed for coupled non-linear freeze-thaw systems require verification. This issue is addressed by means of an intercomparison of thirteen numerical codes for two-dimensional test cases with several performance metrics (PMs). These codes comprise a wide range of numerical approaches, spatial and temporal discretization strategies, and computational efficiencies. Results suggest that the codes provide robust results for the test cases considered and that minor discrepancies are explained by computational precision. However, larger discrepancies are observed for some PMs resulting from differences in the governing equations, discretization issues, or in the freezing curve used by some codes.

Recovery Act. Development and Validation of an Advanced Stimulation Prediction Model for Enhanced Geothermal System

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gutierrez, Marte

The research project aims to develop and validate an advanced computer model that can be used in the planning and design of stimulation techniques to create engineered reservoirs for Enhanced Geothermal Systems. The specific objectives of the proposal are to: 1) Develop a true three-dimensional hydro-thermal fracturing simulator that is particularly suited for EGS reservoir creation. 2) Perform laboratory scale model tests of hydraulic fracturing and proppant flow/transport using a polyaxial loading device, and use the laboratory results to test and validate the 3D simulator. 3) Perform discrete element/particulate modeling of proppant transport in hydraulic fractures, and use the resultsmore » to improve understand of proppant flow and transport. 4) Test and validate the 3D hydro-thermal fracturing simulator against case histories of EGS energy production. 5) Develop a plan to commercialize the 3D fracturing and proppant flow/transport simulator. The project is expected to yield several specific results and benefits. Major technical products from the proposal include: 1) A true-3D hydro-thermal fracturing computer code that is particularly suited to EGS, 2) Documented results of scale model tests on hydro-thermal fracturing and fracture propping in an analogue crystalline rock, 3) Documented procedures and results of discrete element/particulate modeling of flow and transport of proppants for EGS applications, and 4) Database of monitoring data, with focus of Acoustic Emissions (AE) from lab scale modeling and field case histories of EGS reservoir creation.« less

3D DEM analyses of the 1963 Vajont rock slide

NASA Astrophysics Data System (ADS)

Boon, Chia Weng; Houlsby, Guy; Utili, Stefano

2013-04-01

The 1963 Vajont rock slide has been modelled using the distinct element method (DEM). The open-source DEM code, YADE (Kozicki & Donzé, 2008), was used together with the contact detection algorithm proposed by Boon et al. (2012). The critical sliding friction angle at the slide surface was sought using a strength reduction approach. A shear-softening contact model was used to model the shear resistance of the clayey layer at the slide surface. The results suggest that the critical sliding friction angle can be conservative if stability analyses are calculated based on the peak friction angles. The water table was assumed to be horizontal and the pore pressure at the clay layer was assumed to be hydrostatic. The influence of reservoir filling was marginal, increasing the sliding friction angle by only 1.6˚. The results of the DEM calculations were found to be sensitive to the orientations of the bedding planes and cross-joints. Finally, the failure mechanism was investigated and arching was found to be present at the bend of the chair-shaped slope. References Boon C.W., Houlsby G.T., Utili S. (2012). A new algorithm for contact detection between convex polygonal and polyhedral particles in the discrete element method. Computers and Geotechnics, vol 44, 73-82, doi.org/10.1016/j.compgeo.2012.03.012. Kozicki, J., & Donzé, F. V. (2008). A new open-source software developed for numerical simulations using discrete modeling methods. Computer Methods in Applied Mechanics and Engineering, 197(49-50), 4429-4443.

Recovery Act. Development and Validation of an Advanced Stimulation Prediction Model for Enhanced Geothermal Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gutierrez, Marte

2013-12-31

This research project aims to develop and validate an advanced computer model that can be used in the planning and design of stimulation techniques to create engineered reservoirs for Enhanced Geothermal Systems. The specific objectives of the proposal are to; Develop a true three-dimensional hydro-thermal fracturing simulator that is particularly suited for EGS reservoir creation; Perform laboratory scale model tests of hydraulic fracturing and proppant flow/transport using a polyaxial loading device, and use the laboratory results to test and validate the 3D simulator; Perform discrete element/particulate modeling of proppant transport in hydraulic fractures, and use the results to improve understandmore » of proppant flow and transport; Test and validate the 3D hydro-thermal fracturing simulator against case histories of EGS energy production; and Develop a plan to commercialize the 3D fracturing and proppant flow/transport simulator. The project is expected to yield several specific results and benefits. Major technical products from the proposal include; A true-3D hydro-thermal fracturing computer code that is particularly suited to EGS; Documented results of scale model tests on hydro-thermal fracturing and fracture propping in an analogue crystalline rock; Documented procedures and results of discrete element/particulate modeling of flow and transport of proppants for EGS applications; and Database of monitoring data, with focus of Acoustic Emissions (AE) from lab scale modeling and field case histories of EGS reservoir creation.« less

Finite element generation of arbitrary 3-D fracture networks for flow analysis in complicated discrete fracture networks

NASA Astrophysics Data System (ADS)

Zhang, Qi-Hua

2015-10-01

Finite element generation of complicated fracture networks is the core issue and source of technical difficulty in three-dimensional (3-D) discrete fracture network (DFN) flow models. Due to the randomness and uncertainty in the configuration of a DFN, the intersection lines (traces) are arbitrarily distributed in each face (fracture and other surfaces). Hence, subdivision of the fractures is an issue relating to subdivision of two-dimensional (2-D) domains with arbitrarily-distributed constraints. When the DFN configuration is very complicated, the well-known approaches (e.g. Voronoi Delaunay-based methods and advancing-front techniques) cannot operate properly. This paper proposes an algorithm to implement end-to-end connection between traces to subdivide 2-D domains into closed loops. The compositions of the vertices in the common edges between adjacent loops (which may belong to a single fracture or two connected fractures) are thus ensured to be topologically identical. The paper then proposes an approach for triangulating arbitrary loops which does not add any nodes to ensure consistency of the meshes at the common edges. In addition, several techniques relating to tolerance control and improving code robustness are discussed. Finally, the equivalent permeability of the rock mass is calculated for some very complicated DFNs (the DFN may contain 1272 fractures, 633 connected fractures, and 16,270 closed loops). The results are compared with other approaches to demonstrate the veracity and efficiency of the approach proposed in this paper.

New formulation of the discrete element method

NASA Astrophysics Data System (ADS)

Rojek, Jerzy; Zubelewicz, Aleksander; Madan, Nikhil; Nosewicz, Szymon

2018-01-01

A new original formulation of the discrete element method based on the soft contact approach is presented in this work. The standard DEM has heen enhanced by the introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. A simple example of a uniaxial compression of a rectangular specimen, discreti.zed with equal sized particles is simulated to verify the DDEM algorithm. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly. A quantitative study of micro-macro elastic properties proves the enhanced capabilities of the DDEM as compared to standard DEM.

Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Helenbrook, B. T.

2005-01-01

This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

Modelling Dowel Action of Discrete Reinforcing Bars in Cracked Concrete Structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kwan, A. K. H.; Ng, P. L.; Lam, J. Y. K.

2010-05-21

Dowel action is one of the component actions for shear force transfer in cracked reinforced concrete. In finite element analysis of concrete structures, the use of discrete representation of reinforcing bars is considered advantageous over the smeared representation due to the relative ease of modelling the bond-slip behaviour. However, there is very limited research on how to simulate the dowel action of discrete reinforcing bars. Herein, a numerical model for dowel action of discrete reinforcing bars crossing cracks in concrete is developed. The model features the derivation of dowel stiffness matrix based on beam-on-elastic-foundation theory and the direct assemblage ofmore » dowel stiffness into the concrete element stiffness matrices. The dowel action model is incorporated in a nonlinear finite element programme with secant stiffness formulation. Deep beams tested in the literature are analysed and it is found that the incorporation of dowel action model improves the accuracy of analysis.« less

A multigrid solver for the semiconductor equations

NASA Technical Reports Server (NTRS)

Bachmann, Bernhard

1993-01-01

We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.

From 2D to 3D modelling in long term tectonics: Modelling challenges and HPC solutions (Invited)

NASA Astrophysics Data System (ADS)

Le Pourhiet, L.; May, D.

2013-12-01

Over the last decades, 3D thermo-mechanical codes have been made available to the long term tectonics community either as open source (Underworld, Gale) or more limited access (Fantom, Elvis3D, Douar, LaMem etc ...). However, to date, few published results using these methods have included the coupling between crustal and lithospheric dynamics at large strain. The fact that these computations are computational expensive is not the primary reason for the relatively slow development of 3D modeling in the long term tectonics community, as compare to the rapid development observed within the mantle dynamic community, or in the short-term tectonics field. Long term tectonics problems have specific issues not found in either of these two field, including; large strain (not an issue for short-term), the inclusion of free surface and the occurence of large viscosity contrasts. The first issue is typically eliminated using a combined marker-ALE method instead of fully lagrangian method, however, the marker-ALE approach can pose some algorithmic challenges in a massively parallel environment. The two last issues are more problematic because they affect the convergence of the linear/non-linear solver and the memory cost. Two options have been tested so far, using low order element and solving with a sparse direct solver, or using higher order stable elements together with a multi-grid solver. The first options, is simpler to code and to use but reaches its limit at around 80^3 low order elements. The second option requires more operations but allows using iterative solver on extremely large computers. In this presentation, I will describe the design philosophy and highlight results obtained using a code from the second-class method. The presentation will be oriented from an end-user point of view, using an application from 3D continental break up to illustrate key concepts. The description will proceed point by point from implementing physics into the code, to dealing with specific issues related to solving the discrete system of non linear equations.

Spiral waves are stable in discrete element models of two-dimensional homogeneous excitable media

NASA Technical Reports Server (NTRS)

Feldman, A. B.; Chernyak, Y. B.; Cohen, R. J.

1998-01-01

The spontaneous breakup of a single spiral wave of excitation into a turbulent wave pattern has been observed in both discrete element models and continuous reaction-diffusion models of spatially homogeneous 2D excitable media. These results have attracted considerable interest, since spiral breakup is thought to be an important mechanism of transition from the heart rhythm disturbance ventricular tachycardia to the fatal arrhythmia ventricular fibrillation. It is not known whether this process can occur in the absence of disease-induced spatial heterogeneity of the electrical properties of the ventricular tissue. Candidate mechanisms for spiral breakup in uniform 2D media have emerged, but the physical validity of the mechanisms and their applicability to myocardium require further scrutiny. In this letter, we examine the computer simulation results obtained in two discrete element models and show that the instability of each spiral is an artifact resulting from an unphysical dependence of wave speed on wave front curvature in the medium. We conclude that spiral breakup does not occur in these two models at the specified parameter values and that great care must be exercised in the representation of a continuous excitable medium via discrete elements.

A discrete element model for the investigation of the geometrically nonlinear behaviour of solids

NASA Astrophysics Data System (ADS)

Ockelmann, Felix; Dinkler, Dieter

2018-07-01

A three-dimensional discrete element model for elastic solids with large deformations is presented. Therefore, an discontinuum approach is made for solids. The properties of elastic material are transferred analytically into the parameters of a discrete element model. A new and improved octahedron gap-filled face-centred cubic close packing of spheres is split into unit cells, to determine the parameters of the discrete element model. The symmetrical unit cells allow a model with equal shear components in each contact plane and fully isotropic behaviour for Poisson's ratio above 0. To validate and show the broad field of applications of the new model, the pin-pin Euler elastica is presented and investigated. The thin and sensitive structure tends to undergo large deformations and rotations with a highly geometrically nonlinear behaviour. This behaviour of the elastica can be modelled and is compared to reference solutions. Afterwards, an improved more realistic simulation of the elastica is presented which softens secondary buckling phenomena. The model is capable of simulating solids with small strains but large deformations and a strongly geometrically nonlinear behaviour, taking the shear stiffness of the material into account correctly.

7 CFR 1753.80 - Minor construction procedure.

Code of Federal Regulations, 2010 CFR

2010-01-01

... same calendar year is limited to the following amounts for the following discrete categories of minor...) A single minor construction project may be a discrete element of a somewhat larger overall project... placement project. It cannot be a portion, by dividing into smaller segments, of a discrete major...

Application of the control volume mixed finite element method to a triangular discretization

USGS Publications Warehouse

Naff, R.L.

2012-01-01

A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.

An efficient code for the simulation of nonhydrostatic stratified flow over obstacles

NASA Technical Reports Server (NTRS)

Pihos, G. G.; Wurtele, M. G.

1981-01-01

The physical model and computational procedure of the code is described in detail. The code is validated in tests against a variety of known analytical solutions from the literature and is also compared against actual mountain wave observations. The code will receive as initial input either mathematically idealized or discrete observational data. The form of the obstacle or mountain is arbitrary.

SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.

1999-03-01

This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples ofmore » the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.« less

A three-dimensional FEM-DEM technique for predicting the evolution of fracture in geomaterials and concrete

NASA Astrophysics Data System (ADS)

Zárate, Francisco; Cornejo, Alejandro; Oñate, Eugenio

2018-07-01

This paper extends to three dimensions (3D), the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element mesh in a simple manner based on combining the finite element method and the discrete element method (DEM) approach (Zárate and Oñate in Comput Part Mech 2(3):301-314, 2015). Once a crack is detected at an element edge, discrete elements are generated at the adjacent element vertexes and a simple DEM mechanism is considered in order to follow the evolution of the crack. The combination of the DEM with simple four-noded linear tetrahedron elements correctly captures the onset of fracture and its evolution, as shown in several 3D examples of application.

A comprehensive study of MPI parallelism in three-dimensional discrete element method (DEM) simulation of complex-shaped granular particles

NASA Astrophysics Data System (ADS)

Yan, Beichuan; Regueiro, Richard A.

2018-02-01

A three-dimensional (3D) DEM code for simulating complex-shaped granular particles is parallelized using message-passing interface (MPI). The concepts of link-block, ghost/border layer, and migration layer are put forward for design of the parallel algorithm, and theoretical scalability function of 3-D DEM scalability and memory usage is derived. Many performance-critical implementation details are managed optimally to achieve high performance and scalability, such as: minimizing communication overhead, maintaining dynamic load balance, handling particle migrations across block borders, transmitting C++ dynamic objects of particles between MPI processes efficiently, eliminating redundant contact information between adjacent MPI processes. The code executes on multiple US Department of Defense (DoD) supercomputers and tests up to 2048 compute nodes for simulating 10 million three-axis ellipsoidal particles. Performance analyses of the code including speedup, efficiency, scalability, and granularity across five orders of magnitude of simulation scale (number of particles) are provided, and they demonstrate high speedup and excellent scalability. It is also discovered that communication time is a decreasing function of the number of compute nodes in strong scaling measurements. The code's capability of simulating a large number of complex-shaped particles on modern supercomputers will be of value in both laboratory studies on micromechanical properties of granular materials and many realistic engineering applications involving granular materials.

Coupling extended magnetohydrodynamic fluid codes with radiofrequency ray tracing codes for fusion modeling

NASA Astrophysics Data System (ADS)

Jenkins, Thomas G.; Held, Eric D.

2015-09-01

Neoclassical tearing modes are macroscopic (L ∼ 1 m) instabilities in magnetic fusion experiments; if unchecked, these modes degrade plasma performance and may catastrophically destroy plasma confinement by inducing a disruption. Fortunately, the use of properly tuned and directed radiofrequency waves (λ ∼ 1 mm) can eliminate these modes. Numerical modeling of this difficult multiscale problem requires the integration of separate mathematical models for each length and time scale (Jenkins and Kruger, 2012 [21]); the extended MHD model captures macroscopic plasma evolution while the RF model tracks the flow and deposition of injected RF power through the evolving plasma profiles. The scale separation enables use of the eikonal (ray-tracing) approximation to model the RF wave propagation. In this work we demonstrate a technique, based on methods of computational geometry, for mapping the ensuing RF data (associated with discrete ray trajectories) onto the finite-element/pseudospectral grid that is used to model the extended MHD physics. In the new representation, the RF data can then be used to construct source terms in the equations of the extended MHD model, enabling quantitative modeling of RF-induced tearing mode stabilization. Though our specific implementation uses the NIMROD extended MHD (Sovinec et al., 2004 [22]) and GENRAY RF (Smirnov et al., 1994 [23]) codes, the approach presented can be applied more generally to any code coupling requiring the mapping of ray tracing data onto Eulerian grids.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin method for the Biot’s consolidation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity

NASA Astrophysics Data System (ADS)

Lin, Guang; Liu, Jiangguo; Mu, Lin; Ye, Xiu

2014-11-01

This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy flow computation. The WGFEMs are new numerical methods that rely on the novel concept of discrete weak gradients. The WGFEMs solve for pressure unknowns both in element interiors and on the mesh skeleton. The numerical velocity is then obtained from the discrete weak gradient of the numerical pressure. The new methods are quite different than many existing numerical methods in that they are locally conservative by design, the resulting discrete linear systems are symmetric and positive-definite, and there is no need for tuning problem-dependent penalty factors. We test the WGFEMs on benchmark problems to demonstrate the strong potential of these new methods in handling strong anisotropy and heterogeneity in Darcy flow.

Domain decomposition for a mixed finite element method in three dimensions

USGS Publications Warehouse

Cai, Z.; Parashkevov, R.R.; Russell, T.F.; Wilson, J.D.; Ye, X.

2003-01-01

We consider the solution of the discrete linear system resulting from a mixed finite element discretization applied to a second-order elliptic boundary value problem in three dimensions. Based on a decomposition of the velocity space, these equations can be reduced to a discrete elliptic problem by eliminating the pressure through the use of substructures of the domain. The practicality of the reduction relies on a local basis, presented here, for the divergence-free subspace of the velocity space. We consider additive and multiplicative domain decomposition methods for solving the reduced elliptic problem, and their uniform convergence is established.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.

A two-dimensional hydrodynamic model of the St. Clair-Detroit River waterway in the Great Lakes basin

USGS Publications Warehouse

Holtschlag, David J.; Koschik, John A.

2002-01-01

The St. Clair–Detroit River Waterway connects Lake Huron with Lake Erie in the Great Lakes basin to form part of the international boundary between the United States and Canada. A two-dimensional hydrodynamic model is developed to compute flow velocities and water levels as part of a source-water assessment of public water intakes. The model, which uses the generalized finite-element code RMA2, discretizes the waterway into a mesh formed by 13,783 quadratic elements defined by 42,936 nodes. Seven steadystate scenarios are used to calibrate the model by adjusting parameters associated with channel roughness in 25 material zones in sub-areas of the waterway. An inverse modeling code is used to systematically adjust model parameters and to determine their associated uncertainty by use of nonlinear regression. Calibration results show close agreement between simulated and expected flows in major channels and water levels at gaging stations. Sensitivity analyses describe the amount of information available to estimate individual model parameters, and quantify the utility of flow measurements at selected cross sections and water-level measurements at gaging stations. Further data collection, model calibration analysis, and grid refinements are planned to assess and enhance two-dimensional flow simulation capabilities describing the horizontal flow distributions in St. Clair and Detroit Rivers and circulation patterns in Lake St. Clair.

Characteristics of Creep Damage for 60Sn-40Pb Solder Material

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wei, Y.; Chow, C.L.; Fang, H.E.

This paper presents a viscoplasticity model taking into account the effects of change in grain or phase size and damage on the characterization of creep damage in 60Sn-40Pb solder. Based on the theory of damage mechanics, a two-scalar damage model is developed for isotropic materials by introducing the free energy equivalence principle. The damage evolution equations are derived in terms of the damage energy release rates. In addition, a failure criterion is developed based on the postulation that a material element is said to have ruptured when the total damage accumulated in the element reaches a critical value. The damagemore » coupled viscoplasticity model is discretized and coded in a general-purpose finite element program known as ABAQUS through its user-defined material subroutine UMAT. To illustrate the application of the model, several example cases are introduced to analyze, both numerically and experimentally, the tensile creep behaviors of the material at three stress levels. The model is then applied to predict the deformation of a notched specimen under monotonic tension at room temperature (22 C). The results demonstrate that the proposed model can successfully predict the viscoplastic behavior of the solder material.« less

Energy harvesting devices, systems, and related methods

DOEpatents

Kotter, Dale K.

2016-10-18

Energy harvesting devices include a substrate and a plurality of resonance elements coupled to the substrate. Each resonance element is configured to collect energy in the visible and infrared light spectra and to reradiate energy having a wavelength in the range of about 0.8 .mu.m to about 0.9 .mu.m. The resonance elements are arranged in groups of two or more resonance elements. Systems for harvesting electromagnetic radiation include a substrate, a plurality of resonance elements including a conductive material carried by the substrate, and a photovoltaic material coupled to the substrate and to at least one resonance element. The resonance elements are arranged in groups, such as in a dipole, a tripole, or a bowtie configuration. Methods for forming an energy harvesting device include forming groups of two or more discrete resonance elements in a substrate and coupling a photovoltaic material to the groups of discrete resonance elements.

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, Peter G., E-mail: maginot1@llnl.gov; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim E., E-mail: morel@tamu.edu

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-09-29

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

Discontinuous finite volume element discretization for coupled flow-transport problems arising in models of sedimentation

NASA Astrophysics Data System (ADS)

Bürger, Raimund; Kumar, Sarvesh; Ruiz-Baier, Ricardo

2015-10-01

The sedimentation-consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the Stokes problem written in terms of the mixture flow velocity and the pressure field. Here both the viscosity and the forcing term depend on the local solids concentration. A semi-discrete discontinuous finite volume element (DFVE) scheme is proposed for this model. The numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field, whereas the pressure is approximated by piecewise constant elements. The unique solvability of both the nonlinear continuous problem and the semi-discrete DFVE scheme is discussed, and optimal convergence estimates in several spatial norms are derived. Properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples, including flows under gravity with changing direction, a secondary settling tank in an axisymmetric setting, and batch sedimentation in a tilted cylindrical vessel.

Coupled NASTRAN/boundary element formulation for acoustic scattering

NASA Technical Reports Server (NTRS)

Everstine, Gordon C.; Henderson, Francis M.; Schuetz, Luise S.

1987-01-01

A coupled finite element/boundary element capability is described for calculating the sound pressure field scattered by an arbitrary submerged 3-D elastic structure. Structural and fluid impedances are calculated with no approximation other than discretization. The surface fluid pressures and normal velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior field. Far field pressures are then evaluated from the surface solution using the Helmholtz exterior integral equation. The overall approach is illustrated and validated using a known analytic solution for scattering from submerged spherical shells.

Institutional Controls and Educational Research.

ERIC Educational Resources Information Center

Homan, Roger

1990-01-01

Recognizing tendencies toward contract research and possible consequences, advocates creating a conduct code to regulate educational research and protect its integrity. Reports survey responses from 48 British institutions, showing no systematic code. States confidence in supervisory discretion currently guides research. Proposes a specific code…

Evaluation of new techniques for the calculation of internal recirculating flows

NASA Technical Reports Server (NTRS)

Van Doormaal, J. P.; Turan, A.; Raithby, G. D.

1987-01-01

The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This paper evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH code, that has been widely applied to combustor flows, illustrates the substantial gains that can be achieved.

Application of the Finite Element Method to Rotary Wing Aeroelasticity

NASA Technical Reports Server (NTRS)

Straub, F. K.; Friedmann, P. P.

1982-01-01

A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.

Numerical analysis of the three-dimensional swirling flow in centrifugal compressor volutes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ayder, E.; Van den Braembussche, R.

1994-07-01

The improvement of centrifugal compressor performance and the control of the radial forces acting on the impeller due to the circumferential variation of the static pressure caused by the volute require a good understanding of the flow mechanisms and an accurate prediction of the flow pattern inside the volute. A three-dimensional volute calculation method has been developed for this purpose. The volute is discretized by means of hexahedral elements. A cell vertex finite volume approach is used in combination with a time-marching procedure. The numerical procedure makes use of a central space discretization and a four-step Runge-Kutta time-stepping scheme. Themore » artificial dissipation used in the solver is based on the fourth-order differences of the conservative variables. Implicit residual smoothing improves the convergence rate. The loss model implemented in the code accounts for the losses due to internal shear and friction losses on the walls. A comparison of the calculated and measured results inside a volute with elliptical cross section reveals that the modified Euler solver accurately predicts the velocity and pressure distribution inside and upstream of the volute.« less

CMOS Imaging of Pin-Printed Xerogel-Based Luminescent Sensor Microarrays.

PubMed

Yao, Lei; Yung, Ka Yi; Khan, Rifat; Chodavarapu, Vamsy P; Bright, Frank V

2010-12-01

We present the design and implementation of a luminescence-based miniaturized multisensor system using pin-printed xerogel materials which act as host media for chemical recognition elements. We developed a CMOS imager integrated circuit (IC) to image the luminescence response of the xerogel-based sensor array. The imager IC uses a 26 × 20 (520 elements) array of active pixel sensors and each active pixel includes a high-gain phototransistor to convert the detected optical signals into electrical currents. The imager includes a correlated double sampling circuit and pixel address/digital control circuit; the image data is read-out as coded serial signal. The sensor system uses a light-emitting diode (LED) to excite the target analyte responsive luminophores doped within discrete xerogel-based sensor elements. As a prototype, we developed a 4 × 4 (16 elements) array of oxygen (O 2 ) sensors. Each group of 4 sensor elements in the array (arranged in a row) is designed to provide a different and specific sensitivity to the target gaseous O 2 concentration. This property of multiple sensitivities is achieved by using a strategic mix of two oxygen sensitive luminophores ([Ru(dpp) 3 ] 2+ and ([Ru(bpy) 3 ] 2+ ) in each pin-printed xerogel sensor element. The CMOS imager consumes an average power of 8 mW operating at 1 kHz sampling frequency driven at 5 V. The developed prototype system demonstrates a low cost and miniaturized luminescence multisensor system.

Latent hardening size effect in small-scale plasticity

NASA Astrophysics Data System (ADS)

Bardella, Lorenzo; Segurado, Javier; Panteghini, Andrea; Llorca, Javier

2013-07-01

We aim at understanding the multislip behaviour of metals subject to irreversible deformations at small-scales. By focusing on the simple shear of a constrained single-crystal strip, we show that discrete Dislocation Dynamics (DD) simulations predict a strong latent hardening size effect, with smaller being stronger in the range [1.5 µm, 6 µm] for the strip height. We attempt to represent the DD pseudo-experimental results by developing a flow theory of Strain Gradient Crystal Plasticity (SGCP), involving both energetic and dissipative higher-order terms and, as a main novelty, a strain gradient extension of the conventional latent hardening. In order to discuss the capability of the SGCP theory proposed, we implement it into a Finite Element (FE) code and set its material parameters on the basis of the DD results. The SGCP FE code is specifically developed for the boundary value problem under study so that we can implement a fully implicit (Backward Euler) consistent algorithm. Special emphasis is placed on the discussion of the role of the material length scales involved in the SGCP model, from both the mechanical and numerical points of view.

Dislocation mechanisms in stressed crystals with surface effects

NASA Astrophysics Data System (ADS)

Wu, Chi-Chin; Crone, Joshua; Munday, Lynn; Discrete Dislocation Dynamics Team

2014-03-01

Understanding dislocation properties in stressed crystals is the key for important processes in materials science, including the strengthening of metals and the stress relaxation during the growth of hetero-epitaxial structures. Despite existing experimental approaches and theories, many dislocation mechanisms with surface effects still remain elusive in experiments. Even though discrete dislocation dynamics (DDD) simulations are commonly employed to study dislocations, few demonstrate sufficient computational capabilities for massive dislocations with the combined effects of surfaces and stresses. Utilizing the Army's newly developed FED3 code, a DDD computation code coupled with finite elements, this work presents several dislocation mechanisms near different types of surfaces in finite domains. Our simulation models include dislocations in a bended metallic cantilever beam, near voids in stressed metals, as well as threading and misfit dislocations in as-grown semiconductor epitaxial layers and their quantitative inter-correlations to stress relaxation and surface instability. Our studies provide not only detailed physics of individual dislocation mechanisms, but also important collective dislocation properties such as dislocation densities and strain-stress profiles and their interactions with surfaces.

Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Guang; Liu, Jiangguo; Mu, Lin

2014-11-01

This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy flow computation. The WGFEMs are new numerical methods that rely on the novel concept of discrete weak gradients. The WGFEMs solve for pressure unknowns both in element interiors and on the mesh skeleton. The numerical velocity is then obtained from the discrete weak gradient of the numerical pressure. The new methods are quite different than many existing numerical methods in that they are locally conservative by design, the resulting discrete linear systems are symmetric and positive-definite, and there is no need for tuning problem-dependent penalty factors.more » We test the WGFEMs on benchmark problems to demonstrate the strong potential of these new methods in handling strong anisotropy and heterogeneity in Darcy flow.« less

An upwind multigrid method for solving viscous flows on unstructured triangular meshes. M.S. Thesis

NASA Technical Reports Server (NTRS)

Bonhaus, Daryl Lawrence

1993-01-01

A multigrid algorithm is combined with an upwind scheme for solving the two dimensional Reynolds averaged Navier-Stokes equations on triangular meshes resulting in an efficient, accurate code for solving complex flows around multiple bodies. The relaxation scheme uses a backward-Euler time difference and relaxes the resulting linear system using a red-black procedure. Roe's flux-splitting scheme is used to discretize convective and pressure terms, while a central difference is used for the diffusive terms. The multigrid scheme is demonstrated for several flows around single and multi-element airfoils, including inviscid, laminar, and turbulent flows. The results show an appreciable speed up of the scheme for inviscid and laminar flows, and dramatic increases in efficiency for turbulent cases, especially those on increasingly refined grids.

One-dimensional statistical parametric mapping in Python.

PubMed

Pataky, Todd C

2012-01-01

Statistical parametric mapping (SPM) is a topological methodology for detecting field changes in smooth n-dimensional continua. Many classes of biomechanical data are smooth and contained within discrete bounds and as such are well suited to SPM analyses. The current paper accompanies release of 'SPM1D', a free and open-source Python package for conducting SPM analyses on a set of registered 1D curves. Three example applications are presented: (i) kinematics, (ii) ground reaction forces and (iii) contact pressure distribution in probabilistic finite element modelling. In addition to offering a high-level interface to a variety of common statistical tests like t tests, regression and ANOVA, SPM1D also emphasises fundamental concepts of SPM theory through stand-alone example scripts. Source code and documentation are available at: www.tpataky.net/spm1d/.

Development of an integrated BEM for hot fluid-structure interaction

NASA Technical Reports Server (NTRS)

Banerjee, P. K.; Dargush, G. F.

1989-01-01

The Boundary Element Method (BEM) is chosen as a basic analysis tool principally because the definition of quantities like fluxes, temperature, displacements, and velocities is very precise on a boundary base discretization scheme. One fundamental difficulty is, of course, that the entire analysis requires a very considerable amount of analytical work which is not present in other numerical methods. During the last 18 months all of this analytical work was completed and a two-dimensional, general purpose code was written. Some of the early results are described. It is anticipated that within the next two to three months almost all two-dimensional idealizations will be examined. It should be noted that the analytical work for the three-dimensional case has also been done and numerical implementation will begin next year.

Motion of dust particles in nonuniform magnetic field and applicability of smoothed particle hydrodynamics simulation

NASA Astrophysics Data System (ADS)

Saitou, Y.

2018-01-01

An SPH (Smoothed Particle Hydrodynamics) simulation code is developed to reproduce our findings on behavior of dust particles, which were obtained in our previous experiments (Phys. Plasmas, 23, 013709 (2016) and Abst. 18th Intern. Cong. Plasma Phys. (Kaohsiung, 2016)). Usually, in an SPH simulation, a smoothed particle is interpreted as a discretized fluid element. Here we regard the particles as dust particles because it is known that behavior of dust particles in complex plasmas can be described using fluid dynamics equations in many cases. Various rotation velocities that are difficult to achieve in the experiment are given to particles at boundaries in the newly developed simulation and motion of particles is investigated. Preliminary results obtained by the simulation are shown.

Discontinuous Finite Element Quasidiffusion Methods

DOE PAGES

Anistratov, Dmitriy Yurievich; Warsa, James S.

2018-05-21

Here in this paper, two-level methods for solving transport problems in one-dimensional slab geometry based on the quasi-diffusion (QD) method are developed. A linear discontinuous finite element method (LDFEM) is derived for the spatial discretization of the low-order QD (LOQD) equations. It involves special interface conditions at the cell edges based on the idea of QD boundary conditions (BCs). We consider different kinds of QD BCs to formulate the necessary cell-interface conditions. We develop two-level methods with independent discretization of the high-order transport equation and LOQD equations, where the transport equation is discretized using the method of characteristics and themore » LDFEM is applied to the LOQD equations. We also formulate closures that lead to the discretization consistent with a LDFEM discretization of the transport equation. The proposed methods are studied by means of test problems formulated with the method of manufactured solutions. Numerical experiments are presented demonstrating the performance of the proposed methods. Lastly, we also show that the method with independent discretization has the asymptotic diffusion limit.« less

Discontinuous Finite Element Quasidiffusion Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anistratov, Dmitriy Yurievich; Warsa, James S.

Here in this paper, two-level methods for solving transport problems in one-dimensional slab geometry based on the quasi-diffusion (QD) method are developed. A linear discontinuous finite element method (LDFEM) is derived for the spatial discretization of the low-order QD (LOQD) equations. It involves special interface conditions at the cell edges based on the idea of QD boundary conditions (BCs). We consider different kinds of QD BCs to formulate the necessary cell-interface conditions. We develop two-level methods with independent discretization of the high-order transport equation and LOQD equations, where the transport equation is discretized using the method of characteristics and themore » LDFEM is applied to the LOQD equations. We also formulate closures that lead to the discretization consistent with a LDFEM discretization of the transport equation. The proposed methods are studied by means of test problems formulated with the method of manufactured solutions. Numerical experiments are presented demonstrating the performance of the proposed methods. Lastly, we also show that the method with independent discretization has the asymptotic diffusion limit.« less

Higher-Order Advection-Based Remap of Magnetic Fields in an Arbitrary Lagrangian-Eulerian Code

NASA Astrophysics Data System (ADS)

Cornille, Brian; White, Dan

2017-10-01

We will present methods formulated for the Eulerian advection stage of an arbitrary Lagrangian-Eulerian code for the new addition of magnetohydrodynamic (MHD) effects. The various physical fields are advanced in time using a Lagrangian formulation of the system. When this Lagrangian motion produces substantial distortion of the mesh, it can be difficult or impossible to progress the simulation forward. This is overcome by relaxation of the mesh while the physical fields are frozen. The code has already successfully been extended to include evolution of magnetic field diffusion during the Lagrangian motion stage. This magnetic field is discretized using an H(div) compatible finite element basis. The advantage of this basis is that the divergence-free constraint of magnetic fields is maintained exactly during the Lagrangian motion evolution. Our goal is to preserve this property during Eulerian advection as well. We will demonstrate this property and the importance of MHD effects in several numerical experiments. In pulsed-power experiments magnetic fields may be imposed or spontaneously generated. When these magnetic fields are present, the evolution of the experiment may differ from a comparable configuration without magnetic fields. Prepared by LLNL under Contract DE-AC52-07NA27344. Supported by DOE CSGF under Grant Number DE-FG02-97ER25308.

Salvus: A flexible open-source package for waveform modelling and inversion from laboratory to global scales

NASA Astrophysics Data System (ADS)

Afanasiev, M.; Boehm, C.; van Driel, M.; Krischer, L.; May, D.; Rietmann, M.; Fichtner, A.

2016-12-01

Recent years have been witness to the application of waveform inversion to new and exciting domains, ranging from non-destructive testing to global seismology. Often, each new application brings with it novel wave propagation physics, spatial and temporal discretizations, and models of variable complexity. Adapting existing software to these novel applications often requires a significant investment of time, and acts as a barrier to progress. To combat these problems we introduce Salvus, a software package designed to solve large-scale full-waveform inverse problems, with a focus on both flexibility and performance. Based on a high order finite (spectral) element discretization, we have built Salvus to work on unstructured quad/hex meshes in both 2 or 3 dimensions, with support for P1-P3 bases on triangles and tetrahedra. A diverse (and expanding) collection of wave propagation physics are supported (i.e. coupled solid-fluid). With a focus on the inverse problem, functionality is provided to ease integration with internal and external optimization libraries. Additionally, a python-based meshing package is included to simplify the generation and manipulation of regional to global scale Earth models (quad/hex), with interfaces available to external mesh generators for complex engineering-scale applications (quad/hex/tri/tet). Finally, to ensure that the code remains accurate and maintainable, we build upon software libraries such as PETSc and Eigen, and follow modern software design and testing protocols. Salvus bridges the gap between research and production codes with a design based on C++ mixins and Python wrappers that separates the physical equations from the numerical core. This allows domain scientists to add new equations using a high-level interface, without having to worry about optimized implementation details. Our goal in this presentation is to introduce the code, show several examples across the scales, and discuss some of the extensible design points.

Element Verification and Comparison in Sierra/Solid Mechanics Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ohashi, Yuki; Roth, William

2016-05-01

The goal of this project was to study the effects of element selection on the Sierra/SM solutions to five common solid mechanics problems. A total of nine element formulations were used for each problem. The models were run multiple times with varying spatial and temporal discretization in order to ensure convergence. The first four problems have been compared to analytical solutions, and all numerical results were found to be sufficiently accurate. The penetration problem was found to have a high mesh dependence in terms of element type, mesh discretization, and meshing scheme. Also, the time to solution is shown formore » each problem in order to facilitate element selection when computer resources are limited.« less

Characterization of the functional role of nucleotides within the URE2 IRES element and the requirements for eIF2A-mediated repression.

PubMed

Reineke, Lucas C; Merrick, William C

2009-12-01

Cap-independent initiation of translation is thought to promote protein synthesis on some mRNAs during times when cap-dependent initiation is down-regulated. However, the mechanism of cap-independent initiation is poorly understood. We have previously reported the secondary structure within the yeast minimal URE2 IRES element. In this study, we sought to investigate the mechanism of internal initiation in yeast by assessing the functional role of nucleotides within the minimal URE2 IRES element, and delineating the cis-sequences that modulate levels of internal initiation using a monocistronic reporter vector. Furthermore, we compared the eIF2A sensitivity of the URE2 IRES element with some of the invasive growth IRES elements using DeltaeIF2A yeast. We found that the stability of the stem-loop structure within the minimal URE2 IRES element is not a critical determinant of optimal IRES activity, and the downstream sequences that modulate URE2 IRES-mediated translation can be defined to discrete regions within the URE2 coding region. Repression of internal initiation on the URE2 minimal IRES element by eIF2A is not dependent on the stability of the secondary structure within the URE2 IRES element. Our data also indicate that eIF2A-mediated repression is not specific to the URE2 IRES element, as both the GIC1 and PAB1 IRES elements are repressed by eIF2A. These data provide valuable insights into the mRNA requirements for internal initiation in yeast, and insights into the mechanism of eIF2A-mediated suppression.

Space-Time Discrete KPZ Equation

NASA Astrophysics Data System (ADS)

Cannizzaro, G.; Matetski, K.

2018-03-01

We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.

Flexible Automatic Discretization for Finite Differences: Eliminating the Human Factor

NASA Astrophysics Data System (ADS)

Pranger, Casper

2017-04-01

In the geophysical numerical modelling community, finite differences are (in part due to their small footprint) a popular spatial discretization method for PDEs in the regular-shaped continuum that is the earth. However, they rapidly become prone to programming mistakes when physics increase in complexity. To eliminate opportunities for human error, we have designed an automatic discretization algorithm using Wolfram Mathematica, in which the user supplies symbolic PDEs, the number of spatial dimensions, and a choice of symbolic boundary conditions, and the script transforms this information into matrix- and right-hand-side rules ready for use in a C++ code that will accept them. The symbolic PDEs are further used to automatically develop and perform manufactured solution benchmarks, ensuring at all stages physical fidelity while providing pragmatic targets for numerical accuracy. We find that this procedure greatly accelerates code development and provides a great deal of flexibility in ones choice of physics.

Continuous-variable quantum network coding for coherent states

NASA Astrophysics Data System (ADS)

Shang, Tao; Li, Ke; Liu, Jian-wei

2017-04-01

As far as the spectral characteristic of quantum information is concerned, the existing quantum network coding schemes can be looked on as the discrete-variable quantum network coding schemes. Considering the practical advantage of continuous variables, in this paper, we explore two feasible continuous-variable quantum network coding (CVQNC) schemes. Basic operations and CVQNC schemes are both provided. The first scheme is based on Gaussian cloning and ADD/SUB operators and can transmit two coherent states across with a fidelity of 1/2, while the second scheme utilizes continuous-variable quantum teleportation and can transmit two coherent states perfectly. By encoding classical information on quantum states, quantum network coding schemes can be utilized to transmit classical information. Scheme analysis shows that compared with the discrete-variable paradigms, the proposed CVQNC schemes provide better network throughput from the viewpoint of classical information transmission. By modulating the amplitude and phase quadratures of coherent states with classical characters, the first scheme and the second scheme can transmit 4{log _2}N and 2{log _2}N bits of information by a single network use, respectively.

Groundwater flow and heat transport for systems undergoing freeze-thaw: Intercomparison of numerical simulators for 2D test cases

DOE PAGES

Grenier, Christophe; Anbergen, Hauke; Bense, Victor; ...

2018-02-26

In high-elevation, boreal and arctic regions, hydrological processes and associated water bodies can be strongly influenced by the distribution of permafrost. Recent field and modeling studies indicate that a fully-coupled multidimensional thermo-hydraulic approach is required to accurately model the evolution of these permafrost-impacted landscapes and groundwater systems. However, the relatively new and complex numerical codes being developed for coupled non-linear freeze-thaw systems require verification. Here in this paper, this issue is addressed by means of an intercomparison of thirteen numerical codes for two-dimensional test cases with several performance metrics (PMs). These codes comprise a wide range of numerical approaches, spatialmore » and temporal discretization strategies, and computational efficiencies. Results suggest that the codes provide robust results for the test cases considered and that minor discrepancies are explained by computational precision. However, larger discrepancies are observed for some PMs resulting from differences in the governing equations, discretization issues, or in the freezing curve used by some codes.« less

Parallelized direct execution simulation of message-passing parallel programs

NASA Technical Reports Server (NTRS)

Dickens, Phillip M.; Heidelberger, Philip; Nicol, David M.

1994-01-01

As massively parallel computers proliferate, there is growing interest in findings ways by which performance of massively parallel codes can be efficiently predicted. This problem arises in diverse contexts such as parallelizing computers, parallel performance monitoring, and parallel algorithm development. In this paper we describe one solution where one directly executes the application code, but uses a discrete-event simulator to model details of the presumed parallel machine such as operating system and communication network behavior. Because this approach is computationally expensive, we are interested in its own parallelization specifically the parallelization of the discrete-event simulator. We describe methods suitable for parallelized direct execution simulation of message-passing parallel programs, and report on the performance of such a system, Large Application Parallel Simulation Environment (LAPSE), we have built on the Intel Paragon. On all codes measured to date, LAPSE predicts performance well typically within 10 percent relative error. Depending on the nature of the application code, we have observed low slowdowns (relative to natively executing code) and high relative speedups using up to 64 processors.

Groundwater flow and heat transport for systems undergoing freeze-thaw: Intercomparison of numerical simulators for 2D test cases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grenier, Christophe; Anbergen, Hauke; Bense, Victor

In high-elevation, boreal and arctic regions, hydrological processes and associated water bodies can be strongly influenced by the distribution of permafrost. Recent field and modeling studies indicate that a fully-coupled multidimensional thermo-hydraulic approach is required to accurately model the evolution of these permafrost-impacted landscapes and groundwater systems. However, the relatively new and complex numerical codes being developed for coupled non-linear freeze-thaw systems require verification. Here in this paper, this issue is addressed by means of an intercomparison of thirteen numerical codes for two-dimensional test cases with several performance metrics (PMs). These codes comprise a wide range of numerical approaches, spatialmore » and temporal discretization strategies, and computational efficiencies. Results suggest that the codes provide robust results for the test cases considered and that minor discrepancies are explained by computational precision. However, larger discrepancies are observed for some PMs resulting from differences in the governing equations, discretization issues, or in the freezing curve used by some codes.« less

Simulation of 2D Kinetic Effects in Plasmas using the Grid Based Continuum Code LOKI

NASA Astrophysics Data System (ADS)

Banks, Jeffrey; Berger, Richard; Chapman, Tom; Brunner, Stephan

2016-10-01

Kinetic simulation of multi-dimensional plasma waves through direct discretization of the Vlasov equation is a useful tool to study many physical interactions and is particularly attractive for situations where minimal fluctuation levels are desired, for instance, when measuring growth rates of plasma wave instabilities. However, direct discretization of phase space can be computationally expensive, and as a result there are few examples of published results using Vlasov codes in more than a single configuration space dimension. In an effort to fill this gap we have developed the Eulerian-based kinetic code LOKI that evolves the Vlasov-Poisson system in 2+2-dimensional phase space. The code is designed to reduce the cost of phase-space computation by using fully 4th order accurate conservative finite differencing, while retaining excellent parallel scalability that efficiently uses large scale computing resources. In this poster I will discuss the algorithms used in the code as well as some aspects of their parallel implementation using MPI. I will also overview simulation results of basic plasma wave instabilities relevant to laser plasma interaction, which have been obtained using the code.

The inverse of winnowing: a FORTRAN subroutine and discussion of unwinnowing discrete data

USGS Publications Warehouse

Bracken, Robert E.

2004-01-01

This report describes an unwinnowing algorithm that utilizes a discrete Fourier transform, and a resulting Fortran subroutine that winnows or unwinnows a 1-dimensional stream of discrete data; the source code is included. The unwinnowing algorithm effectively increases (by integral factors) the number of available data points while maintaining the original frequency spectrum of a data stream. This has utility when an increased data density is required together with an availability of higher order derivatives that honor the original data.

Engine dynamic analysis with general nonlinear finite element codes. Part 2: Bearing element implementation overall numerical characteristics and benchmaking

NASA Technical Reports Server (NTRS)

Padovan, J.; Adams, M.; Fertis, J.; Zeid, I.; Lam, P.

1982-01-01

Finite element codes are used in modelling rotor-bearing-stator structure common to the turbine industry. Engine dynamic simulation is used by developing strategies which enable the use of available finite element codes. benchmarking the elements developed are benchmarked by incorporation into a general purpose code (ADINA); the numerical characteristics of finite element type rotor-bearing-stator simulations are evaluated through the use of various types of explicit/implicit numerical integration operators. Improving the overall numerical efficiency of the procedure is improved.

Solar Proton Transport Within an ICRU Sphere Surrounded by a Complex Shield: Ray-trace Geometry

NASA Technical Reports Server (NTRS)

Slaba, Tony C.; Wilson, John W.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.

2015-01-01

A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z is less than or equal to 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency.

Solar proton exposure of an ICRU sphere within a complex structure part II: Ray-trace geometry.

PubMed

Slaba, Tony C; Wilson, John W; Badavi, Francis F; Reddell, Brandon D; Bahadori, Amir A

2016-06-01

A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z ≤ 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency. Published by Elsevier Ltd.

Modification of the SAS4A Safety Analysis Code for Integration with the ADAPT Discrete Dynamic Event Tree Framework.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jankovsky, Zachary Kyle; Denman, Matthew R.

It is difficult to assess the consequences of a transient in a sodium-cooled fast reactor (SFR) using traditional probabilistic risk assessment (PRA) methods, as numerous safety-related sys- tems have passive characteristics. Often there is significant dependence on the value of con- tinuous stochastic parameters rather than binary success/failure determinations. One form of dynamic PRA uses a system simulator to represent the progression of a transient, tracking events through time in a discrete dynamic event tree (DDET). In order to function in a DDET environment, a simulator must have characteristics that make it amenable to changing physical parameters midway through themore » analysis. The SAS4A SFR system analysis code did not have these characteristics as received. This report describes the code modifications made to allow dynamic operation as well as the linking to a Sandia DDET driver code. A test case is briefly described to demonstrate the utility of the changes.« less

Progress with the COGENT Edge Kinetic Code: Implementing the Fokker-Plank Collision Operator

DOE PAGES

Dorf, M. A.; Cohen, R. H.; Dorr, M.; ...

2014-06-20

Here, COGENT is a continuum gyrokinetic code for edge plasma simulations being developed by the Edge Simulation Laboratory collaboration. The code is distinguished by application of a fourth-order finite-volume (conservative) discretization, and mapped multiblock grid technology to handle the geometric complexity of the tokamak edge. The distribution function F is discretized in v∥ – μ (parallel velocity – magnetic moment) velocity coordinates, and the code presently solves an axisymmetric full-f gyro-kinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. COGENT capabilities are extended by implementing the fully nonlinear Fokker-Plank operator to model Coulomb collisions in magnetized edge plasmas.more » The corresponding Rosenbluth potentials are computed by making use of a finite-difference scheme and multipole-expansion boundary conditions. Details of the numerical algorithms and results of the initial verification studies are discussed. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)« less

Improving the efficiency of quantum hash function by dense coding of coin operators in discrete-time quantum walk

NASA Astrophysics Data System (ADS)

Yang, YuGuang; Zhang, YuChen; Xu, Gang; Chen, XiuBo; Zhou, Yi-Hua; Shi, WeiMin

2018-03-01

Li et al. first proposed a quantum hash function (QHF) in a quantum-walk architecture. In their scheme, two two-particle interactions, i.e., I interaction and π-phase interaction are introduced and the choice of I or π-phase interactions at each iteration depends on a message bit. In this paper, we propose an efficient QHF by dense coding of coin operators in discrete-time quantum walk. Compared with existing QHFs, our protocol has the following advantages: the efficiency of the QHF can be doubled and even more; only one particle is enough and two-particle interactions are unnecessary so that quantum resources are saved. It is a clue to apply the dense coding technique to quantum cryptographic protocols, especially to the applications with restricted quantum resources.

Statistics of the quantized microwave electromagnetic field in mesoscopic elements at low temperature

NASA Astrophysics Data System (ADS)

Virally, Stéphane; Olivier Simoneau, Jean; Lupien, Christian; Reulet, Bertrand

2018-03-01

The quantum behavior of the electromagnetic field in mesoscopic elements is intimately linked to the quantization of the charge. In order to probe nonclassical aspects of the field in those elements, it is essential that thermal noise be reduced to the quantum level, i.e. to scales where kT ≲ hν. This is easily achieved in dilution refrigerators for frequencies of a few GHz, i.e. in the microwave domain. Several recent experiments have highlighted the link between discrete charge transport and discrete photon emission in simple mesoscopic elements such as a tunnel junction. Photocount statistics are inferred from the measurement of continuous variables such as the quadratures of the field.

Synchronization Control for a Class of Discrete-Time Dynamical Networks With Packet Dropouts: A Coding-Decoding-Based Approach.

PubMed

Wang, Licheng; Wang, Zidong; Han, Qing-Long; Wei, Guoliang

2017-09-06

The synchronization control problem is investigated for a class of discrete-time dynamical networks with packet dropouts via a coding-decoding-based approach. The data is transmitted through digital communication channels and only the sequence of finite coded signals is sent to the controller. A series of mutually independent Bernoulli distributed random variables is utilized to model the packet dropout phenomenon occurring in the transmissions of coded signals. The purpose of the addressed synchronization control problem is to design a suitable coding-decoding procedure for each node, based on which an efficient decoder-based control protocol is developed to guarantee that the closed-loop network achieves the desired synchronization performance. By applying a modified uniform quantization approach and the Kronecker product technique, criteria for ensuring the detectability of the dynamical network are established by means of the size of the coding alphabet, the coding period and the probability information of packet dropouts. Subsequently, by resorting to the input-to-state stability theory, the desired controller parameter is obtained in terms of the solutions to a certain set of inequality constraints which can be solved effectively via available software packages. Finally, two simulation examples are provided to demonstrate the effectiveness of the obtained results.

Efficient simulation of pitch angle collisions in a 2+2-D Eulerian Vlasov code

NASA Astrophysics Data System (ADS)

Banks, Jeff; Berger, R.; Brunner, S.; Tran, T.

2014-10-01

Here we discuss pitch angle scattering collisions in the context of the Eulerian-based kinetic code LOKI that evolves the Vlasov-Poisson system in 2+2-dimensional phase space. The collision operator is discretized using 4th order accurate conservative finite-differencing. The treatment of the Vlasov operator in phase-space uses an approach based on a minimally diffuse, fourth-order-accurate discretization (Banks and Hittinger, IEEE T. Plasma Sci. 39, 2198). The overall scheme is therefore discretely conservative and controls unphysical oscillations. Some details of the numerical scheme will be presented, and the implementation on modern highly concurrent parallel computers will be discussed. We will present results of collisional effects on linear and non-linear Landau damping of electron plasma waves (EPWs). In addition we will present initial results showing the effect of collisions on the evolution of EPWs in two space dimensions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the LDRD program at LLNL under project tracking code 12-ERD-061.

Development and Evaluation of a Hydrostatic Dynamical Core Using the Spectral Element/Discontinuous Galerkin Methods

DTIC Science & Technology

2014-04-01

The CG and DG horizontal discretization employs high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto- Legendre ...and DG horizontal discretization employs high-order nodal basis functions 29 associated with Lagrange polynomials based on Gauss-Lobatto- Legendre ...Inside 235 each element we build ( 1)N + Gauss-Lobatto- Legendre (GLL) quadrature points, where N 236 indicate the polynomial order of the basis

The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes

NASA Astrophysics Data System (ADS)

Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran

2018-04-01

This paper investigates the lowest-order weak Galerkin finite element method for solving the Darcy equation on quadrilateral and hybrid meshes consisting of quadrilaterals and triangles. In this approach, the pressure is approximated by constants in element interiors and on edges. The discrete weak gradients of these constant basis functions are specified in local Raviart-Thomas spaces, specifically RT0 for triangles and unmapped RT[0] for quadrilaterals. These discrete weak gradients are used to approximate the classical gradient when solving the Darcy equation. The method produces continuous normal fluxes and is locally mass-conservative, regardless of mesh quality, and has optimal order convergence in pressure, velocity, and normal flux, when the quadrilaterals are asymptotically parallelograms. Implementation is straightforward and results in symmetric positive-definite discrete linear systems. We present numerical experiments and comparisons with other existing methods.

The effect of catchment discretization on rainfall-runoff model predictions

NASA Astrophysics Data System (ADS)

Goodrich, D.; Grayson, R.; Willgoose, G.; Palacios-Valez, O.; Bloschl, G.

2003-04-01

Application of distributed hydrologic watershed models fundamentally requires watershed partitioning or discretization. In addition to partitioning the watershed into modelling elements, these elements typically represent a further abstraction of the actual watershed surface and its relevant hydrologic properties. A critical issue that must be addressed by any user of these models prior to their application is definition of an acceptable level and type of watershed discretization or geometric model complexity. A quantitative methodology to define a level of geometric model complexity commensurate with a specified level of model performance is developed for watershed rainfall-runoff modelling. The methodology is tested on four subcatchments which cover a range of watershed scales of over three orders of magnitude in the USDA-ARS Walnut Gulch Experimental Watershed in Southeastern Arizona. It was found that distortion of the hydraulic roughness can compensate for a lower level of discretization (fewer channels) to a point. Beyond this point, hydraulic roughness distortion cannot compensate for the topographic distortion of representing the watershed by fewer elements (e.g. less complex channel network). Similarly, differences in representation of topography by different model or digital elevation model (DEM) types (e.g. Triangular Irregular Elements - TINs; contour lines; and regular grid DEMs) also result in difference in runoff routing responses that can be largely compensated for by a distortion in hydraulic roughness or path length. To put the effect of these discretization models in context it will be shown that relatively small non-compliance with Peclet number restrictions on timestep size can overwhelm the relatively modest differences resulting from the type of representation of topography.

Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements

NASA Astrophysics Data System (ADS)

Lohmann, Christoph; Kuzmin, Dmitri; Shadid, John N.; Mabuza, Sibusiso

2017-09-01

This work extends the flux-corrected transport (FCT) methodology to arbitrary order continuous finite element discretizations of scalar conservation laws on simplex meshes. Using Bernstein polynomials as local basis functions, we constrain the total variation of the numerical solution by imposing local discrete maximum principles on the Bézier net. The design of accuracy-preserving FCT schemes for high order Bernstein-Bézier finite elements requires the development of new algorithms and/or generalization of limiting techniques tailored for linear and multilinear Lagrange elements. In this paper, we propose (i) a new discrete upwinding strategy leading to local extremum bounded low order approximations with compact stencils, (ii) high order variational stabilization based on the difference between two gradient approximations, and (iii) new localized limiting techniques for antidiffusive element contributions. The optional use of a smoothness indicator, based on a second derivative test, makes it possible to potentially avoid unnecessary limiting at smooth extrema and achieve optimal convergence rates for problems with smooth solutions. The accuracy of the proposed schemes is assessed in numerical studies for the linear transport equation in 1D and 2D.

A Posteriori Bounds for Linear-Functional Outputs of Crouzeix-Raviart Finite Element Discretizations of the Incompressible Stokes Problem

NASA Technical Reports Server (NTRS)

Patera, Anthony T.; Paraschivoiu, Marius

1998-01-01

We present a finite element technique for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions; the finite element discretization is effected by Crouzeix-Raviart elements, the discontinuous pressure approximation of which is central to our approach. The bounds are based upon the construction of an augmented Lagrangian: the objective is a quadratic "energy" reformulation of the desired output; the constraints are the finite element equilibrium equations (including the incompressibility constraint), and the intersubdomain continuity conditions on velocity. Appeal to the dual max-min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine-mesh discretization; the Lagrange multipliers are generated by exploiting an associated coarse-mesh approximation. In addition to the requisite coarse-mesh calculations, the bound technique requires solution only of local subdomain Stokes problems on the fine-mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flowrate past, and the lift force on, a body immersed in a channel.

Finite Elements Analysis of a Composite Semi-Span Test Article With and Without Discrete Damage

NASA Technical Reports Server (NTRS)

Lovejoy, Andrew E.; Jegley, Dawn C. (Technical Monitor)

2000-01-01

AS&M Inc. performed finite element analysis, with and without discrete damage, of a composite semi-span test article that represents the Boeing 220-passenger transport aircraft composite semi-span test article. A NASTRAN bulk data file and drawings of the test mount fixtures and semi-span components were utilized to generate the baseline finite element model. In this model, the stringer blades are represented by shell elements, and the stringer flanges are combined with the skin. Numerous modeling modifications and discrete source damage scenarios were applied to the test article model throughout the course of the study. This report details the analysis method and results obtained from the composite semi-span study. Analyses were carried out for three load cases: Braked Roll, LOG Down-Bending and 2.5G Up-Bending. These analyses included linear and nonlinear static response, as well as linear and nonlinear buckling response. Results are presented in the form of stress and strain plots. factors of safety for failed elements, buckling loads and modes, deflection prediction tables and plots, and strainage prediction tables and plots. The collected results are presented within this report for comparison to test results.

Application of an enhanced discrete element method to oil and gas drilling processes

NASA Astrophysics Data System (ADS)

Ubach, Pere Andreu; Arrufat, Ferran; Ring, Lev; Gandikota, Raju; Zárate, Francisco; Oñate, Eugenio

2016-03-01

The authors present results on the use of the discrete element method (DEM) for the simulation of drilling processes typical in the oil and gas exploration industry. The numerical method uses advanced DEM techniques using a local definition of the DEM parameters and combined FEM-DEM procedures. This paper presents a step-by-step procedure to build a DEM model for analysis of the soil region coupled to a FEM model for discretizing the drilling tool that reproduces the drilling mechanics of a particular drill bit. A parametric study has been performed to determine the model parameters in order to maintain accurate solutions with reduced computational cost.

Arterial waveguide model for shear wave elastography: implementation and in vitro validation

NASA Astrophysics Data System (ADS)

Vaziri Astaneh, Ali; Urban, Matthew W.; Aquino, Wilkins; Greenleaf, James F.; Guddati, Murthy N.

2017-07-01

Arterial stiffness is found to be an early indicator of many cardiovascular diseases. Among various techniques, shear wave elastography has emerged as a promising tool for estimating local arterial stiffness through the observed dispersion of guided waves. In this paper, we develop efficient models for the computational simulation of guided wave dispersion in arterial walls. The models are capable of considering fluid-loaded tubes, immersed in fluid or embedded in a solid, which are encountered in in vitro/ex vivo, and in vivo experiments. The proposed methods are based on judiciously combining Fourier transformation and finite element discretization, leading to a significant reduction in computational cost while fully capturing complex 3D wave propagation. The developed methods are implemented in open-source code, and verified by comparing them with significantly more expensive, fully 3D finite element models. We also validate the models using the shear wave elastography of tissue-mimicking phantoms. The computational efficiency of the developed methods indicates the possibility of being able to estimate arterial stiffness in real time, which would be beneficial in clinical settings.

Functional Information Stored in the Conserved Structural RNA Domains of Flavivirus Genomes

PubMed Central

Fernández-Sanlés, Alba; Ríos-Marco, Pablo; Romero-López, Cristina; Berzal-Herranz, Alfredo

2017-01-01

The genus Flavivirus comprises a large number of small, positive-sense single-stranded, RNA viruses able to replicate in the cytoplasm of certain arthropod and/or vertebrate host cells. The genus, which has some 70 member species, includes a number of emerging and re-emerging pathogens responsible for outbreaks of human disease around the world, such as the West Nile, dengue, Zika, yellow fever, Japanese encephalitis, St. Louis encephalitis, and tick-borne encephalitis viruses. Like other RNA viruses, flaviviruses have a compact RNA genome that efficiently stores all the information required for the completion of the infectious cycle. The efficiency of this storage system is attributable to supracoding elements, i.e., discrete, structural units with essential functions. This information storage system overlaps and complements the protein coding sequence and is highly conserved across the genus. It therefore offers interesting potential targets for novel therapeutic strategies. This review summarizes our knowledge of the features of flavivirus genome functional RNA domains. It also provides a brief overview of the main achievements reported in the design of antiviral nucleic acid-based drugs targeting functional genomic RNA elements. PMID:28421048

A new constitutive model for simulation of softening, plateau, and densification phenomena for trabecular bone under compression.

PubMed

Lee, Chi-Seung; Lee, Jae-Myung; Youn, BuHyun; Kim, Hyung-Sik; Shin, Jong Ki; Goh, Tae Sik; Lee, Jung Sub

2017-01-01

A new type of constitutive model and its computational implementation procedure for the simulation of a trabecular bone are proposed in the present study. A yield surface-independent Frank-Brockman elasto-viscoplastic model is introduced to express the nonlinear material behavior such as softening beyond yield point, plateau, and densification under compressive loads. In particular, the hardening- and softening-dominant material functions are introduced and adopted in the plastic multiplier to describe each nonlinear material behavior separately. In addition, the elasto-viscoplastic model is transformed into an implicit type discrete model, and is programmed as a user-defined material subroutine in commercial finite element analysis code. In particular, the consistent tangent modulus method is proposed to improve the computational convergence and to save computational time during finite element analysis. Through the developed material library, the nonlinear stress-strain relationship is analyzed qualitatively and quantitatively, and the simulation results are compared with the results of compression test on the trabecular bone to validate the proposed constitutive model, computational method, and material library. Copyright © 2016 Elsevier Ltd. All rights reserved.

Physics Verification Overview

DOE Office of Scientific and Technical Information (OSTI.GOV)

Doebling, Scott William

The purpose of the verification project is to establish, through rigorous convergence analysis, that each ASC computational physics code correctly implements a set of physics models and algorithms (code verification); Evaluate and analyze the uncertainties of code outputs associated with the choice of temporal and spatial discretization (solution or calculation verification); and Develop and maintain the capability to expand and update these analyses on demand. This presentation describes project milestones.

A new splitting scheme to the discrete Boltzmann equation for non-ideal gases on non-uniform meshes

NASA Astrophysics Data System (ADS)

Patel, Saumil; Lee, Taehun

2016-12-01

We present a novel numerical procedure for solving the discrete Boltzmann equations (DBE) on non-uniform meshes. Our scheme is based on the Strang splitting method where we seek to investigate two-phase flow applications. In this note, we investigate the onset of parasitic currents which arise in many computational two-phase algorithms. To the best of our knowledge, the results presented in this work show, for the first time, a spectral element discontinuous Galerkin (SEDG) discretization of a discrete Boltzmann equation which successfully eliminates parasitic currents on non-uniform meshes. With the hope that this technique can be used for applications in complex geometries, calculations are performed on non-uniform mesh distributions by using high-order (spectral), body-fitting quadrilateral elements. Validation and verification of our work is carried out by comparing results against the classical 2D Young-Laplace law problem for a static drop.

Simulating Soft Shadows with Graphics Hardware,

DTIC Science & Technology

1997-01-15

This radiance texture is analogous to the mesh of radiosity values computed in a radiosity algorithm. Unlike a radiosity algorithm, however, our...discretely. Several researchers have explored continuous visibility methods for soft shadow computation and radiosity mesh generation. With this approach...times of several seconds [9]. Most radiosity methods discretize each surface into a mesh of elements and then use discrete methods such as ray

Adaptive Wavelet Modeling of Geophysical Data

NASA Astrophysics Data System (ADS)

Plattner, A.; Maurer, H.; Dahmen, W.; Vorloeper, J.

2009-12-01

Despite the ever-increasing power of modern computers, realistic modeling of complex three-dimensional Earth models is still a challenging task and requires substantial computing resources. The overwhelming majority of current geophysical modeling approaches includes either finite difference or non-adaptive finite element algorithms, and variants thereof. These numerical methods usually require the subsurface to be discretized with a fine mesh to accurately capture the behavior of the physical fields. However, this may result in excessive memory consumption and computing times. A common feature of most of these algorithms is that the modeled data discretizations are independent of the model complexity, which may be wasteful when there are only minor to moderate spatial variations in the subsurface parameters. Recent developments in the theory of adaptive numerical solvers have the potential to overcome this problem. Here, we consider an adaptive wavelet based approach that is applicable to a large scope of problems, also including nonlinear problems. To the best of our knowledge such algorithms have not yet been applied in geophysics. Adaptive wavelet algorithms offer several attractive features: (i) for a given subsurface model, they allow the forward modeling domain to be discretized with a quasi minimal number of degrees of freedom, (ii) sparsity of the associated system matrices is guaranteed, which makes the algorithm memory efficient, and (iii) the modeling accuracy scales linearly with computing time. We have implemented the adaptive wavelet algorithm for solving three-dimensional geoelectric problems. To test its performance, numerical experiments were conducted with a series of conductivity models exhibiting varying degrees of structural complexity. Results were compared with a non-adaptive finite element algorithm, which incorporates an unstructured mesh to best fit subsurface boundaries. Such algorithms represent the current state-of-the-art in geoelectrical modeling. An analysis of the numerical accuracy as a function of the number of degrees of freedom revealed that the adaptive wavelet algorithm outperforms the finite element solver for simple and moderately complex models, whereas the results become comparable for models with spatially highly variable electrical conductivities. The linear dependency of the modeling error and the computing time proved to be model-independent. This feature will allow very efficient computations using large-scale models as soon as our experimental code is optimized in terms of its implementation.

CMOS Imaging of Temperature Effects on Pin-Printed Xerogel Sensor Microarrays.

PubMed

Lei Yao; Ka Yi Yung; Chodavarapu, Vamsy P; Bright, Frank V

2011-04-01

In this paper, we study the effect of temperature on the operation and performance of a xerogel-based sensor microarrays coupled to a complementary metal-oxide semiconductor (CMOS) imager integrated circuit (IC) that images the photoluminescence response from the sensor microarray. The CMOS imager uses a 32 × 32 (1024 elements) array of active pixel sensors and each pixel includes a high-gain phototransistor to convert the detected optical signals into electrical currents. A correlated double sampling circuit and pixel address/digital control/signal integration circuit are also implemented on-chip. The CMOS imager data are read out as a serial coded signal. The sensor system uses a light-emitting diode to excite target analyte responsive organometallic luminophores doped within discrete xerogel-based sensor elements. As a proto type, we developed a 3 × 3 (9 elements) array of oxygen (O2) sensors. Each group of three sensor elements in the array (arranged in a column) is designed to provide a different and specific sensitivity to the target gaseous O2 concentration. This property of multiple sensitivities is achieved by using a mix of two O2 sensitive luminophores in each pin-printed xerogel sensor element. The CMOS imager is designed to be low noise and consumes a static power of 320.4 μW and an average dynamic power of 624.6 μW when operating at 100-Hz sampling frequency and 1.8-V dc power supply.

On the torsional loading of elastoplastic spheres in contact

NASA Astrophysics Data System (ADS)

Nadimi, Sadegh; Fonseca, Joana

2017-06-01

The mechanical interaction between two bodies involves normal loading in combination with tangential, torsional and rotational loading. This paper focuses on the torsional loading of two spherical bodies which leads to twisting moment. The theoretical approach for calculating twisting moment between two spherical bodies has been proposed by Lubkin [1]. Due to the complexity of the solution, this has been simplified by Deresiewicz for discrete element modelling [2]. Here, the application of a simplified model for elastoplastic spheres is verified using computational modelling. The single grain interaction is simulated in a combined finite discrete element domain. In this domain a grain can deform using a finite element formulation and can interact with other objects based on discrete element principles. For an elastoplastic model, the contact area is larger in comparison with the elastic model, under a given normal force. Therefore, the plastic twisting moment is stiffer. The results presented here are important for describing any granular system involving torsional loading of elastoplastic grains. In particular, recent research on the behaviour of soil has clearly shown the importance of plasticity on grain interaction and rearrangement.

A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

NASA Astrophysics Data System (ADS)

Krank, Benjamin; Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin

2017-11-01

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at Reτ = 180 as well as 590.

Accuracy Quantification of the Loci-CHEM Code for Chamber Wall Heat Transfer in a GO2/GH2 Single Element Injector Model Problem

NASA Technical Reports Server (NTRS)

West, Jeff; Westra, Doug; Lin, Jeff; Tucker, Kevin

2006-01-01

A robust rocket engine combustor design and development process must include tools which can accurately predict the multi-dimensional thermal environments imposed on solid surfaces by the hot combustion products. Currently, empirical methods used in the design process are typically one dimensional and do not adequately account for the heat flux rise rate in the near-injector region of the chamber. Computational Fluid Dynamics holds promise to meet the design tool requirement, but requires accuracy quantification, or validation, before it can be confidently applied in the design process. This effort presents the beginning of such a validation process for the Loci-CHEM CFD code. The model problem examined here is a gaseous oxygen (GO2)/gaseous hydrogen (GH2) shear coaxial single element injector operating at a chamber pressure of 5.42 MPa. The GO2/GH2 propellant combination in this geometry represents one the simplest rocket model problems and is thus foundational to subsequent validation efforts for more complex injectors. Multiple steady state solutions have been produced with Loci-CHEM employing different hybrid grids and two-equation turbulence models. Iterative convergence for each solution is demonstrated via mass conservation, flow variable monitoring at discrete flow field locations as a function of solution iteration and overall residual performance. A baseline hybrid was used and then locally refined to demonstrate grid convergence. Solutions were obtained with three variations of the k-omega turbulence model.

Accuracy Quantification of the Loci-CHEM Code for Chamber Wall Heat Fluxes in a G02/GH2 Single Element Injector Model Problem

NASA Technical Reports Server (NTRS)

West, Jeff; Westra, Doug; Lin, Jeff; Tucker, Kevin

2006-01-01

A robust rocket engine combustor design and development process must include tools which can accurately predict the multi-dimensional thermal environments imposed on solid surfaces by the hot combustion products. Currently, empirical methods used in the design process are typically one dimensional and do not adequately account for the heat flux rise rate in the near-injector region of the chamber. Computational Fluid Dynamics holds promise to meet the design tool requirement, but requires accuracy quantification, or validation, before it can be confidently applied in the design process. This effort presents the beginning of such a validation process for the Loci- CHEM CPD code. The model problem examined here is a gaseous oxygen (GO2)/gaseous hydrogen (GH2) shear coaxial single element injector operating at a chamber pressure of 5.42 MPa. The GO2/GH2 propellant combination in this geometry represents one the simplest rocket model problems and is thus foundational to subsequent validation efforts for more complex injectors. Multiple steady state solutions have been produced with Loci-CHEM employing different hybrid grids and two-equation turbulence models. Iterative convergence for each solution is demonstrated via mass conservation, flow variable monitoring at discrete flow field locations as a function of solution iteration and overall residual performance. A baseline hybrid grid was used and then locally refined to demonstrate grid convergence. Solutions were also obtained with three variations of the k-omega turbulence model.

Symplectic discretization for spectral element solution of Maxwell's equations

NASA Astrophysics Data System (ADS)

Zhao, Yanmin; Dai, Guidong; Tang, Yifa; Liu, Qinghuo

2009-08-01

Applying the spectral element method (SEM) based on the Gauss-Lobatto-Legendre (GLL) polynomial to discretize Maxwell's equations, we obtain a Poisson system or a Poisson system with at most a perturbation. For the system, we prove that any symplectic partitioned Runge-Kutta (PRK) method preserves the Poisson structure and its implied symplectic structure. Numerical examples show the high accuracy of SEM and the benefit of conserving energy due to the use of symplectic methods.

Solution of elastic-plastic stress analysis problems by the p-version of the finite element method

NASA Technical Reports Server (NTRS)

Szabo, Barna A.; Actis, Ricardo L.; Holzer, Stefan M.

1993-01-01

The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.

Method of preforming and assembling superconducting circuit elements

NASA Astrophysics Data System (ADS)

Haertling, Gene H.; Buckley, John D.

1991-03-01

The invention is a method of preforming and pretesting rigid and discrete superconductor circuit elements to optimize the superconductivity development of the preformed circuit element prior to its assembly, and encapsulation on a substrate and final environmental testing of the assembled ceramic superconductive elements.

AFMPB: An adaptive fast multipole Poisson-Boltzmann solver for calculating electrostatics in biomolecular systems

NASA Astrophysics Data System (ADS)

Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, J. Andrew

2010-06-01

A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/~lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. Program summaryProgram title: AFMPB: Adaptive fast multipole Poisson-Boltzmann solver Catalogue identifier: AEGB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL 2.0 No. of lines in distributed program, including test data, etc.: 453 649 No. of bytes in distributed program, including test data, etc.: 8 764 754 Distribution format: tar.gz Programming language: Fortran Computer: Any Operating system: Any RAM: Depends on the size of the discretized biomolecular system Classification: 3 External routines: Pre- and post-processing tools are required for generating the boundary elements and for visualization. Users can use MSMS ( http://www.scripps.edu/~sanner/html/msms_home.html) for pre-processing, and VMD ( http://www.ks.uiuc.edu/Research/vmd/) for visualization. Sub-programs included: An iterative Krylov subspace solvers package from SPARSKIT by Yousef Saad ( http://www-users.cs.umn.edu/~saad/software/SPARSKIT/sparskit.html), and the fast multipole methods subroutines from FMMSuite ( http://www.fastmultipole.org/). Nature of problem: Numerical solution of the linearized Poisson-Boltzmann equation that describes electrostatic interactions of molecular systems in ionic solutions. Solution method: A novel node-patch scheme is used to discretize the well-conditioned boundary integral equation formulation of the linearized Poisson-Boltzmann equation. Various Krylov subspace solvers can be subsequently applied to solve the resulting linear system, with a bounded number of iterations independent of the number of discretized unknowns. The matrix-vector multiplication at each iteration is accelerated by the adaptive new versions of fast multipole methods. The AFMPB solver requires other stand-alone pre-processing tools for boundary mesh generation, post-processing tools for data analysis and visualization, and can be conveniently coupled with different time stepping methods for dynamics simulation. Restrictions: Only three or six significant digits options are provided in this version. Unusual features: Most of the codes are in Fortran77 style. Memory allocation functions from Fortran90 and above are used in a few subroutines. Additional comments: The current version of the codes is designed and written for single core/processor desktop machines. Check http://lsec.cc.ac.cn/~lubz/afmpb.html and http://mccammon.ucsd.edu/ for updates and changes. Running time: The running time varies with the number of discretized elements ( N) in the system and their distributions. In most cases, it scales linearly as a function of N.

Discrete element weld model, phase 2

NASA Technical Reports Server (NTRS)

Prakash, C.; Samonds, M.; Singhal, A. K.

1987-01-01

A numerical method was developed for analyzing the tungsten inert gas (TIG) welding process. The phenomena being modeled include melting under the arc and the flow in the melt under the action of buoyancy, surface tension, and electromagnetic forces. The latter entails the calculation of the electric potential and the computation of electric current and magnetic field therefrom. Melting may occur at a single temperature or over a temperature range, and the electrical and thermal conductivities can be a function of temperature. Results of sample calculations are presented and discussed at length. A major research contribution has been the development of numerical methodology for the calculation of phase change problems in a fixed grid framework. The model has been implemented on CHAM's general purpose computer code PHOENICS. The inputs to the computer model include: geometric parameters, material properties, and weld process parameters.

Deformed quantum double realization of the toric code and beyond

NASA Astrophysics Data System (ADS)

Padmanabhan, Pramod; Ibieta-Jimenez, Juan Pablo; Bernabe Ferreira, Miguel Jorge; Teotonio-Sobrinho, Paulo

2016-09-01

Quantum double models, such as the toric code, can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups and parametrized by the center of the gauge group algebra and its dual. For general choices of these parameters the transfer matrix contains operators acting on links which can also be thought of as perturbations to the quantum double model driving it out of its topological phase and destroying the exact solvability of the quantum double model. We modify these transfer matrices with perturbations and extract exactly solvable models which remain in a quantum phase, thus nullifying the effect of the perturbation. The algebra of the modified vertex and plaquette operators now obey a deformed version of the quantum double algebra. The Abelian cases are shown to be in the quantum double phase whereas the non-Abelian phases are shown to be in a modified phase of the corresponding quantum double phase. These are illustrated with the groups Zn and S3. The quantum phases are determined by studying the excitations of these systems namely their fusion rules and the statistics. We then go further to construct a transfer matrix which contains the other Z2 phase namely the double semion phase. More generally for other discrete groups these transfer matrices contain the twisted quantum double models. These transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories. These parameters are central elements belonging to the tensor products of the algebra and its dual and are associated to vertices and volumes of the three dimensional lattice. As in the case of the lattice gauge theories we construct the operators creating the excitations in this case and study their braiding and fusion properties.

Fast discrete cosine transform structure suitable for implementation with integer computation

NASA Astrophysics Data System (ADS)

Jeong, Yeonsik; Lee, Imgeun

2000-10-01

The discrete cosine transform (DCT) has wide applications in speech and image coding. We propose a fast DCT scheme with the property of reduced multiplication stages and fewer additions and multiplications. The proposed algorithm is structured so that most multiplications are performed at the final stage, which reduces the propagation error that could occur in the integer computation.

Lagrangian numerical techniques for modelling multicomponent flow in the presence of large viscosity contrasts: Markers-in-bulk versus Markers-in-chain

NASA Astrophysics Data System (ADS)

Mulyukova, Elvira; Dabrowski, Marcin; Steinberger, Bernhard

2015-04-01

Many problems in geodynamic applications may be described as viscous flow of chemically heterogeneous materials. Examples include subduction of compositionally stratified lithospheric plates, folding of rheologically layered rocks, and thermochemical convection of the Earth's mantle. The associated time scales are significantly shorter than that of chemical diffusion, which justifies the commonly featured phenomena in geodynamic flow models termed contact discontinuities. These are spatially sharp interfaces separating regions of different material properties. Numerical modelling of advection of fields with sharp interfaces is challenging. Typical errors include numerical diffusion, which arises due to the repeated action of numerical interpolation. Mathematically, a material field can be represented by discrete indicator functions, whose values are interpreted as logical statements (e.g. whether or not the location is occupied by a given material). Interpolation of a discrete function boils down to determining where in the intermediate node-positions one material ends, and the other begins. The numerical diffusion error thus manifests itself as an erroneous location of the material-interface. Lagrangian advection-schemes are known to be less prone to numerical diffusion errors, compared to their Eulerian counterparts. The tracer-ratio method, where Lagrangian markers are used to discretize the bulk of materials filling the entire domain, is a popular example of such methods. The Stokes equation in this case is solved on a separate, static grid, and in order to do it - material properties must be interpolated from the markers to the grid. This involves the difficulty related to interpolation of discrete fields. The material distribution, and thus material-properties like viscosity and density, seen by the grid is polluted by the interpolation error, which enters the solution of the momentum equation. Errors due to the uncertainty of interface-location can be avoided when using interface tracking methods for advection. Marker-chain method is one such approach, where rather than discretizing the volume of each material, only their interface is discretized by a connected set of markers. Together with the boundary of the domain, the marker-chain constitutes closed polygon-boundaries which enclose the regions spanned by each material. Communicating material properties to the static grid can be done by determining which polygon each grid-node (or integration point) falls into, eliminating the need for interpolation. In our chosen implementation, an efficient parallelized algorithm for the point-in-polygon location is used, so this part of the code takes up only a small fraction of the CPU-time spent on each time step, and allows for spatial resolution of the compositional field beyond that which is practical with markers-in-bulk methods. An additional advantage of using marker-chains for material advection is that it offers a possibility to use some of its markers, or even edges, to generate a FEM grid. One can tailor a grid for obtaining a Stokes solution with optimal accuracy, while controlling the quality and size of its elements. Where geometry of the interface allows - element-edges may be aligned with it, which is known to significantly improve the quality of Stokes solution, compared to when the interface cuts through the elements (Moresi et al., 1996; Deubelbeiss and Kaus, 2008). In more geometrically complex interface-regions, the grid may simply be refined to reduce the error. As materials get deformed in the course of a simulation, the interface may get stretched and entangled. Addition of new markers along the chain may be required in order to properly resolve the increasingly complicated geometry. Conversely, some markers may be removed from regions where they get clustered. Such resampling of the interface requires additional computational effort (although small compared to other parts of the code), and introduces an error in the interface-location (similar to numerical diffusion). Our implementation of this procedure, which utilizes an auxiliary high-resolution structured grid, allows a high degree of control on the magnitude of this error, although cannot eliminate it completely. We will present our chosen numerical implementation of the markers-in-bulk and markers-in-chain methods outlined above, together with the simulation results of the especially designed benchmarks that demonstrate the relative successes and limitations of these methods.

Serial turbo trellis coded modulation using a serially concatenated coder

NASA Technical Reports Server (NTRS)

Divsalar, Dariush (Inventor); Dolinar, Samuel J. (Inventor); Pollara, Fabrizio (Inventor)

2010-01-01

Serial concatenated trellis coded modulation (SCTCM) includes an outer coder, an interleaver, a recursive inner coder and a mapping element. The outer coder receives data to be coded and produces outer coded data. The interleaver permutes the outer coded data to produce interleaved data. The recursive inner coder codes the interleaved data to produce inner coded data. The mapping element maps the inner coded data to a symbol. The recursive inner coder has a structure which facilitates iterative decoding of the symbols at a decoder system. The recursive inner coder and the mapping element are selected to maximize the effective free Euclidean distance of a trellis coded modulator formed from the recursive inner coder and the mapping element. The decoder system includes a demodulation unit, an inner SISO (soft-input soft-output) decoder, a deinterleaver, an outer SISO decoder, and an interleaver.

FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

NASA Astrophysics Data System (ADS)

Regnier, D.; Dubray, N.; Verrière, M.; Schunck, N.

2018-04-01

The time-dependent generator coordinate method (TDGCM) is a powerful method to study the large amplitude collective motion of quantum many-body systems such as atomic nuclei. Under the Gaussian Overlap Approximation (GOA), the TDGCM leads to a local, time-dependent Schrödinger equation in a multi-dimensional collective space. In this paper, we present the version 2.0 of the code FELIX that solves the collective Schrödinger equation in a finite element basis. This new version features: (i) the ability to solve a generalized TDGCM+GOA equation with a metric term in the collective Hamiltonian, (ii) support for new kinds of finite elements and different types of quadrature to compute the discretized Hamiltonian and overlap matrices, (iii) the possibility to leverage the spectral element scheme, (iv) an explicit Krylov approximation of the time propagator for time integration instead of the implicit Crank-Nicolson method implemented in the first version, (v) an entirely redesigned workflow. We benchmark this release on an analytic problem as well as on realistic two-dimensional calculations of the low-energy fission of 240Pu and 256Fm. Low to moderate numerical precision calculations are most efficiently performed with simplex elements with a degree 2 polynomial basis. Higher precision calculations should instead use the spectral element method with a degree 4 polynomial basis. We emphasize that in a realistic calculation of fission mass distributions of 240Pu, FELIX-2.0 is about 20 times faster than its previous release (within a numerical precision of a few percents).

Terahertz imaging devices and systems, and related methods, for detection of materials

DOEpatents

Kotter, Dale K.

2016-11-15

Terahertz imaging devices may comprise a focal plane array including a substrate and a plurality of resonance elements. The plurality of resonance elements may comprise a conductive material coupled to the substrate. Each resonance element of the plurality of resonance elements may be configured to resonate and produce an output signal responsive to incident radiation having a frequency between about a 0.1 THz and 4 THz range. A method of detecting a hazardous material may comprise receiving incident radiation by a focal plane array having a plurality of discrete pixels including a resonance element configured to absorb the incident radiation at a resonant frequency in the THz, generating an output signal from each of the discrete pixels, and determining a presence of a hazardous material by interpreting spectral information from the output signal.

Unstructured Adaptive Meshes: Bad for Your Memory?

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Feng, Hui-Yu; VanderWijngaart, Rob

2003-01-01

This viewgraph presentation explores the need for a NASA Advanced Supercomputing (NAS) parallel benchmark for problems with irregular dynamical memory access. This benchmark is important and necessary because: 1) Problems with localized error source benefit from adaptive nonuniform meshes; 2) Certain machines perform poorly on such problems; 3) Parallel implementation may provide further performance improvement but is difficult. Some examples of problems which use irregular dynamical memory access include: 1) Heat transfer problem; 2) Heat source term; 3) Spectral element method; 4) Base functions; 5) Elemental discrete equations; 6) Global discrete equations. Nonconforming Mesh and Mortar Element Method are covered in greater detail in this presentation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jones, J E; Vassilevski, P S; Woodward, C S

This paper provides extensions of an element agglomeration AMG method to nonlinear elliptic problems discretized by the finite element method on general unstructured meshes. The method constructs coarse discretization spaces and corresponding coarse nonlinear operators as well as their Jacobians. We introduce both standard (fairly quasi-uniformly coarsened) and non-standard (coarsened away) coarse meshes and respective finite element spaces. We use both kind of spaces in FAS type coarse subspace correction (or Schwarz) algorithms. Their performance is illustrated on a number of model problems. The coarsened away spaces seem to perform better than the standard spaces for problems with nonlinearities inmore » the principal part of the elliptic operator.« less

Solving the incompressible surface Navier-Stokes equation by surface finite elements

NASA Astrophysics Data System (ADS)

Reuther, Sebastian; Voigt, Axel

2018-01-01

We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus g (S ) . The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding R3, penalization of the normal component, a Chorin projection method, and discretization in space by surface finite elements for each component. The approach thus requires only standard ingredients which most finite element implementations can offer. We compare computational results with discrete exterior calculus simulations on a torus and demonstrate the interplay of the flow field with the topology by showing realizations of the Poincaré-Hopf theorem on n-tori.

Multidisciplinary aeroelastic analysis of a generic hypersonic vehicle

NASA Technical Reports Server (NTRS)

Gupta, K. K.; Petersen, K. L.

1993-01-01

This paper presents details of a flutter and stability analysis of aerospace structures such as hypersonic vehicles. Both structural and aerodynamic domains are discretized by the common finite element technique. A vibration analysis is first performed by the STARS code employing a block Lanczos solution scheme. This is followed by the generation of a linear aerodynamic grid for subsequent linear flutter analysis within subsonic and supersonic regimes of the flight envelope; the doublet lattice and constant pressure techniques are employed to generate the unsteady aerodynamic forces. Flutter analysis is then performed for several representative flight points. The nonlinear flutter solution is effected by first implementing a CFD solution of the entire vehicle. Thus, a 3-D unstructured grid for the entire flow domain is generated by a moving front technique. A finite element Euler solution is then implemented employing a quasi-implicit as well as an explicit solution scheme. A novel multidisciplinary analysis is next effected that employs modal and aerodynamic data to yield aerodynamic damping characteristics. Such analyses are performed for a number of flight points to yield a large set of pertinent data that define flight flutter characteristics of the vehicle. This paper outlines the finite-element-based integrated analysis procedures in detail, which is followed by the results of numerical analyses of flight flutter simulation.

Application of Jacobian-free Newton–Krylov method in implicitly solving two-fluid six-equation two-phase flow problems: Implementation, validation and benchmark

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-03-09

This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3Dmore » code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. As a result, this in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.« less

Iterative methods for elliptic finite element equations on general meshes

NASA Technical Reports Server (NTRS)

Nicolaides, R. A.; Choudhury, Shenaz

1986-01-01

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.

NUCLEAR REACTOR FUEL-BREEDER FUEL ELEMENT

DOEpatents

Currier, E.L. Jr.; Nicklas, J.H.

1962-08-14

A fuel-breeder fuel element was developed for a nuclear reactor wherein discrete particles of fissionable material are dispersed in a matrix of fertile breeder material. The fuel element combines the advantages of a dispersion type and a breeder-type. (AEC)

Mixed finite element - discontinuous finite volume element discretization of a general class of multicontinuum models

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo; Lunati, Ivan

2016-10-01

We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation, deformation of a cantilever bracket, and Boycott effects). The applicability of the method is not limited to flow in porous media, but can also be employed to describe many other physical systems governed by a similar set of equations, including e.g. multi-component materials.

Multi-scale and multi-physics simulations using the multi-fluid plasma model

DTIC Science & Technology

2017-04-25

small The simulation uses 512 second-order elements Bz = 1.0, Te = Ti = 0.01, ui = ue = 0 ne = ni = 1.0 + e−10(x−6) 2 Baboolal, Math . and Comp. Sim. 55...DISTRIBUTION Clearance No. 17211 23 / 31 SUMMARY The blended finite element method (BFEM) is presented DG spatial discretization with explicit Runge...Kutta (i+, n) CG spatial discretization with implicit Crank-Nicolson (e−, fileds) DG captures shocks and discontinuities CG is efficient and robust for

Digital Material Assembly by Passive Means and Modular Isotropic Lattice Extruder System

NASA Technical Reports Server (NTRS)

Gershenfeld, Neil (Inventor); Carney, Matthew Eli (Inventor); Jenett, Benjamin (Inventor)

2017-01-01

A set of machines and related systems build structures by the additive assembly of discrete parts. These digital material assemblies constrain the constituent parts to a discrete set of possible positions and orientations. In doing so, the structures exhibit many of the properties inherent in digital communication such as error correction, fault tolerance and allow the assembly of precise structures with comparatively imprecise tools. Assembly of discrete cellular lattices by a Modular Isotropic Lattice Extruder System (MILES) is implemented by pulling strings of lattice elements through a forming die that enforces geometry constraints that lock the elements into a rigid structure that can then be pushed against and extruded out of the die as an assembled, loadbearing structure.

MCNP (Monte Carlo Neutron Photon) capabilities for nuclear well logging calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Forster, R.A.; Little, R.C.; Briesmeister, J.F.

The Los Alamos Radiation Transport Code System (LARTCS) consists of state-of-the-art Monte Carlo and discrete ordinates transport codes and data libraries. The general-purpose continuous-energy Monte Carlo code MCNP (Monte Carlo Neutron Photon), part of the LARTCS, provides a computational predictive capability for many applications of interest to the nuclear well logging community. The generalized three-dimensional geometry of MCNP is well suited for borehole-tool models. SABRINA, another component of the LARTCS, is a graphics code that can be used to interactively create a complex MCNP geometry. Users can define many source and tally characteristics with standard MCNP features. The time-dependent capabilitymore » of the code is essential when modeling pulsed sources. Problems with neutrons, photons, and electrons as either single particle or coupled particles can be calculated with MCNP. The physics of neutron and photon transport and interactions is modeled in detail using the latest available cross-section data. A rich collections of variance reduction features can greatly increase the efficiency of a calculation. MCNP is written in FORTRAN 77 and has been run on variety of computer systems from scientific workstations to supercomputers. The next production version of MCNP will include features such as continuous-energy electron transport and a multitasking option. Areas of ongoing research of interest to the well logging community include angle biasing, adaptive Monte Carlo, improved discrete ordinates capabilities, and discrete ordinates/Monte Carlo hybrid development. Los Alamos has requested approval by the Department of Energy to create a Radiation Transport Computational Facility under their User Facility Program to increase external interactions with industry, universities, and other government organizations. 21 refs.« less

Aorta modeling with the element-based zero-stress state and isogeometric discretization

NASA Astrophysics Data System (ADS)

Takizawa, Kenji; Tezduyar, Tayfun E.; Sasaki, Takafumi

2017-02-01

Patient-specific arterial fluid-structure interaction computations, including aorta computations, require an estimation of the zero-stress state (ZSS), because the image-based arterial geometries do not come from a ZSS. We have earlier introduced a method for estimation of the element-based ZSS (EBZSS) in the context of finite element discretization of the arterial wall. The method has three main components. 1. An iterative method, which starts with a calculated initial guess, is used for computing the EBZSS such that when a given pressure load is applied, the image-based target shape is matched. 2. A method for straight-tube segments is used for computing the EBZSS so that we match the given diameter and longitudinal stretch in the target configuration and the "opening angle." 3. An element-based mapping between the artery and straight-tube is extracted from the mapping between the artery and straight-tube segments. This provides the mapping from the arterial configuration to the straight-tube configuration, and from the estimated EBZSS of the straight-tube configuration back to the arterial configuration, to be used as the initial guess for the iterative method that matches the image-based target shape. Here we present the version of the EBZSS estimation method with isogeometric wall discretization. With isogeometric discretization, we can obtain the element-based mapping directly, instead of extracting it from the mapping between the artery and straight-tube segments. That is because all we need for the element-based mapping, including the curvatures, can be obtained within an element. With NURBS basis functions, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and much fewer elements. Higher-order NURBS basis functions allow representation of more complex shapes within an element. To show how the new EBZSS estimation method performs, we first present 2D test computations with straight-tube configurations. Then we show how the method can be used in a 3D computation where the target geometry is coming from medical image of a human aorta.

Phase-space finite elements in a least-squares solution of the transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Drumm, C.; Fan, W.; Pautz, S.

2013-07-01

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshingmore » tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)« less

Palindromic repetitive DNA elements with coding potential in Methanocaldococcus jannaschii.

PubMed

Suyama, Mikita; Lathe, Warren C; Bork, Peer

2005-10-10

We have identified 141 novel palindromic repetitive elements in the genome of euryarchaeon Methanocaldococcus jannaschii. The total length of these elements is 14.3kb, which corresponds to 0.9% of the total genomic sequence and 6.3% of all extragenic regions. The elements can be divided into three groups (MJRE1-3) based on the sequence similarity. The low sequence identity within each of the groups suggests rather old origin of these elements in M. jannaschii. Three MJRE2 elements were located within the protein coding regions without disrupting the coding potential of the host genes, indicating that insertion of repeats might be a widespread mechanism to enhance sequence diversity in coding regions.

Decisions: "Carltona" and the CUC Code

ERIC Educational Resources Information Center

Evans, G. R.

2006-01-01

The Committee of University Chairman publishes a code of good practice designed, among other things, to ensure clarity about the authority on which decisions are taken on behalf of universities, subordinate domestic legislation created and the exercise of discretion regulated. In Carltona Ltd.v. Commissioners of Works [1943] 2 All ER 560 AC the…

Monte Carlo and discrete-ordinate simulations of spectral radiances in a coupled air-tissue system.

PubMed

Hestenes, Kjersti; Nielsen, Kristian P; Zhao, Lu; Stamnes, Jakob J; Stamnes, Knut

2007-04-20

We perform a detailed comparison study of Monte Carlo (MC) simulations and discrete-ordinate radiative-transfer (DISORT) calculations of spectral radiances in a 1D coupled air-tissue (CAT) system consisting of horizontal plane-parallel layers. The MC and DISORT models have the same physical basis, including coupling between the air and the tissue, and we use the same air and tissue input parameters for both codes. We find excellent agreement between radiances obtained with the two codes, both above and in the tissue. Our tests cover typical optical properties of skin tissue at the 280, 540, and 650 nm wavelengths. The normalized volume scattering function for internal structures in the skin is represented by the one-parameter Henyey-Greenstein function for large particles and the Rayleigh scattering function for small particles. The CAT-DISORT code is found to be approximately 1000 times faster than the CAT-MC code. We also show that the spectral radiance field is strongly dependent on the inherent optical properties of the skin tissue.

Error correcting coding-theory for structured light illumination systems

NASA Astrophysics Data System (ADS)

Porras-Aguilar, Rosario; Falaggis, Konstantinos; Ramos-Garcia, Ruben

2017-06-01

Intensity discrete structured light illumination systems project a series of projection patterns for the estimation of the absolute fringe order using only the temporal grey-level sequence at each pixel. This work proposes the use of error-correcting codes for pixel-wise correction of measurement errors. The use of an error correcting code is advantageous in many ways: it allows reducing the effect of random intensity noise, it corrects outliners near the border of the fringe commonly present when using intensity discrete patterns, and it provides a robustness in case of severe measurement errors (even for burst errors where whole frames are lost). The latter aspect is particular interesting in environments with varying ambient light as well as in critical safety applications as e.g. monitoring of deformations of components in nuclear power plants, where a high reliability is ensured even in case of short measurement disruptions. A special form of burst errors is the so-called salt and pepper noise, which can largely be removed with error correcting codes using only the information of a given pixel. The performance of this technique is evaluated using both simulations and experiments.

The theta/gamma discrete phase code occuring during the hippocampal phase precession may be a more general brain coding scheme.

PubMed

Lisman, John

2005-01-01

In the hippocampus, oscillations in the theta and gamma frequency range occur together and interact in several ways, indicating that they are part of a common functional system. It is argued that these oscillations form a coding scheme that is used in the hippocampus to organize the readout from long-term memory of the discrete sequence of upcoming places, as cued by current position. This readout of place cells has been analyzed in several ways. First, plots of the theta phase of spikes vs. position on a track show a systematic progression of phase as rats run through a place field. This is termed the phase precession. Second, two cells with nearby place fields have a systematic difference in phase, as indicated by a cross-correlation having a peak with a temporal offset that is a significant fraction of a theta cycle. Third, several different decoding algorithms demonstrate the information content of theta phase in predicting the animal's position. It appears that small phase differences corresponding to jitter within a gamma cycle do not carry information. This evidence, together with the finding that principle cells fire preferentially at a given gamma phase, supports the concept of theta/gamma coding: a given place is encoded by the spatial pattern of neurons that fire in a given gamma cycle (the exact timing within a gamma cycle being unimportant); sequential places are encoded in sequential gamma subcycles of the theta cycle (i.e., with different discrete theta phase). It appears that this general form of coding is not restricted to readout of information from long-term memory in the hippocampus because similar patterns of theta/gamma oscillations have been observed in multiple brain regions, including regions involved in working memory and sensory integration. It is suggested that dual oscillations serve a general function: the encoding of multiple units of information (items) in a way that preserves their serial order. The relationship of such coding to that proposed by Singer and von der Malsburg is discussed; in their scheme, theta is not considered. It is argued that what theta provides is the absolute phase reference needed for encoding order. Theta/gamma coding therefore bears some relationship to the concept of "word" in digital computers, with word length corresponding to the number of gamma cycles within a theta cycle, and discrete phase corresponding to the ordered "place" within a word. Copyright 2005 Wiley-Liss, Inc.

Blocking Mechanism Study of Self-Compacting Concrete Based on Discrete Element Method

NASA Astrophysics Data System (ADS)

Zhang, Xuan; Li, Zhida; Zhang, Zhihua

2017-11-01

In order to study the influence factors of blocking mechanism of Self-Compaction Concrete (SCC), Roussel’s granular blocking model was verified and extended by establishing the discrete element model of SCC. The influence of different parameters on the filling capacity and blocking mechanism of SCC were also investigated. The results showed that: it was feasible to simulate the blocking mechanism of SCC by using Discrete Element Method (DEM). The passing ability of pebble aggregate was superior to the gravel aggregate and the passing ability of hexahedron particles was bigger than tetrahedron particles, while the tetrahedron particle simulation results were closer to the actual situation. The flow of SCC as another significant factor affected the passing ability that with the flow increased, the passing ability increased. The correction coefficient λ of the steel arrangement (channel section shape) and flow rate γ in the block model were introduced that the value of λ was 0.90-0.95 and the maximum casting rate was 7.8 L/min.

Cross-Paradigm Simulation Modeling: Challenges and Successes

DTIC Science & Technology

2011-12-01

is also highlighted. 2.1 Discrete-Event Simulation Discrete-event simulation ( DES ) is a modeling method for stochastic, dynamic models where...which almost anything can be coded; models can be incredibly detailed. Most commercial DES software has a graphical interface which allows the user to...results. Although the above definition is the commonly accepted definition of DES , there are two different worldviews that dominate DES modeling today: a

A Mechanistic Design Approach for Graphite Nanoplatelet (GNP) Reinforced Asphalt Mixtures for Low-Temperature Applications

DOT National Transportation Integrated Search

2018-01-01

This report explores the application of a discrete computational model for predicting the fracture behavior of asphalt mixtures at low temperatures based on the results of simple laboratory experiments. In this discrete element model, coarse aggregat...

An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions

NASA Astrophysics Data System (ADS)

Zahr, M. J.; Persson, P.-O.

2018-07-01

This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous Galerkin or finite volume methods. The proposed method aims to align inter-element boundaries with discontinuities in the solution by deforming the computational mesh. A discontinuity-aligned mesh ensures the discontinuity is represented through inter-element jumps while smooth basis functions interior to elements are only used to approximate smooth regions of the solution, thereby avoiding Gibbs' phenomena that create well-known stability issues. Therefore, very coarse high-order discretizations accurately resolve the piecewise smooth solution throughout the domain, provided the discontinuity is tracked. Central to the proposed discontinuity-tracking framework is a discrete PDE-constrained optimization formulation that simultaneously aligns the computational mesh with discontinuities in the solution and solves the discretized conservation law on this mesh. The optimization objective is taken as a combination of the deviation of the finite-dimensional solution from its element-wise average and a mesh distortion metric to simultaneously penalize Gibbs' phenomena and distorted meshes. It will be shown that our objective function satisfies two critical properties that are required for this discontinuity-tracking framework to be practical: (1) possesses a local minima at a discontinuity-aligned mesh and (2) decreases monotonically to this minimum in a neighborhood of radius approximately h / 2, whereas other popular discontinuity indicators fail to satisfy the latter. Another important contribution of this work is the observation that traditional reduced space PDE-constrained optimization solvers that repeatedly solve the conservation law at various mesh configurations are not viable in this context since severe overshoot and undershoot in the solution, i.e., Gibbs' phenomena, may make it impossible to solve the discrete conservation law on non-aligned meshes. Therefore, we advocate a gradient-based, full space solver where the mesh and conservation law solution converge to their optimal values simultaneously and therefore never require the solution of the discrete conservation law on a non-aligned mesh. The merit of the proposed method is demonstrated on a number of one- and two-dimensional model problems including the L2 projection of discontinuous functions, Burgers' equation with a discontinuous source term, transonic flow through a nozzle, and supersonic flow around a bluff body. We demonstrate optimal O (h p + 1) convergence rates in the L1 norm for up to polynomial order p = 6 and show that accurate solutions can be obtained on extremely coarse meshes.

Discretized Streams: A Fault-Tolerant Model for Scalable Stream Processing

DTIC Science & Technology

2012-12-14

Discretized Streams: A Fault-Tolerant Model for Scalable Stream Processing Matei Zaharia Tathagata Das Haoyuan Li Timothy Hunter Scott Shenker Ion...SUBTITLE Discretized Streams: A Fault-Tolerant Model for Scalable Stream Processing 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER...time. However, current programming models for distributed stream processing are relatively low-level often leaving the user to worry about consistency of

Implementation of radiation shielding calculation methods. Volume 1: Synopsis of methods and summary of results

NASA Technical Reports Server (NTRS)

Capo, M. A.; Disney, R. K.

1971-01-01

The work performed in the following areas is summarized: (1) Analysis of Realistic nuclear-propelled vehicle was analyzed using the Marshall Space Flight Center computer code package. This code package includes one and two dimensional discrete ordinate transport, point kernel, and single scatter techniques, as well as cross section preparation and data processing codes, (2) Techniques were developed to improve the automated data transfer in the coupled computation method of the computer code package and improve the utilization of this code package on the Univac-1108 computer system. (3) The MSFC master data libraries were updated.

Survey of computer programs for heat transfer analysis

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.

1986-01-01

An overview is given of the current capabilities of thirty-three computer programs that are used to solve heat transfer problems. The programs considered range from large general-purpose codes with broad spectrum of capabilities, large user community, and comprehensive user support (e.g., ABAQUS, ANSYS, EAL, MARC, MITAS II, MSC/NASTRAN, and SAMCEF) to the small, special-purpose codes with limited user community such as ANDES, NTEMP, TAC2D, TAC3D, TEPSA and TRUMP. The majority of the programs use either finite elements or finite differences for the spatial discretization. The capabilities of the programs are listed in tabular form followed by a summary of the major features of each program. The information presented herein is based on a questionnaire sent to the developers of each program. This information is preceded by a brief background material needed for effective evaluation and use of computer programs for heat transfer analysis. The present survey is useful in the initial selection of the programs which are most suitable for a particular application. The final selection of the program to be used should, however, be based on a detailed examination of the documentation and the literature about the program.

Generalized Fourier analyses of the advection-diffusion equation - Part I: one-dimensional domains

NASA Astrophysics Data System (ADS)

Christon, Mark A.; Martinez, Mario J.; Voth, Thomas E.

2004-07-01

This paper presents a detailed multi-methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. The errors are reported in terms of non-dimensional phase and group speed, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy. It is demonstrated that Fourier analysis provides an automatic process for separating the discrete advective operator into its symmetric and skew-symmetric components and characterizing the spectral behaviour of each operator. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. It is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, the streamline upwind control-volume method, produce both an artificial diffusivity and a concomitant phase speed adjustment in addition to the usual semi-discrete artifacts observed in the phase speed, group speed and diffusivity. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behaviour in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behaviour. In Part II of this paper, we consider two-dimensional semi-discretizations of the advection-diffusion equation and also assess the affects of grid-induced anisotropy observed in the non-dimensional phase speed, and the discrete and artificial diffusivities. Although this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common analysis framework. Published in 2004 by John Wiley & Sons, Ltd.

Discrete-Layer Piezoelectric Plate and Shell Models for Active Tip-Clearance Control

NASA Technical Reports Server (NTRS)

Heyliger, P. R.; Ramirez, G.; Pei, K. C.

1994-01-01

The objectives of this work were to develop computational tools for the analysis of active-sensory composite structures with added or embedded piezoelectric layers. The targeted application for this class of smart composite laminates and the analytical development is the accomplishment of active tip-clearance control in turbomachinery components. Two distinct theories and analytical models were developed and explored under this contract: (1) a discrete-layer plate theory and corresponding computational models, and (2) a three dimensional general discrete-layer element generated in curvilinear coordinates for modeling laminated composite piezoelectric shells. Both models were developed from the complete electromechanical constitutive relations of piezoelectric materials, and incorporate both displacements and potentials as state variables. This report describes the development and results of these models. The discrete-layer theories imply that the displacement field and electrostatic potential through-the-thickness of the laminate are described over an individual layer rather than as a smeared function over the thickness of the entire plate or shell thickness. This is especially crucial for composites with embedded piezoelectric layers, as the actuating and sensing elements within these layers are poorly represented by effective or smeared properties. Linear Lagrange interpolation polynomials were used to describe the through-thickness laminate behavior. Both analytic and finite element approximations were used in the plane or surface of the structure. In this context, theoretical developments are presented for the discrete-layer plate theory, the discrete-layer shell theory, and the formulation of an exact solution for simply-supported piezoelectric plates. Finally, evaluations and results from a number of separate examples are presented for the static and dynamic analysis of the plate geometry. Comparisons between the different approaches are provided when possible, and initial conclusions regarding the accuracy and limitations of these models are given.

Stabilized Finite Elements in FUN3D

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Newman, James C.; Karman, Steve L.

2017-01-01

A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

Stable finite element approximations of two-phase flow with soluble surfactant

NASA Astrophysics Data System (ADS)

Barrett, John W.; Garcke, Harald; Nürnberg, Robert

2015-09-01

A parametric finite element approximation of incompressible two-phase flow with soluble surfactants is presented. The Navier-Stokes equations are coupled to bulk and surfaces PDEs for the surfactant concentrations. At the interface adsorption, desorption and stress balances involving curvature effects and Marangoni forces have to be considered. A parametric finite element approximation for the advection of the interface, which maintains good mesh properties, is coupled to the evolving surface finite element method, which is used to discretize the surface PDE for the interface surfactant concentration. The resulting system is solved together with standard finite element approximations of the Navier-Stokes equations and of the bulk parabolic PDE for the surfactant concentration. Semidiscrete and fully discrete approximations are analyzed with respect to stability, conservation and existence/uniqueness issues. The approach is validated for simple test cases and for complex scenarios, including colliding drops in a shear flow, which are computed in two and three space dimensions.

Transition from Target to Gaze Coding in Primate Frontal Eye Field during Memory Delay and Memory-Motor Transformation.

PubMed

Sajad, Amirsaman; Sadeh, Morteza; Yan, Xiaogang; Wang, Hongying; Crawford, John Douglas

2016-01-01

The frontal eye fields (FEFs) participate in both working memory and sensorimotor transformations for saccades, but their role in integrating these functions through time remains unclear. Here, we tracked FEF spatial codes through time using a novel analytic method applied to the classic memory-delay saccade task. Three-dimensional recordings of head-unrestrained gaze shifts were made in two monkeys trained to make gaze shifts toward briefly flashed targets after a variable delay (450-1500 ms). A preliminary analysis of visual and motor response fields in 74 FEF neurons eliminated most potential models for spatial coding at the neuron population level, as in our previous study (Sajad et al., 2015). We then focused on the spatiotemporal transition from an eye-centered target code (T; preferred in the visual response) to an eye-centered intended gaze position code (G; preferred in the movement response) during the memory delay interval. We treated neural population codes as a continuous spatiotemporal variable by dividing the space spanning T and G into intermediate T-G models and dividing the task into discrete steps through time. We found that FEF delay activity, especially in visuomovement cells, progressively transitions from T through intermediate T-G codes that approach, but do not reach, G. This was followed by a final discrete transition from these intermediate T-G delay codes to a "pure" G code in movement cells without delay activity. These results demonstrate that FEF activity undergoes a series of sensory-memory-motor transformations, including a dynamically evolving spatial memory signal and an imperfect memory-to-motor transformation.

Calculations of axisymmetric vortex sheet roll-up using a panel and a filament model

NASA Technical Reports Server (NTRS)

Kantelis, J. P.; Widnall, S. E.

1986-01-01

A method for calculating the self-induced motion of a vortex sheet using discrete vortex elements is presented. Vortex panels and vortex filaments are used to simulate two-dimensional and axisymmetric vortex sheet roll-up. A straight forward application using vortex elements to simulate the motion of a disk of vorticity with an elliptic circulation distribution yields unsatisfactroy results where the vortex elements move in a chaotic manner. The difficulty is assumed to be due to the inability of a finite number of discrete vortex elements to model the singularity at the sheet edge and due to large velocity calculation errors which result from uneven sheet stretching. A model of the inner portion of the spiral is introduced to eliminate the difficulty with the sheet edge singularity. The model replaces the outermost portion of the sheet with a single vortex of equivalent circulation and a number of higher order terms which account for the asymmetry of the spiral. The resulting discrete vortex model is applied to both two-dimensional and axisymmetric sheets. The two-dimensional roll-up is compared to the solution for a semi-infinite sheet with good results.

A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models

DOE PAGES

Guerra, Jorge E.; Ullrich, Paul A.

2016-06-01

Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δ x) modes. Furthermore, high-order accuracymore » also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Lastly, our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.« less

A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guerra, Jorge E.; Ullrich, Paul A.

Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δ x) modes. Furthermore, high-order accuracymore » also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Lastly, our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.« less

Geometric Structure-Preserving Discretization Schemes for Nonlinear Elasticity

DTIC Science & Technology

2015-08-13

conditions. 15.  SUBJECT TERMS geometric theory for nonlinear elasticity, discrete exterior calculus 16.  SECURITY CLASSIFICATION OF: 17.  LIMITATION...associated Laplacian. We use the general theory for approximation of Hilbert complexes and the finite element exterior calculus and introduce some stable mixed

Influence of muscle-tendon complex geometrical parameters on modeling passive stretch behavior with the Discrete Element Method.

PubMed

Roux, A; Laporte, S; Lecompte, J; Gras, L-L; Iordanoff, I

2016-01-25

The muscle-tendon complex (MTC) is a multi-scale, anisotropic, non-homogeneous structure. It is composed of fascicles, gathered together in a conjunctive aponeurosis. Fibers are oriented into the MTC with a pennation angle. Many MTC models use the Finite Element Method (FEM) to simulate the behavior of the MTC as a hyper-viscoelastic material. The Discrete Element Method (DEM) could be adapted to model fibrous materials, such as the MTC. DEM could capture the complex behavior of a material with a simple discretization scheme and help in understanding the influence of the orientation of fibers on the MTC׳s behavior. The aims of this study were to model the MTC in DEM at the macroscopic scale and to obtain the force/displacement curve during a non-destructive passive tensile test. Another aim was to highlight the influence of the geometrical parameters of the MTC on the global mechanical behavior. A geometrical construction of the MTC was done using discrete element linked by springs. Young׳s modulus values of the MTC׳s components were retrieved from the literature to model the microscopic stiffness of each spring. Alignment and re-orientation of all of the muscle׳s fibers with the tensile axis were observed numerically. The hyper-elastic behavior of the MTC was pointed out. The structure׳s effects, added to the geometrical parameters, highlight the MTC׳s mechanical behavior. It is also highlighted by the heterogeneity of the strain of the MTC׳s components. DEM seems to be a promising method to model the hyper-elastic macroscopic behavior of the MTC with simple elastic microscopic elements. Copyright © 2015 Elsevier Ltd. All rights reserved.

An advanced environment for hybrid modeling of biological systems based on modelica.

PubMed

Pross, Sabrina; Bachmann, Bernhard

2011-01-20

Biological systems are often very complex so that an appropriate formalism is needed for modeling their behavior. Hybrid Petri Nets, consisting of time-discrete Petri Net elements as well as continuous ones, have proven to be ideal for this task. Therefore, a new Petri Net library was implemented based on the object-oriented modeling language Modelica which allows the modeling of discrete, stochastic and continuous Petri Net elements by differential, algebraic and discrete equations. An appropriate Modelica-tool performs the hybrid simulation with discrete events and the solution of continuous differential equations. A special sub-library contains so-called wrappers for specific reactions to simplify the modeling process. The Modelica-models can be connected to Simulink-models for parameter optimization, sensitivity analysis and stochastic simulation in Matlab. The present paper illustrates the implementation of the Petri Net component models, their usage within the modeling process and the coupling between the Modelica-tool Dymola and Matlab/Simulink. The application is demonstrated by modeling the metabolism of Chinese Hamster Ovary Cells.

Reactive transport simulation via combination of a multiphase-capable transport code for unstructured meshes with a Gibbs energy minimization solver of geochemical equilibria

NASA Astrophysics Data System (ADS)

Fowler, S. J.; Driesner, T.; Hingerl, F. F.; Kulik, D. A.; Wagner, T.

2011-12-01

We apply a new, C++-based computational model for hydrothermal fluid-rock interaction and scale formation in geothermal reservoirs. The model couples the Complex System Modelling Platform (CSMP++) code for fluid flow in porous and fractured media (Matthai et al., 2007) with the Gibbs energy minimization numerical kernel GEMS3K of the GEM-Selektor (GEMS3) geochemical modelling package (Kulik et al., 2010) in a modular fashion. CSMP++ includes interfaces to commercial file formats, accommodating complex geometry construction using CAD (Rhinoceros) and meshing (ANSYS) software. The CSMP++ approach employs finite element-finite volume spatial discretization, implicit or explicit time discretization, and operator splitting. GEMS3K can calculate complex fluid-mineral equilibria based on a variety of equation of state and activity models. A selection of multi-electrolyte aqueous solution models, such as extended Debye-Huckel, Pitzer (Harvie et al., 1984), EUNIQUAC (Thomsen et al., 1996), and the new ELVIS model (Hingerl et al., this conference), makes it well-suited for application to a wide range of geothermal conditions. An advantage of the GEMS3K solver is simultaneous consideration of complex solid solutions (e.g., clay minerals), gases, fluids, and aqueous solutions. Each coupled simulation results in a thermodynamically-based description of the geochemical and physical state of a hydrothermal system evolving along a complex P-T-X path. The code design allows efficient, flexible incorporation of numerical and thermodynamic database improvements. We demonstrate the coupled code workflow and applicability to compositionally and physically complex natural systems relevant to enhanced geothermal systems, where temporally and spatially varying chemical interactions may take place within diverse lithologies of varying geometry. Engesgaard, P. & Kipp, K. L. (1992). Water Res. Res. 28: 2829-2843. Harvie, C. E.; Møller, N. & Weare, J. H. (1984). Geochim. Cosmochim. Acta 48: 723-751. Kulik, D. A., Wagner, T., Dmytrieva S. V, et al. (2010). GEM-Selektor home page, Paul Scherrer Institut. Available at http://gems.web.psi.ch. Matthäi, S. K., Geiger, S., Roberts, S. G., Paluszny, A., Belayneh, M., Burri, A., Mezentsev, A., Lu, H., Coumou, D., Driesner, T. & Heinrich C. A. (2007). Geol. Soc. London, Spec. Publ. 292: 405-429. Thomsen, K. Rasmussen, P. & Gani, R. (1996). Chem. Eng. Sci. 51: 3675-3683.

Parallelization of PANDA discrete ordinates code using spatial decomposition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Humbert, P.

2006-07-01

We present the parallel method, based on spatial domain decomposition, implemented in the 2D and 3D versions of the discrete Ordinates code PANDA. The spatial mesh is orthogonal and the spatial domain decomposition is Cartesian. For 3D problems a 3D Cartesian domain topology is created and the parallel method is based on a domain diagonal plane ordered sweep algorithm. The parallel efficiency of the method is improved by directions and octants pipelining. The implementation of the algorithm is straightforward using MPI blocking point to point communications. The efficiency of the method is illustrated by an application to the 3D-Ext C5G7more » benchmark of the OECD/NEA. (authors)« less

Improving Our Ability to Evaluate Underlying Mechanisms of Behavioral Onset and Other Event Occurrence Outcomes: A Discrete-Time Survival Mediation Model

PubMed Central

Fairchild, Amanda J.; Abara, Winston E.; Gottschall, Amanda C.; Tein, Jenn-Yun; Prinz, Ronald J.

2015-01-01

The purpose of this article is to introduce and describe a statistical model that researchers can use to evaluate underlying mechanisms of behavioral onset and other event occurrence outcomes. Specifically, the article develops a framework for estimating mediation effects with outcomes measured in discrete-time epochs by integrating the statistical mediation model with discrete-time survival analysis. The methodology has the potential to help strengthen health research by targeting prevention and intervention work more effectively as well as by improving our understanding of discretized periods of risk. The model is applied to an existing longitudinal data set to demonstrate its use, and programming code is provided to facilitate its implementation. PMID:24296470

Multi-level adaptive finite element methods. 1: Variation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1979-01-01

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Conrady, Florian; Hnybida, Jeff; Department of Physics, University of Waterloo, Waterloo, Ontario

2011-01-15

We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete basis diagonalized by J{sup 3} and a continuous basis diagonalized by K{sup 1}, and for both the discrete and continuous series of SU(1,1). For completeness, we also treat the more conventional SU(2) decomposition as a fifth case. The derivation proceeds in a functional/differential framework and exploits the fact that state functions and differential operators have a similar structure in all five cases. The states aremore » defined explicitly and related to SU(1,1) and SU(2) matrix elements.« less

Efficient Polar Coding of Quantum Information

NASA Astrophysics Data System (ADS)

Renes, Joseph M.; Dupuis, Frédéric; Renner, Renato

2012-08-01

Polar coding, introduced 2008 by Arıkan, is the first (very) efficiently encodable and decodable coding scheme whose information transmission rate provably achieves the Shannon bound for classical discrete memoryless channels in the asymptotic limit of large block sizes. Here, we study the use of polar codes for the transmission of quantum information. Focusing on the case of qubit Pauli channels and qubit erasure channels, we use classical polar codes to construct a coding scheme that asymptotically achieves a net transmission rate equal to the coherent information using efficient encoding and decoding operations and code construction. Our codes generally require preshared entanglement between sender and receiver, but for channels with a sufficiently low noise level we demonstrate that the rate of preshared entanglement required is zero.

Development of Multiobjective Optimization Techniques for Sonic Boom Minimization

NASA Technical Reports Server (NTRS)

Chattopadhyay, Aditi; Rajadas, John Narayan; Pagaldipti, Naryanan S.

1996-01-01

A discrete, semi-analytical sensitivity analysis procedure has been developed for calculating aerodynamic design sensitivities. The sensitivities of the flow variables and the grid coordinates are numerically calculated using direct differentiation of the respective discretized governing equations. The sensitivity analysis techniques are adapted within a parabolized Navier Stokes equations solver. Aerodynamic design sensitivities for high speed wing-body configurations are calculated using the semi-analytical sensitivity analysis procedures. Representative results obtained compare well with those obtained using the finite difference approach and establish the computational efficiency and accuracy of the semi-analytical procedures. Multidisciplinary design optimization procedures have been developed for aerospace applications namely, gas turbine blades and high speed wing-body configurations. In complex applications, the coupled optimization problems are decomposed into sublevels using multilevel decomposition techniques. In cases with multiple objective functions, formal multiobjective formulation such as the Kreisselmeier-Steinhauser function approach and the modified global criteria approach have been used. Nonlinear programming techniques for continuous design variables and a hybrid optimization technique, based on a simulated annealing algorithm, for discrete design variables have been used for solving the optimization problems. The optimization procedure for gas turbine blades improves the aerodynamic and heat transfer characteristics of the blades. The two-dimensional, blade-to-blade aerodynamic analysis is performed using a panel code. The blade heat transfer analysis is performed using an in-house developed finite element procedure. The optimization procedure yields blade shapes with significantly improved velocity and temperature distributions. The multidisciplinary design optimization procedures for high speed wing-body configurations simultaneously improve the aerodynamic, the sonic boom and the structural characteristics of the aircraft. The flow solution is obtained using a comprehensive parabolized Navier Stokes solver. Sonic boom analysis is performed using an extrapolation procedure. The aircraft wing load carrying member is modeled as either an isotropic or a composite box beam. The isotropic box beam is analyzed using thin wall theory. The composite box beam is analyzed using a finite element procedure. The developed optimization procedures yield significant improvements in all the performance criteria and provide interesting design trade-offs. The semi-analytical sensitivity analysis techniques offer significant computational savings and allow the use of comprehensive analysis procedures within design optimization studies.

Master standard data quantity food production code. Macro elements for synthesizing production labor time.

PubMed

Matthews, M E; Waldvogel, C F; Mahaffey, M J; Zemel, P C

1978-06-01

Preparation procedures of standardized quantity formulas were analyzed for similarities and differences in production activities, and three entrée classifications were developed, based on these activities. Two formulas from each classification were selected, preparation procedures were divided into elements of production, and the MSD Quantity Food Production Code was applied. Macro elements not included in the existing Code were simulated, coded, assigned associated Time Measurement Units, and added to the MSD Quantity Food Production Code. Repeated occurrence of similar elements within production methods indicated that macro elements could be synthesized for use within one or more entrée classifications. Basic elements were grouped, simulated, and macro elements were derived. Macro elements were applied in the simulated production of 100 portions of each entrée formula. Total production time for each formula and average production time for each entrée classification were calculated. Application of macro elements indicated that this method of predetermining production time was feasible and could be adapted by quantity foodservice managers as a decision technique used to evaluate menu mix, production personnel schedules, and allocation of equipment usage. These macro elements could serve as a basis for further development and refinement of other macro elements which could be applied to a variety of menu item formulas.

Conceptual structure and the procedural affordances of rational numbers: relational reasoning with fractions and decimals.

PubMed

DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J

2015-02-01

The standard number system includes several distinct types of notations, which differ conceptually and afford different procedures. Among notations for rational numbers, the bipartite format of fractions (a/b) enables them to represent 2-dimensional relations between sets of discrete (i.e., countable) elements (e.g., red marbles/all marbles). In contrast, the format of decimals is inherently 1-dimensional, expressing a continuous-valued magnitude (i.e., proportion) but not a 2-dimensional relation between sets of countable elements. Experiment 1 showed that college students indeed view these 2-number notations as conceptually distinct. In a task that did not involve mathematical calculations, participants showed a strong preference to represent partitioned displays of discrete objects with fractions and partitioned displays of continuous masses with decimals. Experiment 2 provided evidence that people are better able to identify and evaluate ratio relationships using fractions than decimals, especially for discrete (or discretized) quantities. Experiments 3 and 4 found a similar pattern of performance for a more complex analogical reasoning task. When solving relational reasoning problems based on discrete or discretized quantities, fractions yielded greater accuracy than decimals; in contrast, when quantities were continuous, accuracy was lower for both symbolic notations. Whereas previous research has established that decimals are more effective than fractions in supporting magnitude comparisons, the present study reveals that fractions are relatively advantageous in supporting relational reasoning with discrete (or discretized) concepts. These findings provide an explanation for the effectiveness of natural frequency formats in supporting some types of reasoning, and have implications for teaching of rational numbers.

77 FR 12098 - Self-Regulatory Organizations; Financial Industry Regulatory Authority, Inc.; Notice of Filing of...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-02-28

... Change FINRA is proposing to amend FINRA Rule 14107 of the Code of Mediation Procedure (``Mediation Code'') to provide the Director of Mediation (``Mediation Director'') with discretion to determine whether parties to a FINRA mediation may select a mediator who is not on FINRA's mediator roster. The text of the...

On the computational aspects of comminution in discrete element method

NASA Astrophysics Data System (ADS)

Chaudry, Mohsin Ali; Wriggers, Peter

2018-04-01

In this paper, computational aspects of crushing/comminution of granular materials are addressed. For crushing, maximum tensile stress-based criterion is used. Crushing model in discrete element method (DEM) is prone to problems of mass conservation and reduction in critical time step. The first problem is addressed by using an iterative scheme which, depending on geometric voids, recovers mass of a particle. In addition, a global-local framework for DEM problem is proposed which tends to alleviate the local unstable motion of particles and increases the computational efficiency.

Discrete element method for emergency flow of pedestrian in S-type corridor.

PubMed

Song, Gyeongwon; Park, Junyoung

2014-10-01

Pedestrian flow in curved corridor should be modeled before design because this type of corridor can be most dangerous part during emergency evacuation. In this study, this flow is analyzed by Discrete Element Method with psychological effects. As the turning slope of corridor increases, the evacuation time is linearly increases. However, in the view of crashed death accident, the case with 90 degree turning slope can be dangerous because there are 3 dangerous points. To solve this matter, the pedestrian gathering together in curved part should be dispersed.

Escript: Open Source Environment For Solving Large-Scale Geophysical Joint Inversion Problems in Python

NASA Astrophysics Data System (ADS)

Gross, Lutz; Altinay, Cihan; Fenwick, Joel; Smith, Troy

2014-05-01

The program package escript has been designed for solving mathematical modeling problems using python, see Gross et al. (2013). Its development and maintenance has been funded by the Australian Commonwealth to provide open source software infrastructure for the Australian Earth Science community (recent funding by the Australian Geophysical Observing System EIF (AGOS) and the AuScope Collaborative Research Infrastructure Scheme (CRIS)). The key concepts of escript are based on the terminology of spatial functions and partial differential equations (PDEs) - an approach providing abstraction from the underlying spatial discretization method (i.e. the finite element method (FEM)). This feature presents a programming environment to the user which is easy to use even for complex models. Due to the fact that implementations are independent from data structures simulations are easily portable across desktop computers and scalable compute clusters without modifications to the program code. escript has been successfully applied in a variety of applications including modeling mantel convection, melting processes, volcanic flow, earthquakes, faulting, multi-phase flow, block caving and mineralization (see Poulet et al. 2013). The recent escript release (see Gross et al. (2013)) provides an open framework for solving joint inversion problems for geophysical data sets (potential field, seismic and electro-magnetic). The strategy bases on the idea to formulate the inversion problem as an optimization problem with PDE constraints where the cost function is defined by the data defect and the regularization term for the rock properties, see Gross & Kemp (2013). This approach of first-optimize-then-discretize avoids the assemblage of the - in general- dense sensitivity matrix as used in conventional approaches where discrete programming techniques are applied to the discretized problem (first-discretize-then-optimize). In this paper we will discuss the mathematical framework for inversion and appropriate solution schemes in escript. We will also give a brief introduction into escript's open framework for defining and solving geophysical inversion problems. Finally we will show some benchmark results to demonstrate the computational scalability of the inversion method across a large number of cores and compute nodes in a parallel computing environment. References: - L. Gross et al. (2013): Escript Solving Partial Differential Equations in Python Version 3.4, The University of Queensland, https://launchpad.net/escript-finley - L. Gross and C. Kemp (2013) Large Scale Joint Inversion of Geophysical Data using the Finite Element Method in escript. ASEG Extended Abstracts 2013, http://dx.doi.org/10.1071/ASEG2013ab306 - T. Poulet, L. Gross, D. Georgiev, J. Cleverley (2012): escript-RT: Reactive transport simulation in Python using escript, Computers & Geosciences, Volume 45, 168-176. http://dx.doi.org/10.1016/j.cageo.2011.11.005.

Analysis of reinforced concrete structures with occurrence of discrete cracks at arbitrary positions

NASA Technical Reports Server (NTRS)

Blaauwendraad, J.; Grootenboer, H. J.; Bouma, A. L.; Reinhardt, H. W.

1980-01-01

A nonlinear analysis of in-plane loaded plates is presented, which eliminates the disadvantages of the smeared crack approach. The elements used and the computational method are discussed. An example is shown in which one or more discrete cracks are dominant.

Blasting, graphical interfaces and Unix

DOE Office of Scientific and Technical Information (OSTI.GOV)

Knudsen, S.; Preece, D.S.

1993-11-01

A discrete element computer program, DMC (Distinct Motion Code) was developed to simulate blast-induced rock motion. To simplify the complex task of entering material and explosive design parameters as well as bench configuration, a full-featured graphical interface has been developed. DMC is currently executed on both Sun SPARCstation 2 and Sun SPARCstation 10 platforms and routinely used to model bench and crater blasting problems. This paper will document the design and development of the full-featured interface to DMC. The development of the interface will be tracked through the various stages, highlighting the adjustments made to allow the necessary parameters tomore » be entered in terms and units that field blasters understand. The paper also discusses a novel way of entering non-integer numbers and the techniques necessary to display blasting parameters in an understandable visual manner. A video presentation will demonstrate the graphics interface and explains its use.« less

Blasting, graphical interfaces and Unix

DOE Office of Scientific and Technical Information (OSTI.GOV)

Knudsen, S.; Preece, D.S.

1994-12-31

A discrete element computer program, DMC (Distinct Motion Code) was developed to simulate blast-induced rock motion. To simplify the complex task of entering material and explosive design parameters as well as bench configuration, a full-featured graphical interface has been developed. DMC is currently executed on both Sun SPARCstation 2 and Sun SPARCstation 10 platforms and routinely used to model bench and crater blasting problems. This paper will document the design and development of the full-featured interface to DMC. The development of the interface will be tracked through the various stages, highlighting the adjustments made to allow the necessary parameters tomore » be entered in terms and units that field blasters understand. The paper also discusses a novel way of entering non-integer numbers and the techniques necessary to display blasting parameters in an understandable visual manner. A video presentation will demonstrate the graphics interface and explains its use.« less

Extension of the frequency-domain pFFT method for wave structure interaction in finite depth

NASA Astrophysics Data System (ADS)

Teng, Bin; Song, Zhi-jie

2017-06-01

To analyze wave interaction with a large scale body in the frequency domain, a precorrected Fast Fourier Transform (pFFT) method has been proposed for infinite depth problems with the deep water Green function, as it can form a matrix with Toeplitz and Hankel properties. In this paper, a method is proposed to decompose the finite depth Green function into two terms, which can form matrices with the Toeplitz and a Hankel properties respectively. Then, a pFFT method for finite depth problems is developed. Based on the pFFT method, a numerical code pFFT-HOBEM is developed with the discretization of high order elements. The model is validated, and examinations on the computing efficiency and memory requirement of the new method have also been carried out. It shows that the new method has the same advantages as that for infinite depth.

Interactive Finite Elements for General Engine Dynamics Analysis

NASA Technical Reports Server (NTRS)

Adams, M. L.; Padovan, J.; Fertis, D. G.

1984-01-01

General nonlinear finite element codes were adapted for the purpose of analyzing the dynamics of gas turbine engines. In particular, this adaptation required the development of a squeeze-film damper element software package and its implantation into a representative current generation code. The ADINA code was selected because of prior use of it and familiarity with its internal structure and logic. This objective was met and the results indicate that such use of general purpose codes is viable alternative to specialized codes for general dynamics analysis of engines.

Displaying radiologic images on personal computers: image storage and compression--Part 2.

PubMed

Gillespy, T; Rowberg, A H

1994-02-01

This is part 2 of our article on image storage and compression, the third article of our series for radiologists and imaging scientists on displaying, manipulating, and analyzing radiologic images on personal computers. Image compression is classified as lossless (nondestructive) or lossy (destructive). Common lossless compression algorithms include variable-length bit codes (Huffman codes and variants), dictionary-based compression (Lempel-Ziv variants), and arithmetic coding. Huffman codes and the Lempel-Ziv-Welch (LZW) algorithm are commonly used for image compression. All of these compression methods are enhanced if the image has been transformed into a differential image based on a differential pulse-code modulation (DPCM) algorithm. The LZW compression after the DPCM image transformation performed the best on our example images, and performed almost as well as the best of the three commercial compression programs tested. Lossy compression techniques are capable of much higher data compression, but reduced image quality and compression artifacts may be noticeable. Lossy compression is comprised of three steps: transformation, quantization, and coding. Two commonly used transformation methods are the discrete cosine transformation and discrete wavelet transformation. In both methods, most of the image information is contained in a relatively few of the transformation coefficients. The quantization step reduces many of the lower order coefficients to 0, which greatly improves the efficiency of the coding (compression) step. In fractal-based image compression, image patterns are stored as equations that can be reconstructed at different levels of resolution.

Note: A non-invasive electronic measurement technique to measure the embedded four resistive elements in a Wheatstone bridge sensor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ravelo Arias, S. I.; Ramírez Muñoz, D.; Cardoso, S.

2015-06-15

The work shows a measurement technique to obtain the correct value of the four elements in a resistive Wheatstone bridge without the need to separate the physical connections existing between them. Two electronic solutions are presented, based on a source-and-measure unit and using discrete electronic components. The proposed technique brings the possibility to know the mismatching or the tolerance between the bridge resistive elements and then to pass or reject it in terms of its related common-mode rejection. Experimental results were taken in various Wheatstone resistive bridges (discrete and magnetoresistive integrated bridges) validating the proposed measurement technique specially when themore » bridge is micro-fabricated and there is no physical way to separate one resistive element from the others.« less

High mobility of large mass movements: a study by means of FEM/DEM simulations

NASA Astrophysics Data System (ADS)

Manzella, I.; Lisjak, A.; Grasselli, G.

2013-12-01

Large mass movements, such as rock avalanches and large volcanic debris avalanches are characterized by extremely long propagation, which cannot be modelled using normal sliding friction law. For this reason several studies and theories derived from field observation, physical theories and laboratory experiments, exist to try to explain their high mobility. In order to investigate more into deep some of the processes recalled by these theories, simulations have been run with a new numerical tool called Y-GUI based on the Finite Element-Discrete Element Method FEM/DEM. The FEM/DEM method is a numerical technique developed by Munjiza et al. (1995) where Discrete Element Method (DEM) algorithms are used to model the interaction between different solids, while Finite Element Method (FEM) principles are used to analyze their deformability being also able to explicitly simulate material sudden loss of cohesion (i.e. brittle failure). In particular numerical tests have been run, inspired by the small-scale experiments done by Manzella and Labiouse (2013). They consist of rectangular blocks released on a slope; each block is a rectangular discrete element made of a mesh of finite elements enabled to fragment. These simulations have highlighted the influence on the propagation of block packing, i.e. whether the elements are piled into geometrical ordinate structure before failure or they are chaotically disposed as a loose material, and of the topography, i.e. whether the slope break is smooth and regular or not. In addition the effect of fracturing, i.e. fragmentation, on the total runout have been studied and highlighted.

Hybrid Discrete Element - Finite Element Simulation for Railway Bridge-Track Interaction

NASA Astrophysics Data System (ADS)

Kaewunruen, S.; Mirza, O.

2017-10-01

At the transition zone or sometimes called ‘bridge end’ or ‘bridge approach’, the stiffness difference between plain track and track over bridge often causes aggravated impact loading due to uneven train movement onto the area. The differential track settlement over the transition has been a classical problem in railway networks, especially for the aging rail infrastructures around the world. This problem is also additionally worsened by the fact that the construction practice over the area is difficult, resulting in a poor compaction of formation and subgrade. This paper presents an advanced hybrid simulation using coupled discrete elements and finite elements to investigate dynamic interaction at the transition zone. The goal is to evaluate the dynamic stresses and to better understand the impact dynamics redistribution at the bridge end. An existing bridge ‘Salt Pan Creek Railway Bridge’, located between Revesby and Kingsgrove, has been chosen for detailed investigation. The Salt Pan Bridge currently demonstrates crushing of the ballast causing significant deformation and damage. Thus, it’s imperative to assess the behaviours of the ballast under dynamic loads. This can be achieved by modelling the nonlinear interactions between the steel rail and sleeper, and sleeper to ballast. The continuum solid elements of track components have been modelled using finite element approach, while the granular media (i.e. ballast) have been simulated by discrete element method. The hybrid DE/FE model demonstrates that ballast experiences significant stresses at the contacts between the sleeper and concrete section. These overburden stress exists in the regions below the outer rails, identify fouling and permanent deformation of the ballast.

Hybrid parallelization of the XTOR-2F code for the simulation of two-fluid MHD instabilities in tokamaks

NASA Astrophysics Data System (ADS)

Marx, Alain; Lütjens, Hinrich

2017-03-01

A hybrid MPI/OpenMP parallel version of the XTOR-2F code [Lütjens and Luciani, J. Comput. Phys. 229 (2010) 8130] solving the two-fluid MHD equations in full tokamak geometry by means of an iterative Newton-Krylov matrix-free method has been developed. The present work shows that the code has been parallelized significantly despite the numerical profile of the problem solved by XTOR-2F, i.e. a discretization with pseudo-spectral representations in all angular directions, the stiffness of the two-fluid stability problem in tokamaks, and the use of a direct LU decomposition to invert the physical pre-conditioner at every Krylov iteration of the solver. The execution time of the parallelized version is an order of magnitude smaller than the sequential one for low resolution cases, with an increasing speedup when the discretization mesh is refined. Moreover, it allows to perform simulations with higher resolutions, previously forbidden because of memory limitations.

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST.

PubMed

Xu, X Q

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (psi,theta,micro) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST

NASA Astrophysics Data System (ADS)

Xu, X. Q.

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (ψ,θ,γ,μ) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

A Multiscale Progressive Failure Modeling Methodology for Composites that Includes Fiber Strength Stochastics

NASA Technical Reports Server (NTRS)

Ricks, Trenton M.; Lacy, Thomas E., Jr.; Bednarcyk, Brett A.; Arnold, Steven M.; Hutchins, John W.

2014-01-01

A multiscale modeling methodology was developed for continuous fiber composites that incorporates a statistical distribution of fiber strengths into coupled multiscale micromechanics/finite element (FE) analyses. A modified two-parameter Weibull cumulative distribution function, which accounts for the effect of fiber length on the probability of failure, was used to characterize the statistical distribution of fiber strengths. A parametric study using the NASA Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) was performed to assess the effect of variable fiber strengths on local composite failure within a repeating unit cell (RUC) and subsequent global failure. The NASA code FEAMAC and the ABAQUS finite element solver were used to analyze the progressive failure of a unidirectional SCS-6/TIMETAL 21S metal matrix composite tensile dogbone specimen at 650 degC. Multiscale progressive failure analyses were performed to quantify the effect of spatially varying fiber strengths on the RUC-averaged and global stress-strain responses and failure. The ultimate composite strengths and distribution of failure locations (predominately within the gage section) reasonably matched the experimentally observed failure behavior. The predicted composite failure behavior suggests that use of macroscale models that exploit global geometric symmetries are inappropriate for cases where the actual distribution of local fiber strengths displays no such symmetries. This issue has not received much attention in the literature. Moreover, the model discretization at a specific length scale can have a profound effect on the computational costs associated with multiscale simulations.models that yield accurate yet tractable results.

External details revisited - A new taxonomy for coding 'non-episodic' content during autobiographical memory retrieval.

PubMed

Strikwerda-Brown, Cherie; Mothakunnel, Annu; Hodges, John R; Piguet, Olivier; Irish, Muireann

2018-04-24

Autobiographical memory (ABM) is typically held to comprise episodic and semantic elements, with the vast majority of studies to date focusing on profiles of episodic details in health and disease. In this context, 'non-episodic' elements are often considered to reflect semantic processing or are discounted from analyses entirely. Mounting evidence suggests that rather than reflecting one unitary entity, semantic autobiographical information may contain discrete subcomponents, which vary in their relative degree of semantic or episodic content. This study aimed to (1) review the existing literature to formally characterize the variability in analysis of 'non-episodic' content (i.e., external details) on the Autobiographical Interview and (2) use these findings to create a theoretically grounded framework for coding external details. Our review exposed discrepancies in the reporting and interpretation of external details across studies, reinforcing the need for a new, consistent approach. We validated our new external details scoring protocol (the 'NExt' taxonomy) in patients with Alzheimer's disease (n = 18) and semantic dementia (n = 13), and 20 healthy older Control participants and compared profiles of the NExt subcategories across groups and time periods. Our results revealed increased sensitivity of the NExt taxonomy in discriminating between ABM profiles of patient groups, when compared to traditionally used internal and external detail metrics. Further, remote and recent autobiographical memories displayed distinct compositions of the NExt detail types. This study is the first to provide a fine-grained and comprehensive taxonomy to parse external details into intuitive subcategories and to validate this protocol in neurodegenerative disorders. © 2018 The British Psychological Society.

RINGMesh: A programming library for developing mesh-based geomodeling applications

NASA Astrophysics Data System (ADS)

Pellerin, Jeanne; Botella, Arnaud; Bonneau, François; Mazuyer, Antoine; Chauvin, Benjamin; Lévy, Bruno; Caumon, Guillaume

2017-07-01

RINGMesh is a C++ open-source programming library for manipulating discretized geological models. It is designed to ease the development of applications and workflows that use discretized 3D models. It is neither a geomodeler, nor a meshing software. RINGMesh implements functionalities to read discretized surface-based or volumetric structural models and to check their validity. The models can be then exported in various file formats. RINGMesh provides data structures to represent geological structural models, either defined by their discretized boundary surfaces, and/or by discretized volumes. A programming interface allows to develop of new geomodeling methods, and to plug in external software. The goal of RINGMesh is to help researchers to focus on the implementation of their specific method rather than on tedious tasks common to many applications. The documented code is open-source and distributed under the modified BSD license. It is available at https://www.ring-team.org/index.php/software/ringmesh.

Codestream-Based Identification of JPEG 2000 Images with Different Coding Parameters

NASA Astrophysics Data System (ADS)

Watanabe, Osamu; Fukuhara, Takahiro; Kiya, Hitoshi

A method of identifying JPEG 2000 images with different coding parameters, such as code-block sizes, quantization-step sizes, and resolution levels, is presented. It does not produce false-negative matches regardless of different coding parameters (compression rate, code-block size, and discrete wavelet transform (DWT) resolutions levels) or quantization step sizes. This feature is not provided by conventional methods. Moreover, the proposed approach is fast because it uses the number of zero-bit-planes that can be extracted from the JPEG 2000 codestream by only parsing the header information without embedded block coding with optimized truncation (EBCOT) decoding. The experimental results revealed the effectiveness of image identification based on the new method.

FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Regnier, D.; Dubray, N.; Verriere, M.

The time-dependent generator coordinate method (TDGCM) is a powerful method to study the large amplitude collective motion of quantum many-body systems such as atomic nuclei. Under the Gaussian Overlap Approximation (GOA), the TDGCM leads to a local, time-dependent Schrödinger equation in a multi-dimensional collective space. In this study, we present the version 2.0 of the code FELIX that solves the collective Schrödinger equation in a finite element basis. This new version features: (i) the ability to solve a generalized TDGCM+GOA equation with a metric term in the collective Hamiltonian, (ii) support for new kinds of finite elements and different typesmore » of quadrature to compute the discretized Hamiltonian and overlap matrices, (iii) the possibility to leverage the spectral element scheme, (iv) an explicit Krylov approximation of the time propagator for time integration instead of the implicit Crank–Nicolson method implemented in the first version, (v) an entirely redesigned workflow. We benchmark this release on an analytic problem as well as on realistic two-dimensional calculations of the low-energy fission of 240Pu and 256Fm. Low to moderate numerical precision calculations are most efficiently performed with simplex elements with a degree 2 polynomial basis. Higher precision calculations should instead use the spectral element method with a degree 4 polynomial basis. Finally, we emphasize that in a realistic calculation of fission mass distributions of 240Pu, FELIX-2.0 is about 20 times faster than its previous release (within a numerical precision of a few percents).« less

FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

DOE PAGES

Regnier, D.; Dubray, N.; Verriere, M.; ...

2017-12-20

The time-dependent generator coordinate method (TDGCM) is a powerful method to study the large amplitude collective motion of quantum many-body systems such as atomic nuclei. Under the Gaussian Overlap Approximation (GOA), the TDGCM leads to a local, time-dependent Schrödinger equation in a multi-dimensional collective space. In this study, we present the version 2.0 of the code FELIX that solves the collective Schrödinger equation in a finite element basis. This new version features: (i) the ability to solve a generalized TDGCM+GOA equation with a metric term in the collective Hamiltonian, (ii) support for new kinds of finite elements and different typesmore » of quadrature to compute the discretized Hamiltonian and overlap matrices, (iii) the possibility to leverage the spectral element scheme, (iv) an explicit Krylov approximation of the time propagator for time integration instead of the implicit Crank–Nicolson method implemented in the first version, (v) an entirely redesigned workflow. We benchmark this release on an analytic problem as well as on realistic two-dimensional calculations of the low-energy fission of 240Pu and 256Fm. Low to moderate numerical precision calculations are most efficiently performed with simplex elements with a degree 2 polynomial basis. Higher precision calculations should instead use the spectral element method with a degree 4 polynomial basis. Finally, we emphasize that in a realistic calculation of fission mass distributions of 240Pu, FELIX-2.0 is about 20 times faster than its previous release (within a numerical precision of a few percents).« less

Discrete elements for 3D microfluidics.

PubMed

Bhargava, Krisna C; Thompson, Bryant; Malmstadt, Noah

2014-10-21

Microfluidic systems are rapidly becoming commonplace tools for high-precision materials synthesis, biochemical sample preparation, and biophysical analysis. Typically, microfluidic systems are constructed in monolithic form by means of microfabrication and, increasingly, by additive techniques. These methods restrict the design and assembly of truly complex systems by placing unnecessary emphasis on complete functional integration of operational elements in a planar environment. Here, we present a solution based on discrete elements that liberates designers to build large-scale microfluidic systems in three dimensions that are modular, diverse, and predictable by simple network analysis techniques. We develop a sample library of standardized components and connectors manufactured using stereolithography. We predict and validate the flow characteristics of these individual components to design and construct a tunable concentration gradient generator with a scalable number of parallel outputs. We show that these systems are rapidly reconfigurable by constructing three variations of a device for generating monodisperse microdroplets in two distinct size regimes and in a high-throughput mode by simple replacement of emulsifier subcircuits. Finally, we demonstrate the capability for active process monitoring by constructing an optical sensing element for detecting water droplets in a fluorocarbon stream and quantifying their size and frequency. By moving away from large-scale integration toward standardized discrete elements, we demonstrate the potential to reduce the practice of designing and assembling complex 3D microfluidic circuits to a methodology comparable to that found in the electronics industry.

A finite element-based algorithm for rubbing induced vibration prediction in rotors

NASA Astrophysics Data System (ADS)

Behzad, Mehdi; Alvandi, Mehdi; Mba, David; Jamali, Jalil

2013-10-01

In this paper, an algorithm is developed for more realistic investigation of rotor-to-stator rubbing vibration, based on finite element theory with unilateral contact and friction conditions. To model the rotor, cross sections are assumed to be radially rigid. A finite element discretization based on traditional beam theories which sufficiently accounts for axial and transversal flexibility of the rotor is used. A general finite element discretization model considering inertial and viscoelastic characteristics of the stator is used for modeling the stator. Therefore, for contact analysis, only the boundary of the stator is discretized. The contact problem is defined as the contact between the circular rigid cross section of the rotor and “nodes” of the stator only. Next, Gap function and contact conditions are described for the contact problem. Two finite element models of the rotor and the stator are coupled via the Lagrange multipliers method in order to obtain the constrained equation of motion. A case study of the partial rubbing is simulated using the algorithm. The synchronous and subsynchronous responses of the partial rubbing are obtained for different rotational speeds. In addition, a sensitivity analysis is carried out with respect to the initial clearance, the stator stiffness, the damping parameter, and the coefficient of friction. There is a good agreement between the result of this research and the experimental result in the literature.

Writing analytic element programs in Python.

PubMed

Bakker, Mark; Kelson, Victor A

2009-01-01

The analytic element method is a mesh-free approach for modeling ground water flow at both the local and the regional scale. With the advent of the Python object-oriented programming language, it has become relatively easy to write analytic element programs. In this article, an introduction is given of the basic principles of the analytic element method and of the Python programming language. A simple, yet flexible, object-oriented design is presented for analytic element codes using multiple inheritance. New types of analytic elements may be added without the need for any changes in the existing part of the code. The presented code may be used to model flow to wells (with either a specified discharge or drawdown) and streams (with a specified head). The code may be extended by any hydrogeologist with a healthy appetite for writing computer code to solve more complicated ground water flow problems. Copyright © 2009 The Author(s). Journal Compilation © 2009 National Ground Water Association.

1963 Vajont rock slide: a comparison between 3D DEM and 3D FEM

NASA Astrophysics Data System (ADS)

Crosta, Giovanni; Utili, Stefano; Castellanza, Riccardo; Agliardi, Federico; Bistacchi, Andrea; Weng Boon, Chia

2013-04-01

Data on the exact location of the failure surface of the landslide have been used as the starting point for the modelling of the landslide. 3 dimensional numerical analyses were run employing both the discrete element method (DEM) and a Finite Element Method (FEM) code. In this work the focus is on the prediction of the movement of the landlside during its initial phase of detachment from Mount Toc. The results obtained by the two methods are compared and conjectures on the observed discrepancies of the predictions between the two methods are formulated. In the DEM simulations the internal interaction of the sliding blocks and the expansion of the debris is obtained as a result of the kinematic interaction among the rock blocks resulting from the jointing of the rock mass involved in the slide. In the FEM analyses, the c-phi reduction technique was employed along the predefine failure surface until the onset of the landslide occurred. In particular, two major blocks of the landslide were identified and the stress, strain and displacement fields at the interface between the two blocks were analysed in detail.

An efficient numerical model for multicomponent compressible flow in fractured porous media

NASA Astrophysics Data System (ADS)

Zidane, Ali; Firoozabadi, Abbas

2014-12-01

An efficient and accurate numerical model for multicomponent compressible single-phase flow in fractured media is presented. The discrete-fracture approach is used to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross flow equilibrium in the fractures. This will allow large matrix elements in the neighborhood of the fractures and considerable speed up of the algorithm. We use an implicit finite volume (FV) scheme to solve the species mass balance equation in the fractures. This step avoids the use of Courant-Freidricks-Levy (CFL) condition and contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix. Four numerical examples are presented to demonstrate the robustness and efficiency of the proposed model. We show that the combination of the fracture cross-flow equilibrium and the implicit composition calculation in the fractures increase the computational speed 20-130 times in 2D. In 3D, one may expect even a higher computational efficiency.

Verification of continuum drift kinetic equation solvers in NIMROD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Held, E. D.; Ji, J.-Y.; Kruger, S. E.

Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speedmore » coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.« less

Dynamic Response of Functionally Graded Carbon Nanotube Reinforced Sandwich Plate

NASA Astrophysics Data System (ADS)

Mehar, Kulmani; Panda, Subrata Kumar

2018-03-01

In this article, the dynamic response of the carbon nanotube-reinforced functionally graded sandwich composite plate has been studied numerically with the help of finite element method. The face sheets of the sandwich composite plate are made of carbon nanotube- reinforced composite for two different grading patterns whereas the core phase is taken as isotropic material. The final properties of the structure are calculated using the rule of mixture. The geometrical model of the sandwich plate is developed and discretized suitably with the help of available shell element in ANSYS library. Subsequently, the corresponding numerical dynamic responses computed via batch input technique (parametric design language code in ANSYS) of ANSYS including Newmark’s integration scheme. The stability of the sandwich structural numerical model is established through the proper convergence study. Further, the reliability of the sandwich model is checked by comparison study between present and available results from references. As a final point, some numerical problems have been solved to examine the effect of different design constraints (carbon nanotube distribution pattern, core to face thickness ratio, volume fractions of the nanotube, length to thickness ratio, aspect ratio and constraints at edges) on the time-responses of sandwich plate.

Computer-Aided Transformation of PDE Models: Languages, Representations, and a Calculus of Operations

DTIC Science & Technology

2016-01-05

discretizations . We maintain that what is clear at the mathematical level should be equally clear in computation. In this small STIR project, we separate the...concerns of describing and discretizing such models by defining an input language representing PDE, including steady-state and tran- sient, linear and...solvers, such as [8, 9], focused on the solvers themselves and particular families of discretizations (e. g. finite elements), and now it is natural to

Finite Element Aircraft Simulation of Turbulence

DOT National Transportation Integrated Search

1997-02-01

A Simulation of Rotor Blade Element Turbulence (SORBET) model has been : developed for realtime aircraft simulation that accommodates stochastic : turbulence and distributed discrete gusts as a function of the terrain. This : model is applicable to c...

Parallel, adaptive finite element methods for conservation laws

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Devine, Karen D.; Flaherty, Joseph E.

1994-01-01

We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.

The nonconforming virtual element method for eigenvalue problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gardini, Francesca; Manzini, Gianmarco; Vacca, Giuseppe

We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L 2-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numericalmore » tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.« less

Transition from Target to Gaze Coding in Primate Frontal Eye Field during Memory Delay and Memory–Motor Transformation123

PubMed Central

Sajad, Amirsaman; Sadeh, Morteza; Yan, Xiaogang; Wang, Hongying

2016-01-01

Abstract The frontal eye fields (FEFs) participate in both working memory and sensorimotor transformations for saccades, but their role in integrating these functions through time remains unclear. Here, we tracked FEF spatial codes through time using a novel analytic method applied to the classic memory-delay saccade task. Three-dimensional recordings of head-unrestrained gaze shifts were made in two monkeys trained to make gaze shifts toward briefly flashed targets after a variable delay (450-1500 ms). A preliminary analysis of visual and motor response fields in 74 FEF neurons eliminated most potential models for spatial coding at the neuron population level, as in our previous study (Sajad et al., 2015). We then focused on the spatiotemporal transition from an eye-centered target code (T; preferred in the visual response) to an eye-centered intended gaze position code (G; preferred in the movement response) during the memory delay interval. We treated neural population codes as a continuous spatiotemporal variable by dividing the space spanning T and G into intermediate T–G models and dividing the task into discrete steps through time. We found that FEF delay activity, especially in visuomovement cells, progressively transitions from T through intermediate T–G codes that approach, but do not reach, G. This was followed by a final discrete transition from these intermediate T–G delay codes to a “pure” G code in movement cells without delay activity. These results demonstrate that FEF activity undergoes a series of sensory–memory–motor transformations, including a dynamically evolving spatial memory signal and an imperfect memory-to-motor transformation. PMID:27092335

SilMush: A procedure for modeling of the geochemical evolution of silicic magmas and granitic rocks

NASA Astrophysics Data System (ADS)

Hertogen, Jan; Mareels, Joyce

2016-07-01

A boundary layer crystallization modeling program is presented that specifically addresses the chemical fractionation in silicic magma systems and the solidification of plutonic bodies. The model is a Langmuir (1989) type approach and does not invoke crystal settling in high-viscosity silicic melts. The primary aim is to model a granitic rock as a congealed crystal-liquid mush, and to integrate major element and trace element modeling. The procedure allows for some exploratory investigation of the exsolution of H2O-fluids and of the fluid/melt partitioning of trace elements. The procedure is implemented as a collection of subroutines for the MS Excel spreadsheet environment and is coded in the Visual Basic for Applications (VBA) language. To increase the flexibility of the modeling, the procedure is based on discrete numeric process simulation rather than on solution of continuous differential equations. The program is applied to a study of the geochemical variation within and among three granitic units (Senones, Natzwiller, Kagenfels) from the Variscan Northern Vosges Massif, France. The three units cover the compositional range from monzogranite, over syenogranite to alkali-feldspar granite. An extensive set of new major element and trace element data is presented. Special attention is paid to the essential role of accessory minerals in the fractionation of the Rare Earth Elements. The crystallization model is able to reproduce the essential major and trace element variation trends in the data sets of the three separate granitic plutons. The Kagenfels alkali-feldspar leucogranite couples very limited variation in major element composition to a considerable and complex variation of trace elements. The modeling results can serve as a guide for the reconstruction of the emplacement sequence of petrographically distinct units. Although the modeling procedure essentially deals with geochemical fractionation within a single pluton, the modeling results bring up a number of questions about the petrogenetic relationships among parental magmas of nearly coeval granitic units emplaced in close proximity.

Discrete space charge affected field emission: Flat and hemisphere emitters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jensen, Kevin L., E-mail: kevin.jensen@nrl.navy.mil; Shiffler, Donald A.; Tang, Wilkin

Models of space-charge affected thermal-field emission from protrusions, able to incorporate the effects of both surface roughness and elongated field emitter structures in beam optics codes, are desirable but difficult. The models proposed here treat the meso-scale diode region separate from the micro-scale regions characteristic of the emission sites. The consequences of discrete emission events are given for both one-dimensional (sheets of charge) and three dimensional (rings of charge) models: in the former, results converge to steady state conditions found by theory (e.g., Rokhlenko et al. [J. Appl. Phys. 107, 014904 (2010)]) but show oscillatory structure as they do. Surfacemore » roughness or geometric features are handled using a ring of charge model, from which the image charges are found and used to modify the apex field and emitted current. The roughness model is shown to have additional constraints related to the discrete nature of electron charge. The ability of a unit cell model to treat field emitter structures and incorporate surface roughness effects inside a beam optics code is assessed.« less

Computation of Steady and Unsteady Laminar Flames: Theory

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Radhakrishnan, Krishnan; Zhou, Ruhai

1999-01-01

In this paper we describe the numerical analysis underlying our efforts to develop an accurate and reliable code for simulating flame propagation using complex physical and chemical models. We discuss our spatial and temporal discretization schemes, which in our current implementations range in order from two to six. In space we use staggered meshes to define discrete divergence and gradient operators, allowing us to approximate complex diffusion operators while maintaining ellipticity. Our temporal discretization is based on the use of preconditioning to produce a highly efficient linearly implicit method with good stability properties. High order for time accurate simulations is obtained through the use of extrapolation or deferred correction procedures. We also discuss our techniques for computing stationary flames. The primary issue here is the automatic generation of initial approximations for the application of Newton's method. We use a novel time-stepping procedure, which allows the dynamic updating of the flame speed and forces the flame front towards a specified location. Numerical experiments are presented, primarily for the stationary flame problem. These illustrate the reliability of our techniques, and the dependence of the results on various code parameters.

Matrix-Free Polynomial-Based Nonlinear Least Squares Optimized Preconditioning and its Application to Discontinuous Galerkin Discretizations of the Euler Equations

DTIC Science & Technology

2015-06-01

cient parallel code for applying the operator. Our method constructs a polynomial preconditioner using a nonlinear least squares (NLLS) algorithm. We show...apply the underlying operator. Such a preconditioner can be very attractive in scenarios where one has a highly efficient parallel code for applying...repeatedly solve a large system of linear equations where one has an extremely fast parallel code for applying an underlying fixed linear operator

APC: A New Code for Atmospheric Polarization Computations

NASA Technical Reports Server (NTRS)

Korkin, Sergey V.; Lyapustin, Alexei I.; Rozanov, Vladimir V.

2014-01-01

A new polarized radiative transfer code Atmospheric Polarization Computations (APC) is described. The code is based on separation of the diffuse light field into anisotropic and smooth (regular) parts. The anisotropic part is computed analytically. The smooth regular part is computed numerically using the discrete ordinates method. Vertical stratification of the atmosphere, common types of bidirectional surface reflection and scattering by spherical particles or spheroids are included. A particular consideration is given to computation of the bidirectional polarization distribution function (BPDF) of the waved ocean surface.

A discrete Fourier transform for virtual memory machines

NASA Technical Reports Server (NTRS)

Galant, David C.

1992-01-01

An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.

Visual Tracking via Sparse and Local Linear Coding.

PubMed

Wang, Guofeng; Qin, Xueying; Zhong, Fan; Liu, Yue; Li, Hongbo; Peng, Qunsheng; Yang, Ming-Hsuan

2015-11-01

The state search is an important component of any object tracking algorithm. Numerous algorithms have been proposed, but stochastic sampling methods (e.g., particle filters) are arguably one of the most effective approaches. However, the discretization of the state space complicates the search for the precise object location. In this paper, we propose a novel tracking algorithm that extends the state space of particle observations from discrete to continuous. The solution is determined accurately via iterative linear coding between two convex hulls. The algorithm is modeled by an optimal function, which can be efficiently solved by either convex sparse coding or locality constrained linear coding. The algorithm is also very flexible and can be combined with many generic object representations. Thus, we first use sparse representation to achieve an efficient searching mechanism of the algorithm and demonstrate its accuracy. Next, two other object representation models, i.e., least soft-threshold squares and adaptive structural local sparse appearance, are implemented with improved accuracy to demonstrate the flexibility of our algorithm. Qualitative and quantitative experimental results demonstrate that the proposed tracking algorithm performs favorably against the state-of-the-art methods in dynamic scenes.

Direct Discrete Method for Neutronic Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vosoughi, Naser; Akbar Salehi, Ali; Shahriari, Majid

The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for amore » cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution. (authors)« less

A Bell-Curved Based Algorithm for Mixed Continuous and Discrete Structural Optimization

NASA Technical Reports Server (NTRS)

Kincaid, Rex K.; Weber, Michael; Sobieszczanski-Sobieski, Jaroslaw

2001-01-01

An evolutionary based strategy utilizing two normal distributions to generate children is developed to solve mixed integer nonlinear programming problems. This Bell-Curve Based (BCB) evolutionary algorithm is similar in spirit to (mu + mu) evolutionary strategies and evolutionary programs but with fewer parameters to adjust and no mechanism for self adaptation. First, a new version of BCB to solve purely discrete optimization problems is described and its performance tested against a tabu search code for an actuator placement problem. Next, the performance of a combined version of discrete and continuous BCB is tested on 2-dimensional shape problems and on a minimum weight hub design problem. In the latter case the discrete portion is the choice of the underlying beam shape (I, triangular, circular, rectangular, or U).

Convergence Analysis of Triangular MAC Schemes for Two Dimensional Stokes Equations

PubMed Central

Wang, Ming; Zhong, Lin

2015-01-01

In this paper, we consider the use of H(div) elements in the velocity–pressure formulation to discretize Stokes equations in two dimensions. We address the error estimate of the element pair RT0–P0, which is known to be suboptimal, and render the error estimate optimal by the symmetry of the grids and by the superconvergence result of Lagrange inter-polant. By enlarging RT0 such that it becomes a modified BDM-type element, we develop a new discretization BDM1b–P0. We, therefore, generalize the classical MAC scheme on rectangular grids to triangular grids and retain all the desirable properties of the MAC scheme: exact divergence-free, solver-friendly, and local conservation of physical quantities. Further, we prove that the proposed discretization BDM1b–P0 achieves the optimal convergence rate for both velocity and pressure on general quasi-uniform grids, and one and half order convergence rate for the vorticity and a recovered pressure. We demonstrate the validity of theories developed here by numerical experiments. PMID:26041948

SECIS elements in the coding regions of selenoprotein transcripts are functional in higher eukaryotes

PubMed Central

Mix, Heiko; Lobanov, Alexey V.; Gladyshev, Vadim N.

2007-01-01

Expression of selenocysteine (Sec)-containing proteins requires the presence of a cis-acting mRNA structure, called selenocysteine insertion sequence (SECIS) element. In bacteria, this structure is located in the coding region immediately downstream of the Sec-encoding UGA codon, whereas in eukaryotes a completely different SECIS element has evolved in the 3′-untranslated region. Here, we report that SECIS elements in the coding regions of selenoprotein mRNAs support Sec insertion in higher eukaryotes. Comprehensive computational analysis of all available viral genomes revealed a SECIS element within the ORF of a naturally occurring selenoprotein homolog of glutathione peroxidase 4 in fowlpox virus. The fowlpox SECIS element supported Sec insertion when expressed in mammalian cells as part of the coding region of viral or mammalian selenoproteins. In addition, readthrough at UGA was observed when the viral SECIS element was located upstream of the Sec codon. We also demonstrate successful de novo design of a functional SECIS element in the coding region of a mammalian selenoprotein. Our data provide evidence that the location of the SECIS element in the untranslated region is not a functional necessity but rather is an evolutionary adaptation to enable a more efficient synthesis of selenoproteins. PMID:17169995

Ice Shape Characterization Using Self-Organizing Maps

NASA Technical Reports Server (NTRS)

McClain, Stephen T.; Tino, Peter; Kreeger, Richard E.

2011-01-01

A method for characterizing ice shapes using a self-organizing map (SOM) technique is presented. Self-organizing maps are neural-network techniques for representing noisy, multi-dimensional data aligned along a lower-dimensional and possibly nonlinear manifold. For a large set of noisy data, each element of a finite set of codebook vectors is iteratively moved in the direction of the data closest to the winner codebook vector. Through successive iterations, the codebook vectors begin to align with the trends of the higher-dimensional data. In information processing, the intent of SOM methods is to transmit the codebook vectors, which contains far fewer elements and requires much less memory or bandwidth, than the original noisy data set. When applied to airfoil ice accretion shapes, the properties of the codebook vectors and the statistical nature of the SOM methods allows for a quantitative comparison of experimentally measured mean or average ice shapes to ice shapes predicted using computer codes such as LEWICE. The nature of the codebook vectors also enables grid generation and surface roughness descriptions for use with the discrete-element roughness approach. In the present study, SOM characterizations are applied to a rime ice shape, a glaze ice shape at an angle of attack, a bi-modal glaze ice shape, and a multi-horn glaze ice shape. Improvements and future explorations will be discussed.

BRYNTRN: A baryon transport model

NASA Technical Reports Server (NTRS)

Wilson, John W.; Townsend, Lawrence W.; Nealy, John E.; Chun, Sang Y.; Hong, B. S.; Buck, Warren W.; Lamkin, S. L.; Ganapol, Barry D.; Khan, Ferdous; Cucinotta, Francis A.

1989-01-01

The development of an interaction data base and a numerical solution to the transport of baryons through an arbitrary shield material based on a straight ahead approximation of the Boltzmann equation are described. The code is most accurate for continuous energy boundary values, but gives reasonable results for discrete spectra at the boundary using even a relatively coarse energy grid (30 points) and large spatial increments (1 cm in H2O). The resulting computer code is self-contained, efficient and ready to use. The code requires only a very small fraction of the computer resources required for Monte Carlo codes.

Code CUGEL: A code to unfold Ge(Li) spectrometer polyenergetic gamma photon experimental distributions

NASA Technical Reports Server (NTRS)

Steyn, J. J.; Born, U.

1970-01-01

A FORTRAN code was developed for the Univac 1108 digital computer to unfold lithium-drifted germanium semiconductor spectrometers, polyenergetic gamma photon experimental distributions. It was designed to analyze the combination continuous and monoenergetic gamma radiation field of radioisotope volumetric sources. The code generates the detector system response matrix function and applies it to monoenergetic spectral components discretely and to the continuum iteratively. It corrects for system drift, source decay, background, and detection efficiency. Results are presented in digital form for differential and integrated photon number and energy distributions, and for exposure dose.

Three-dimensional geoelectric modelling with optimal work/accuracy rate using an adaptive wavelet algorithm

NASA Astrophysics Data System (ADS)

Plattner, A.; Maurer, H. R.; Vorloeper, J.; Dahmen, W.

2010-08-01

Despite the ever-increasing power of modern computers, realistic modelling of complex 3-D earth models is still a challenging task and requires substantial computing resources. The overwhelming majority of current geophysical modelling approaches includes either finite difference or non-adaptive finite element algorithms and variants thereof. These numerical methods usually require the subsurface to be discretized with a fine mesh to accurately capture the behaviour of the physical fields. However, this may result in excessive memory consumption and computing times. A common feature of most of these algorithms is that the modelled data discretizations are independent of the model complexity, which may be wasteful when there are only minor to moderate spatial variations in the subsurface parameters. Recent developments in the theory of adaptive numerical solvers have the potential to overcome this problem. Here, we consider an adaptive wavelet-based approach that is applicable to a large range of problems, also including nonlinear problems. In comparison with earlier applications of adaptive solvers to geophysical problems we employ here a new adaptive scheme whose core ingredients arose from a rigorous analysis of the overall asymptotically optimal computational complexity, including in particular, an optimal work/accuracy rate. Our adaptive wavelet algorithm offers several attractive features: (i) for a given subsurface model, it allows the forward modelling domain to be discretized with a quasi minimal number of degrees of freedom, (ii) sparsity of the associated system matrices is guaranteed, which makes the algorithm memory efficient and (iii) the modelling accuracy scales linearly with computing time. We have implemented the adaptive wavelet algorithm for solving 3-D geoelectric problems. To test its performance, numerical experiments were conducted with a series of conductivity models exhibiting varying degrees of structural complexity. Results were compared with a non-adaptive finite element algorithm, which incorporates an unstructured mesh to best-fitting subsurface boundaries. Such algorithms represent the current state-of-the-art in geoelectric modelling. An analysis of the numerical accuracy as a function of the number of degrees of freedom revealed that the adaptive wavelet algorithm outperforms the finite element solver for simple and moderately complex models, whereas the results become comparable for models with high spatial variability of electrical conductivities. The linear dependence of the modelling error and the computing time proved to be model-independent. This feature will allow very efficient computations using large-scale models as soon as our experimental code is optimized in terms of its implementation.

Assessment of Different Discrete Particle Methods Ability To Predict Gas-Particle Flow in a Small-Scale Fluidized Bed

DOE PAGES

Lu, Liqiang; Gopalan, Balaji; Benyahia, Sofiane

2017-06-21

Several discrete particle methods exist in the open literature to simulate fluidized bed systems, such as discrete element method (DEM), time driven hard sphere (TDHS), coarse-grained particle method (CGPM), coarse grained hard sphere (CGHS), and multi-phase particle-in-cell (MP-PIC). These different approaches usually solve the fluid phase in a Eulerian fixed frame of reference and the particle phase using the Lagrangian method. The first difference between these models lies in tracking either real particles or lumped parcels. The second difference is in the treatment of particle-particle interactions: by calculating collision forces (DEM and CGPM), using momentum conservation laws (TDHS and CGHS),more » or based on particle stress model (MP-PIC). These major model differences lead to a wide range of results accuracy and computation speed. However, these models have never been compared directly using the same experimental dataset. In this research, a small-scale fluidized bed is simulated with these methods using the same open-source code MFIX. The results indicate that modeling the particle-particle collision by TDHS increases the computation speed while maintaining good accuracy. Also, lumping few particles in a parcel increases the computation speed with little loss in accuracy. However, modeling particle-particle interactions with solids stress leads to a big loss in accuracy with a little increase in computation speed. The MP-PIC method predicts an unphysical particle-particle overlap, which results in incorrect voidage distribution and incorrect overall bed hydrodynamics. Based on this study, we recommend using the CGHS method for fluidized bed simulations due to its computational speed that rivals that of MPPIC while maintaining a much better accuracy.« less

Seismic response of rock slopes: Numerical investigations on the role of internal structure

NASA Astrophysics Data System (ADS)

Arnold, L.; Applegate, K.; Gibson, M.; Wartman, J.; Adams, S.; Maclaughlin, M.; Smith, S.; Keefer, D. K.

2013-12-01

The stability of rock slopes is significantly influenced and often controlled by the internal structure of the slope created by such discontinuities as joints, shear zones, and faults. Under seismic conditions, these discontinuities influence both the resistance of a slope to failure and its response to dynamic loading. The dynamic response, which can be characterized by the slope's natural frequency and amplification of ground motion, governs the loading experienced by the slope in a seismic event and, therefore, influences the slope's stability. In support of the Network for Earthquake Engineering Simulation (NEES) project Seismically-Induced Rock Slope Failure: Mechanisms and Prediction (NEESROCK), we conducted a 2D numerical investigation using the discrete element method (DEM) coupled with simple discrete fracture networks (DFNs). The intact rock mass is simulated with a bonded assembly of discrete particles, commonly referred to as the bonded-particle model (BPM) for rock. Discontinuities in the BPM are formed by the insertion of smooth, unbonded contacts along specified planes. The influence of discontinuity spacing, orientation, and stiffness on slope natural frequency and amplification was investigated with the commercially available Particle Flow Code (PFC2D). Numerical results indicate that increased discontinuity spacing has a non-linear effect in decreasing the amplification and increasing the natural frequency of the slope. As discontinuity dip changes from sub-horizontal to sub-vertical, the slope's level of amplification increases while the natural frequency of the slope decreases. Increased joint stiffness decreases amplification and increases natural frequency. The results reveal that internal structure has a strong influence on rock slope dynamics that can significantly change the system's dynamic response and stability during seismic loading. Financial support for this research was provided by the United States National Science Foundation (NSF) under grant CMMI-1156413.

Assessment of Different Discrete Particle Methods Ability To Predict Gas-Particle Flow in a Small-Scale Fluidized Bed

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Liqiang; Gopalan, Balaji; Benyahia, Sofiane

Several discrete particle methods exist in the open literature to simulate fluidized bed systems, such as discrete element method (DEM), time driven hard sphere (TDHS), coarse-grained particle method (CGPM), coarse grained hard sphere (CGHS), and multi-phase particle-in-cell (MP-PIC). These different approaches usually solve the fluid phase in a Eulerian fixed frame of reference and the particle phase using the Lagrangian method. The first difference between these models lies in tracking either real particles or lumped parcels. The second difference is in the treatment of particle-particle interactions: by calculating collision forces (DEM and CGPM), using momentum conservation laws (TDHS and CGHS),more » or based on particle stress model (MP-PIC). These major model differences lead to a wide range of results accuracy and computation speed. However, these models have never been compared directly using the same experimental dataset. In this research, a small-scale fluidized bed is simulated with these methods using the same open-source code MFIX. The results indicate that modeling the particle-particle collision by TDHS increases the computation speed while maintaining good accuracy. Also, lumping few particles in a parcel increases the computation speed with little loss in accuracy. However, modeling particle-particle interactions with solids stress leads to a big loss in accuracy with a little increase in computation speed. The MP-PIC method predicts an unphysical particle-particle overlap, which results in incorrect voidage distribution and incorrect overall bed hydrodynamics. Based on this study, we recommend using the CGHS method for fluidized bed simulations due to its computational speed that rivals that of MPPIC while maintaining a much better accuracy.« less

Accurate interlaminar stress recovery from finite element analysis

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Riggs, H. Ronald

1994-01-01

The accuracy and robustness of a two-dimensional smoothing methodology is examined for the problem of recovering accurate interlaminar shear stress distributions in laminated composite and sandwich plates. The smoothing methodology is based on a variational formulation which combines discrete least-squares and penalty-constraint functionals in a single variational form. The smoothing analysis utilizes optimal strains computed at discrete locations in a finite element analysis. These discrete strain data are smoothed with a smoothing element discretization, producing superior accuracy strains and their first gradients. The approach enables the resulting smooth strain field to be practically C1-continuous throughout the domain of smoothing, exhibiting superconvergent properties of the smoothed quantity. The continuous strain gradients are also obtained directly from the solution. The recovered strain gradients are subsequently employed in the integration o equilibrium equations to obtain accurate interlaminar shear stresses. The problem is a simply-supported rectangular plate under a doubly sinusoidal load. The problem has an exact analytic solution which serves as a measure of goodness of the recovered interlaminar shear stresses. The method has the versatility of being applicable to the analysis of rather general and complex structures built of distinct components and materials, such as found in aircraft design. For these types of structures, the smoothing is achieved with 'patches', each patch covering the domain in which the smoothed quantity is physically continuous.

Numerical computation of transonic flows by finite-element and finite-difference methods

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.

1978-01-01

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

A survey of mixed finite element methods

NASA Technical Reports Server (NTRS)

Brezzi, F.

1987-01-01

This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.

Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

Probabilistic finite elements for transient analysis in nonlinear continua

NASA Technical Reports Server (NTRS)

Liu, W. K.; Belytschko, T.; Mani, A.

1985-01-01

The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

Analysis of Tire Tractive Performance on Deformable Terrain by Finite Element-Discrete Element Method

NASA Astrophysics Data System (ADS)

Nakashima, Hiroshi; Takatsu, Yuzuru

The goal of this study is to develop a practical and fast simulation tool for soil-tire interaction analysis, where finite element method (FEM) and discrete element method (DEM) are coupled together, and which can be realized on a desktop PC. We have extended our formerly proposed dynamic FE-DE method (FE-DEM) to include practical soil-tire system interaction, where not only the vertical sinkage of a tire, but also the travel of a driven tire was considered. Numerical simulation by FE-DEM is stable, and the relationships between variables, such as load-sinkage and sinkage-travel distance, and the gross tractive effort and running resistance characteristics, are obtained. Moreover, the simulation result is accurate enough to predict the maximum drawbar pull for a given tire, once the appropriate parameter values are provided. Therefore, the developed FE-DEM program can be applied with sufficient accuracy to interaction problems in soil-tire systems.

Primal-mixed formulations for reaction-diffusion systems on deforming domains

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo

2015-10-01

We propose a finite element formulation for a coupled elasticity-reaction-diffusion system written in a fully Lagrangian form and governing the spatio-temporal interaction of species inside an elastic, or hyper-elastic body. A primal weak formulation is the baseline model for the reaction-diffusion system written in the deformed domain, and a finite element method with piecewise linear approximations is employed for its spatial discretization. On the other hand, the strain is introduced as mixed variable in the equations of elastodynamics, which in turn acts as coupling field needed to update the diffusion tensor of the modified reaction-diffusion system written in a deformed domain. The discrete mechanical problem yields a mixed finite element scheme based on row-wise Raviart-Thomas elements for stresses, Brezzi-Douglas-Marini elements for displacements, and piecewise constant pressure approximations. The application of the present framework in the study of several coupled biological systems on deforming geometries in two and three spatial dimensions is discussed, and some illustrative examples are provided and extensively analyzed.

Techniques for forced response involving discrete nonlinearities. I - Theory. II - Applications

NASA Astrophysics Data System (ADS)

Avitabile, Peter; Callahan, John O.

Several new techniques developed for the forced response analysis of systems containing discrete nonlinear connection elements are presented and compared to the traditional methods. In particular, the techniques examined are the Equivalent Reduced Model Technique (ERMT), Modal Modification Response Technique (MMRT), and Component Element Method (CEM). The general theory of the techniques is presented, and applications are discussed with particular reference to the beam nonlinear system model using ERMT, MMRT, and CEM; frame nonlinear response using the three techniques; and comparison of the results obtained by using the ERMT, MMRT, and CEM models.

Discrete Element Method Simulation of a Boulder Extraction From an Asteroid

NASA Technical Reports Server (NTRS)

Kulchitsky, Anton K.; Johnson, Jerome B.; Reeves, David M.; Wilkinson, Allen

2014-01-01

The force required to pull 7t and 40t polyhedral boulders from the surface of an asteroid is simulated using the discrete element method considering the effects of microgravity, regolith cohesion and boulder acceleration. The connection between particle surface energy and regolith cohesion is estimated by simulating a cohesion sample tearing test. An optimal constant acceleration is found where the peak net force from inertia and cohesion is a minimum. Peak pulling forces can be further reduced by using linear and quadratic acceleration functions with up to a 40% reduction in force for quadratic acceleration.

Electro-impulse de-icing electrodynamic solution by discrete elements

NASA Technical Reports Server (NTRS)

Bernhart, W. D.; Schrag, R. L.

1988-01-01

This paper describes a technique for analyzing the electrodynamic phenomena associated with electro-impulse deicing. The analysis is done in the time domain and utilizes a discrete element formulation concept expressed in state variable form. Calculated results include coil current, eddy currents in the target (aircraft leading edge skin), pressure distribution on the target, and total force and impulse on the target. Typical results are presented and described. Some comparisons are made between calculated and experimental results, and also between calculated values from other theoretical approaches. Application to the problem of a nonrigid target is treated briefly.

Evaluating the Discrete Element Method as a Tool for Predicting the Seasonal Evolution of the MIZ

DTIC Science & Technology

2014-09-30

distribution (Hopkins & Thorndike 2006). The DEM treats sea ice as a collection of discrete pieces of ice, thus affording the method certain...Annals of Glaciology, 33(1), 355-360. Hopkins, M. A., & Thorndike , A. S. (2006) Floe formation in Arctic sea ice. Journal of Geophysical Research

A Discretization Algorithm for Meteorological Data and its Parallelization Based on Hadoop

NASA Astrophysics Data System (ADS)

Liu, Chao; Jin, Wen; Yu, Yuting; Qiu, Taorong; Bai, Xiaoming; Zou, Shuilong

2017-10-01

In view of the large amount of meteorological observation data, the property is more and the attribute values are continuous values, the correlation between the elements is the need for the application of meteorological data, this paper is devoted to solving the problem of how to better discretize large meteorological data to more effectively dig out the hidden knowledge in meteorological data and research on the improvement of discretization algorithm for large scale data, in order to achieve data in the large meteorological data discretization for the follow-up to better provide knowledge to provide protection, a discretization algorithm based on information entropy and inconsistency of meteorological attributes is proposed and the algorithm is parallelized under Hadoop platform. Finally, the comparison test validates the effectiveness of the proposed algorithm for discretization in the area of meteorological large data.

Accelerating cardiac bidomain simulations using graphics processing units.

PubMed

Neic, A; Liebmann, M; Hoetzl, E; Mitchell, L; Vigmond, E J; Haase, G; Plank, G

2012-08-01

Anatomically realistic and biophysically detailed multiscale computer models of the heart are playing an increasingly important role in advancing our understanding of integrated cardiac function in health and disease. Such detailed simulations, however, are computationally vastly demanding, which is a limiting factor for a wider adoption of in-silico modeling. While current trends in high-performance computing (HPC) hardware promise to alleviate this problem, exploiting the potential of such architectures remains challenging since strongly scalable algorithms are necessitated to reduce execution times. Alternatively, acceleration technologies such as graphics processing units (GPUs) are being considered. While the potential of GPUs has been demonstrated in various applications, benefits in the context of bidomain simulations where large sparse linear systems have to be solved in parallel with advanced numerical techniques are less clear. In this study, the feasibility of multi-GPU bidomain simulations is demonstrated by running strong scalability benchmarks using a state-of-the-art model of rabbit ventricles. The model is spatially discretized using the finite element methods (FEM) on fully unstructured grids. The GPU code is directly derived from a large pre-existing code, the Cardiac Arrhythmia Research Package (CARP), with very minor perturbation of the code base. Overall, bidomain simulations were sped up by a factor of 11.8 to 16.3 in benchmarks running on 6-20 GPUs compared to the same number of CPU cores. To match the fastest GPU simulation which engaged 20 GPUs, 476 CPU cores were required on a national supercomputing facility.

Accelerating Cardiac Bidomain Simulations Using Graphics Processing Units

PubMed Central

Neic, Aurel; Liebmann, Manfred; Hoetzl, Elena; Mitchell, Lawrence; Vigmond, Edward J.; Haase, Gundolf

2013-01-01

Anatomically realistic and biophysically detailed multiscale computer models of the heart are playing an increasingly important role in advancing our understanding of integrated cardiac function in health and disease. Such detailed simulations, however, are computationally vastly demanding, which is a limiting factor for a wider adoption of in-silico modeling. While current trends in high-performance computing (HPC) hardware promise to alleviate this problem, exploiting the potential of such architectures remains challenging since strongly scalable algorithms are necessitated to reduce execution times. Alternatively, acceleration technologies such as graphics processing units (GPUs) are being considered. While the potential of GPUs has been demonstrated in various applications, benefits in the context of bidomain simulations where large sparse linear systems have to be solved in parallel with advanced numerical techniques are less clear. In this study, the feasibility of multi-GPU bidomain simulations is demonstrated by running strong scalability benchmarks using a state-of-the-art model of rabbit ventricles. The model is spatially discretized using the finite element methods (FEM) on fully unstructured grids. The GPU code is directly derived from a large pre-existing code, the Cardiac Arrhythmia Research Package (CARP), with very minor perturbation of the code base. Overall, bidomain simulations were sped up by a factor of 11.8 to 16.3 in benchmarks running on 6–20 GPUs compared to the same number of CPU cores. To match the fastest GPU simulation which engaged 20GPUs, 476 CPU cores were required on a national supercomputing facility. PMID:22692867

Coding "We-ness" in couple's relationship stories: A method for assessing mutuality in couple therapy.

PubMed

Gildersleeve, Sara; Singer, Jefferson A; Skerrett, Karen; Wein, Shelter

2017-05-01

"We-ness," a couple's mutual investment in their relationship and in each other, has been found to be a potent dimension of couple resilience. This study examined the development of a method to capture We-ness in psychotherapy through the coding of relationship narratives co-constructed by couples ("We-Stories"). It used a coding system to identify the core thematic elements that make up these narratives. Couples that self-identified as "happy" (N = 53) generated We-Stories and completed measures of relationship satisfaction and mutuality. These stories were then coded using the We-Stories coding manual. Findings indicated that security, an element that involves aspects of safety, support, and commitment, was most common, appearing in 58.5% of all narratives. This element was followed by the elements of pleasure (49.1%) and shared meaning/vision (37.7%). The number of "We-ness" elements was also correlated with and predictive of discrepancy scores on measures of relationship mutuality, indicating the validity of the We-Stories coding manual. Limitations and future directions are discussed.

Imitation Learning Errors Are Affected by Visual Cues in Both Performance and Observation Phases.

PubMed

Mizuguchi, Takashi; Sugimura, Ryoko; Shimada, Hideaki; Hasegawa, Takehiro

2017-08-01

Mechanisms of action imitation were examined. Previous studies have suggested that success or failure of imitation is determined at the point of observing an action. In other words, cognitive processing after observation is not related to the success of imitation; 20 university students participated in each of three experiments in which they observed a series of object manipulations consisting of four elements (hands, tools, object, and end points) and then imitated the manipulations. In Experiment 1, a specific intially observed element was color coded, and the specific manipulated object at the imitation stage was identically color coded; participants accurately imitated the color coded element. In Experiment 2, a specific element was color coded at the observation but not at the imitation stage, and there were no effects of color coding on imitation. In Experiment 3, participants were verbally instructed to attend to a specific element at the imitation stage, but the verbal instructions had no effect. Thus, the success of imitation may not be determined at the stage of observing an action and color coding can provide a clue for imitation at the imitation stage.

SU-F-T-111: Investigation of the Attila Deterministic Solver as a Supplement to Monte Carlo for Calculating Out-Of-Field Radiotherapy Dose

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mille, M; Lee, C; Failla, G

Purpose: To use the Attila deterministic solver as a supplement to Monte Carlo for calculating out-of-field organ dose in support of epidemiological studies looking at the risks of second cancers. Supplemental dosimetry tools are needed to speed up dose calculations for studies involving large-scale patient cohorts. Methods: Attila is a multi-group discrete ordinates code which can solve the 3D photon-electron coupled linear Boltzmann radiation transport equation on a finite-element mesh. Dose is computed by multiplying the calculated particle flux in each mesh element by a medium-specific energy deposition cross-section. The out-of-field dosimetry capability of Attila is investigated by comparing averagemore » organ dose to that which is calculated by Monte Carlo simulation. The test scenario consists of a 6 MV external beam treatment of a female patient with a tumor in the left breast. The patient is simulated by a whole-body adult reference female computational phantom. Monte Carlo simulations were performed using MCNP6 and XVMC. Attila can export a tetrahedral mesh for MCNP6, allowing for a direct comparison between the two codes. The Attila and Monte Carlo methods were also compared in terms of calculation speed and complexity of simulation setup. A key perquisite for this work was the modeling of a Varian Clinac 2100 linear accelerator. Results: The solid mesh of the torso part of the adult female phantom for the Attila calculation was prepared using the CAD software SpaceClaim. Preliminary calculations suggest that Attila is a user-friendly software which shows great promise for our intended application. Computational performance is related to the number of tetrahedral elements included in the Attila calculation. Conclusion: Attila is being explored as a supplement to the conventional Monte Carlo radiation transport approach for performing retrospective patient dosimetry. The goal is for the dosimetry to be sufficiently accurate for use in retrospective epidemiological investigations.« less

Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation

NASA Astrophysics Data System (ADS)

Litaker, Eric T.

1994-12-01

The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.

Multigrid finite element method in stress analysis of three-dimensional elastic bodies of heterogeneous structure

NASA Astrophysics Data System (ADS)

Matveev, A. D.

2016-11-01

To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.

Multidimensional incremental parsing for universal source coding.

PubMed

Bae, Soo Hyun; Juang, Biing-Hwang

2008-10-01

A multidimensional incremental parsing algorithm (MDIP) for multidimensional discrete sources, as a generalization of the Lempel-Ziv coding algorithm, is investigated. It consists of three essential component schemes, maximum decimation matching, hierarchical structure of multidimensional source coding, and dictionary augmentation. As a counterpart of the longest match search in the Lempel-Ziv algorithm, two classes of maximum decimation matching are studied. Also, an underlying behavior of the dictionary augmentation scheme for estimating the source statistics is examined. For an m-dimensional source, m augmentative patches are appended into the dictionary at each coding epoch, thus requiring the transmission of a substantial amount of information to the decoder. The property of the hierarchical structure of the source coding algorithm resolves this issue by successively incorporating lower dimensional coding procedures in the scheme. In regard to universal lossy source coders, we propose two distortion functions, the local average distortion and the local minimax distortion with a set of threshold levels for each source symbol. For performance evaluation, we implemented three image compression algorithms based upon the MDIP; one is lossless and the others are lossy. The lossless image compression algorithm does not perform better than the Lempel-Ziv-Welch coding, but experimentally shows efficiency in capturing the source structure. The two lossy image compression algorithms are implemented using the two distortion functions, respectively. The algorithm based on the local average distortion is efficient at minimizing the signal distortion, but the images by the one with the local minimax distortion have a good perceptual fidelity among other compression algorithms. Our insights inspire future research on feature extraction of multidimensional discrete sources.

Achievable Information Rates for Coded Modulation With Hard Decision Decoding for Coherent Fiber-Optic Systems

NASA Astrophysics Data System (ADS)

Sheikh, Alireza; Amat, Alexandre Graell i.; Liva, Gianluigi

2017-12-01

We analyze the achievable information rates (AIRs) for coded modulation schemes with QAM constellations with both bit-wise and symbol-wise decoders, corresponding to the case where a binary code is used in combination with a higher-order modulation using the bit-interleaved coded modulation (BICM) paradigm and to the case where a nonbinary code over a field matched to the constellation size is used, respectively. In particular, we consider hard decision decoding, which is the preferable option for fiber-optic communication systems where decoding complexity is a concern. Recently, Liga \\emph{et al.} analyzed the AIRs for bit-wise and symbol-wise decoders considering what the authors called \\emph{hard decision decoder} which, however, exploits \\emph{soft information} of the transition probabilities of discrete-input discrete-output channel resulting from the hard detection. As such, the complexity of the decoder is essentially the same as the complexity of a soft decision decoder. In this paper, we analyze instead the AIRs for the standard hard decision decoder, commonly used in practice, where the decoding is based on the Hamming distance metric. We show that if standard hard decision decoding is used, bit-wise decoders yield significantly higher AIRs than symbol-wise decoders. As a result, contrary to the conclusion by Liga \\emph{et al.}, binary decoders together with the BICM paradigm are preferable for spectrally-efficient fiber-optic systems. We also design binary and nonbinary staircase codes and show that, in agreement with the AIRs, binary codes yield better performance.

CELFE/NASTRAN Code for the Analysis of Structures Subjected to High Velocity Impact

NASA Technical Reports Server (NTRS)

Chamis, C. C.

1978-01-01

CELFE (Coupled Eulerian Lagrangian Finite Element)/NASTRAN Code three-dimensional finite element code has the capability for analyzing of structures subjected to high velocity impact. The local response is predicted by CELFE and, for large problems, the far-field impact response is predicted by NASTRAN. The coupling of the CELFE code with NASTRAN (CELFE/NASTRAN code) and the application of the code to selected three-dimensional high velocity impact problems are described.

Designing for Compressive Sensing: Compressive Art, Camouflage, Fonts, and Quick Response Codes

DTIC Science & Technology

2018-01-01

an example where the signal is non-sparse in the standard basis, but sparse in the discrete cosine basis . The top plot shows the signal from the...previous example, now used as sparse discrete cosine transform (DCT) coefficients . The next plot shows the non-sparse signal in the standard...Romberg JK, Tao T. Stable signal recovery from incomplete and inaccurate measurements. Commun Pure Appl Math . 2006;59(8):1207–1223. 3. Donoho DL

Enhanced verification test suite for physics simulation codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamm, James R.; Brock, Jerry S.; Brandon, Scott T.

2008-09-01

This document discusses problems with which to augment, in quantity and in quality, the existing tri-laboratory suite of verification problems used by Los Alamos National Laboratory (LANL), Lawrence Livermore National Laboratory (LLNL), and Sandia National Laboratories (SNL). The purpose of verification analysis is demonstrate whether the numerical results of the discretization algorithms in physics and engineering simulation codes provide correct solutions of the corresponding continuum equations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strauss, H.R.

This paper describes the code FEMHD, an adaptive finite element MHD code, which is applied in a number of different manners to model MHD behavior and edge plasma phenomena on a diverted tokamak. The code uses an unstructured triangular mesh in 2D and wedge shaped mesh elements in 3D. The code has been adapted to look at neutral and charged particle dynamics in the plasma scrape off region, and into a full MHD-particle code.

Dynamic mortar finite element method for modeling of shear rupture on frictional rough surfaces

NASA Astrophysics Data System (ADS)

Tal, Yuval; Hager, Bradford H.

2017-09-01

This paper presents a mortar-based finite element formulation for modeling the dynamics of shear rupture on rough interfaces governed by slip-weakening and rate and state (RS) friction laws, focusing on the dynamics of earthquakes. The method utilizes the dual Lagrange multipliers and the primal-dual active set strategy concepts, together with a consistent discretization and linearization of the contact forces and constraints, and the friction laws to obtain a semi-smooth Newton method. The discretization of the RS friction law involves a procedure to condense out the state variables, thus eliminating the addition of another set of unknowns into the system. Several numerical examples of shear rupture on frictional rough interfaces demonstrate the efficiency of the method and examine the effects of the different time discretization schemes on the convergence, energy conservation, and the time evolution of shear traction and slip rate.

Properties of quantum systems via diagonalization of transition amplitudes. II. Systematic improvements of short-time propagation

NASA Astrophysics Data System (ADS)

Vidanović, Ivana; Bogojević, Aleksandar; Balaž, Antun; Belić, Aleksandar

2009-12-01

In this paper, building on a previous analysis [I. Vidanović, A. Bogojević, and A. Belić, preceding paper, Phys. Rev. E 80, 066705 (2009)] of exact diagonalization of the space-discretized evolution operator for the study of properties of nonrelativistic quantum systems, we present a substantial improvement to this method. We apply recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator. This improves by many orders of magnitude previously used approximations for discretized matrix elements and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. We illustrate this approach on several one- and two-dimensional models. The quality of numerically calculated higher-order eigenstates is assessed by comparison with semiclassical cumulative density of states.

On simulation of no-slip condition in the method of discrete vortices

NASA Astrophysics Data System (ADS)

Shmagunov, O. A.

2017-10-01

When modeling flows of an incompressible fluid, it is convenient sometimes to use the method of discrete vortices (MDV), where the continuous vorticity field is approximated by a set of discrete vortex elements moving in the velocity field. The vortex elements have a clear physical interpretation, they do not require the construction of grids and are automatically adaptive, since they concentrate in the regions of greatest interest and successfully describe the flows of a non-viscous fluid. The possibility of using MDV in simulating flows of a viscous fluid was considered in the previous papers using the examples of flows past bodies with sharp edges with the no-penetration condition at solid boundaries. However, the appearance of vorticity on smooth boundaries requires the no-slip condition to be met when MDV is realized, which substantially complicates the initially simple method. In this connection, an approach is considered that allows solving the problem by simple means.

Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization

NASA Astrophysics Data System (ADS)

Burman, Erik; Hansbo, Peter; Larson, Mats G.

2018-03-01

Tikhonov regularization is one of the most commonly used methods for the regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably weighted least squares terms of the control variable, or derivatives thereof, to the Lagrangian determining the optimality system. In this note we show that the stabilization methods for discretely ill-posed problems developed in the setting of convection-dominated convection-diffusion problems, can be highly suitable for stabilizing optimal control problems, and that Tikhonov regularization will lead to less accurate discrete solutions. We consider some inverse problems for Poisson’s equation as an illustration and derive new error estimates both for the reconstruction of the solution from the measured data and reconstruction of the source term from the measured data. These estimates include both the effect of the discretization error and error in the measurements.

Discrete and continuum modelling of soil cutting

NASA Astrophysics Data System (ADS)

Coetzee, C. J.

2014-12-01

Both continuum and discrete methods are used to investigate the soil cutting process. The Discrete Element Method ( dem) is used for the discrete modelling and the Material-Point Method ( mpm) is used for continuum modelling. M pmis a so-called particle method or meshless finite element method. Standard finite element methods have difficulty in modelling the entire cutting process due to large displacements and deformation of the mesh. The use of meshless methods overcomes this problem. M pm can model large deformations, frictional contact at the soil-tool interface, and dynamic effects (inertia forces). In granular materials the discreteness of the system is often important and rotational degrees of freedom are active, which might require enhanced theoretical approaches like polar continua. In polar continuum theories, the material points are considered to possess orientations. A material point has three degrees-of-freedom for rigid rotations, in addition to the three classic translational degrees-of-freedom. The Cosserat continuum is the most transparent and straightforward extension of the nonpolar (classic) continuum. Two-dimensional dem and mpm (polar and nonpolar) simulations of the cutting problem are compared to experiments. The drag force and flow patterns are compared using cohesionless corn grains as material. The corn macro (continuum) and micro ( dem) properties were obtained from shear and oedometer tests. Results show that the dilatancy angle plays a significant role in the flow of material but has less of an influence on the draft force. Nonpolar mpm is the most accurate in predicting blade forces, blade-soil interface stresses and the position and orientation of shear bands. Polar mpm fails in predicting the orientation of the shear band, but is less sensitive to mesh size and mesh orientation compared to nonpolar mpm. dem simulations show less material dilation than observed during experiments.

Three-dimensional flat shell-to-shell coupling: numerical challenges

NASA Astrophysics Data System (ADS)

Guo, Kuo; Haikal, Ghadir

2017-11-01

The node-to-surface formulation is widely used in contact simulations with finite elements because it is relatively easy to implement using different types of element discretizations. This approach, however, has a number of well-known drawbacks, including locking due to over-constraint when this formulation is used as a twopass method. Most studies on the node-to-surface contact formulation, however, have been conducted using solid elements and little has been done to investigate the effectiveness of this approach for beam or shell elements. In this paper we show that locking can also be observed with the node-to-surface contact formulation when applied to plate and flat shell elements even with a singlepass implementation with distinct master/slave designations, which is the standard solution to locking with solid elements. In our study, we use the quadrilateral four node flat shell element for thin (Kirchhoff-Love) plate and thick (Reissner-Mindlin) plate theory, both in their standard forms and with improved formulations such as the linked interpolation [1] and the Discrete Kirchhoff [2] elements for thick and thin plates, respectively. The Lagrange multiplier method is used to enforce the node-to-surface constraints for all elements. The results show clear locking when compared to those obtained using a conforming mesh configuration.

A mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method

PubMed Central

Kojic, Milos; Filipovic, Nenad; Tsuda, Akira

2012-01-01

A multiscale procedure to couple a mesoscale discrete particle model and a macroscale continuum model of incompressible fluid flow is proposed in this study. We call this procedure the mesoscopic bridging scale (MBS) method since it is developed on the basis of the bridging scale method for coupling molecular dynamics and finite element models [G.J. Wagner, W.K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys. 190 (2003) 249–274]. We derive the governing equations of the MBS method and show that the differential equations of motion of the mesoscale discrete particle model and finite element (FE) model are only coupled through the force terms. Based on this coupling, we express the finite element equations which rely on the Navier–Stokes and continuity equations, in a way that the internal nodal FE forces are evaluated using viscous stresses from the mesoscale model. The dissipative particle dynamics (DPD) method for the discrete particle mesoscale model is employed. The entire fluid domain is divided into a local domain and a global domain. Fluid flow in the local domain is modeled with both DPD and FE method, while fluid flow in the global domain is modeled by the FE method only. The MBS method is suitable for modeling complex (colloidal) fluid flows, where continuum methods are sufficiently accurate only in the large fluid domain, while small, local regions of particular interest require detailed modeling by mesoscopic discrete particles. Solved examples – simple Poiseuille and driven cavity flows illustrate the applicability of the proposed MBS method. PMID:23814322

SAM Theory Manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Rui

The System Analysis Module (SAM) is an advanced and modern system analysis tool being developed at Argonne National Laboratory under the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. SAM development aims for advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability for reactor transient analyses. To facilitate the code development, SAM utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage modern advanced software environments and numerical methods. SAM focuses on modeling advanced reactormore » concepts such as SFRs (sodium fast reactors), LFRs (lead-cooled fast reactors), and FHRs (fluoride-salt-cooled high temperature reactors) or MSRs (molten salt reactors). These advanced concepts are distinguished from light-water reactors in their use of single-phase, low-pressure, high-temperature, and low Prandtl number (sodium and lead) coolants. As a new code development, the initial effort has been focused on modeling and simulation capabilities of heat transfer and single-phase fluid dynamics responses in Sodium-cooled Fast Reactor (SFR) systems. The system-level simulation capabilities of fluid flow and heat transfer in general engineering systems and typical SFRs have been verified and validated. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As the code is still under ongoing development, this SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.« less

Federal Logistics Information Systems. FLIS Procedures Manual. Document Identifier Code Input/Output Formats (Variable Length). Volume 9.

DTIC Science & Technology

1997-04-01

DATA COLLABORATORS 0001N B NQ 8380 NUMBER OF DATA RECEIVERS 0001N B NQ 2533 AUTHORIZED ITEM IDENTIFICATION DATA COLLABORATOR CODE 0002 ,X B 03 18 TD...01 NC 8268 DATA ELEMENT TERMINATOR CODE 000iX VT 9505 TYPE OF SCREENING CODE 0001A 01 NC 8268 DATA ELEMENT TERMINATOR CODE 000iX VT 4690 OUTPUT DATA... 9505 TYPE OF SCREENING CODE 0001A 2 89 2910 REFERENCE NUMBER CATEGORY CODE (RNCC) 0001X 2 89 4780 REFERENCE NUMBER VARIATION CODE (RNVC) 0001 N 2 89

A MATLAB based 3D modeling and inversion code for MT data

NASA Astrophysics Data System (ADS)

Singh, Arun; Dehiya, Rahul; Gupta, Pravin K.; Israil, M.

2017-07-01

The development of a MATLAB based computer code, AP3DMT, for modeling and inversion of 3D Magnetotelluric (MT) data is presented. The code comprises two independent components: grid generator code and modeling/inversion code. The grid generator code performs model discretization and acts as an interface by generating various I/O files. The inversion code performs core computations in modular form - forward modeling, data functionals, sensitivity computations and regularization. These modules can be readily extended to other similar inverse problems like Controlled-Source EM (CSEM). The modular structure of the code provides a framework useful for implementation of new applications and inversion algorithms. The use of MATLAB and its libraries makes it more compact and user friendly. The code has been validated on several published models. To demonstrate its versatility and capabilities the results of inversion for two complex models are presented.

Modular architecture for robotics and teleoperation

DOEpatents

Anderson, Robert J.

1996-12-03

Systems and methods for modularization and discretization of real-time robot, telerobot and teleoperation systems using passive, network based control laws. Modules consist of network one-ports and two-ports. Wave variables and position information are passed between modules. The behavior of each module is decomposed into uncoupled linear-time-invariant, and coupled, nonlinear memoryless elements and then are separately discretized.

Three-dimensional analysis of a faulted CO 2 reservoir using an Eshelby-Mori-Tanaka approach to rock elastic properties and fault permeability

DOE PAGES

Nguyen, Ba Nghiep; Hou, Zhangshuan; Last, George V.; ...

2016-09-29

This work develops a three-dimensional multiscale model to analyze a complex CO 2 faulted reservoir that includes some key geological features of the San Andreas and nearby faults southwest of the Kimberlina site. The model uses the STOMP-CO 2 code for flow modeling that is coupled to the ABAQUS® finite element package for geomechanical analysis. A 3D ABAQUS® finite element model is developed that contains a large number of 3D solid elements with two nearly parallel faults whose damage zones and cores are discretized using the same continuum elements. Five zones with different mineral compositions are considered: shale, sandstone, faultmore » damaged sandstone, fault damaged shale, and fault core. Rocks’ elastic properties that govern their poroelastic behavior are modeled by an Eshelby-Mori-Tanka approach (EMTA). EMTA can account for up to 15 mineral phases. The permeability of fault damage zones affected by crack density and orientations is also predicted by an EMTA formulation. A STOMP-CO 2 grid that exactly maps the ABAQUS® finite element model is built for coupled hydro-mechanical analyses. Simulations of the reservoir assuming three different crack pattern situations (including crack volume fraction and orientation) for the fault damage zones are performed to predict the potential leakage of CO 2 due to cracks that enhance the permeability of the fault damage zones. Here, the results illustrate the important effect of the crack orientation on fault permeability that can lead to substantial leakage along the fault attained by the expansion of the CO 2 plume. Potential hydraulic fracture and the tendency for the faults to slip are also examined and discussed in terms of stress distributions and geomechanical properties.« less

Three-dimensional analysis of a faulted CO 2 reservoir using an Eshelby-Mori-Tanaka approach to rock elastic properties and fault permeability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nguyen, Ba Nghiep; Hou, Zhangshuan; Last, George V.

This work develops a three-dimensional multiscale model to analyze a complex CO 2 faulted reservoir that includes some key geological features of the San Andreas and nearby faults southwest of the Kimberlina site. The model uses the STOMP-CO 2 code for flow modeling that is coupled to the ABAQUS® finite element package for geomechanical analysis. A 3D ABAQUS® finite element model is developed that contains a large number of 3D solid elements with two nearly parallel faults whose damage zones and cores are discretized using the same continuum elements. Five zones with different mineral compositions are considered: shale, sandstone, faultmore » damaged sandstone, fault damaged shale, and fault core. Rocks’ elastic properties that govern their poroelastic behavior are modeled by an Eshelby-Mori-Tanka approach (EMTA). EMTA can account for up to 15 mineral phases. The permeability of fault damage zones affected by crack density and orientations is also predicted by an EMTA formulation. A STOMP-CO 2 grid that exactly maps the ABAQUS® finite element model is built for coupled hydro-mechanical analyses. Simulations of the reservoir assuming three different crack pattern situations (including crack volume fraction and orientation) for the fault damage zones are performed to predict the potential leakage of CO 2 due to cracks that enhance the permeability of the fault damage zones. Here, the results illustrate the important effect of the crack orientation on fault permeability that can lead to substantial leakage along the fault attained by the expansion of the CO 2 plume. Potential hydraulic fracture and the tendency for the faults to slip are also examined and discussed in terms of stress distributions and geomechanical properties.« less

A computer code for calculations in the algebraic collective model of the atomic nucleus

NASA Astrophysics Data System (ADS)

Welsh, T. A.; Rowe, D. J.

2016-03-01

A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1 , 1) × SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functions of the model's quadrupole moments qˆM and are at most quadratic in the corresponding conjugate momenta πˆN (- 2 ≤ M , N ≤ 2). The code makes use of expressions for matrix elements derived elsewhere and newly derived matrix elements of the operators [ π ˆ ⊗ q ˆ ⊗ π ˆ ] 0 and [ π ˆ ⊗ π ˆ ] LM. The code is made efficient by use of an analytical expression for the needed SO(5)-reduced matrix elements, and use of SO(5) ⊃ SO(3) Clebsch-Gordan coefficients obtained from precomputed data files provided with the code.

Weight-lattice discretization of Weyl-orbit functions

NASA Astrophysics Data System (ADS)

Hrivnák, Jiří; Walton, Mark A.

2016-08-01

Weyl-orbit functions have been defined for each simple Lie algebra, and permit Fourier-like analysis on the fundamental region of the corresponding affine Weyl group. They have also been discretized, using a refinement of the coweight lattice, so that digitized data on the fundamental region can be Fourier-analyzed. The discretized orbit function has arguments that are redundant if related by the affine Weyl group, while its labels, the Weyl-orbit representatives, invoke the dual affine Weyl group. Here we discretize the orbit functions in a novel way, by using the weight lattice. A cleaner theory results with symmetry between the arguments and labels of the discretized orbit functions. Orthogonality of the new discretized orbit functions is proved, and leads to the construction of unitary, symmetric matrices with Weyl-orbit-valued elements. For one type of orbit function, the matrix coincides with the Kac-Peterson modular S matrix, important for Wess-Zumino-Novikov-Witten conformal field theory.

Mutual Information between Discrete Variables with Many Categories using Recursive Adaptive Partitioning

PubMed Central

Seok, Junhee; Seon Kang, Yeong

2015-01-01

Mutual information, a general measure of the relatedness between two random variables, has been actively used in the analysis of biomedical data. The mutual information between two discrete variables is conventionally calculated by their joint probabilities estimated from the frequency of observed samples in each combination of variable categories. However, this conventional approach is no longer efficient for discrete variables with many categories, which can be easily found in large-scale biomedical data such as diagnosis codes, drug compounds, and genotypes. Here, we propose a method to provide stable estimations for the mutual information between discrete variables with many categories. Simulation studies showed that the proposed method reduced the estimation errors by 45 folds and improved the correlation coefficients with true values by 99 folds, compared with the conventional calculation of mutual information. The proposed method was also demonstrated through a case study for diagnostic data in electronic health records. This method is expected to be useful in the analysis of various biomedical data with discrete variables. PMID:26046461

Analyzing neuronal networks using discrete-time dynamics

NASA Astrophysics Data System (ADS)

Ahn, Sungwoo; Smith, Brian H.; Borisyuk, Alla; Terman, David

2010-05-01

We develop mathematical techniques for analyzing detailed Hodgkin-Huxley like models for excitatory-inhibitory neuronal networks. Our strategy for studying a given network is to first reduce it to a discrete-time dynamical system. The discrete model is considerably easier to analyze, both mathematically and computationally, and parameters in the discrete model correspond directly to parameters in the original system of differential equations. While these networks arise in many important applications, a primary focus of this paper is to better understand mechanisms that underlie temporally dynamic responses in early processing of olfactory sensory information. The models presented here exhibit several properties that have been described for olfactory codes in an insect’s Antennal Lobe. These include transient patterns of synchronization and decorrelation of sensory inputs. By reducing the model to a discrete system, we are able to systematically study how properties of the dynamics, including the complex structure of the transients and attractors, depend on factors related to connectivity and the intrinsic and synaptic properties of cells within the network.

40 CFR Appendix A to Subpart A of... - Tables

Code of Federal Regulations, 2011 CFR

2011-07-01

... precursor of PM2.5. Table 2a to Appendix A of Subpart A—Data Elements for Reporting on Emissions From Point Sources, Where Required by 40 CFR 51.30 Data elements Every-yearreporting Three-yearreporting (1... phone number ✓ ✓ (6) FIPS code ✓ ✓ (7) Facility ID codes ✓ ✓ (8) Unit ID code ✓ ✓ (9) Process ID code...

Numerical treatment of a geometrically nonlinear planar Cosserat shell model

NASA Astrophysics Data System (ADS)

Sander, Oliver; Neff, Patrizio; Bîrsan, Mircea

2016-05-01

We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general six-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite elements (GFEs), which leads to an objective discrete model which naturally allows arbitrarily large rotations. GFEs of any approximation order can be constructed. The resulting algebraic problem is a minimization problem posed on a nonlinear finite-dimensional Riemannian manifold. We solve this problem using a Riemannian trust-region method, which is a generalization of Newton's method that converges globally without intermediate loading steps. We present the continuous model and the discretization, discuss the properties of the discrete model, and show several numerical examples, including wrinkling of thin elastic sheets in shear.

Solutions of the Taylor-Green Vortex Problem Using High-Resolution Explicit Finite Difference Methods

NASA Technical Reports Server (NTRS)

DeBonis, James R.

2013-01-01

A computational fluid dynamics code that solves the compressible Navier-Stokes equations was applied to the Taylor-Green vortex problem to examine the code s ability to accurately simulate the vortex decay and subsequent turbulence. The code, WRLES (Wave Resolving Large-Eddy Simulation), uses explicit central-differencing to compute the spatial derivatives and explicit Low Dispersion Runge-Kutta methods for the temporal discretization. The flow was first studied and characterized using Bogey & Bailley s 13-point dispersion relation preserving (DRP) scheme. The kinetic energy dissipation rate, computed both directly and from the enstrophy field, vorticity contours, and the energy spectra are examined. Results are in excellent agreement with a reference solution obtained using a spectral method and provide insight into computations of turbulent flows. In addition the following studies were performed: a comparison of 4th-, 8th-, 12th- and DRP spatial differencing schemes, the effect of the solution filtering on the results, the effect of large-eddy simulation sub-grid scale models, and the effect of high-order discretization of the viscous terms.

Neoclassical Simulation of Tokamak Plasmas using Continuum Gyrokinetc Code TEMPEST

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, X Q

We present gyrokinetic neoclassical simulations of tokamak plasmas with self-consistent electric field for the first time using a fully nonlinear (full-f) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five dimensional computational grid in phase space. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving gyrokinetic Poisson equation with self-consistent poloidal variation. Withmore » our 4D ({psi}, {theta}, {epsilon}, {mu}) version of the TEMPEST code we compute radial particle and heat flux, the Geodesic-Acoustic Mode (GAM), and the development of neoclassical electric field, which we compare with neoclassical theory with a Lorentz collision model. The present work provides a numerical scheme and a new capability for self-consistently studying important aspects of neoclassical transport and rotations in toroidal magnetic fusion devices.« less

A Computer Program for Flow-Log Analysis of Single Holes (FLASH)

USGS Publications Warehouse

Day-Lewis, F. D.; Johnson, C.D.; Paillet, Frederick L.; Halford, K.J.

2011-01-01

A new computer program, FLASH (Flow-Log Analysis of Single Holes), is presented for the analysis of borehole vertical flow logs. The code is based on an analytical solution for steady-state multilayer radial flow to a borehole. The code includes options for (1) discrete fractures and (2) multilayer aquifers. Given vertical flow profiles collected under both ambient and stressed (pumping or injection) conditions, the user can estimate fracture (or layer) transmissivities and far-field hydraulic heads. FLASH is coded in Microsoft Excel with Visual Basic for Applications routines. The code supports manual and automated model calibration. ?? 2011, The Author(s). Ground Water ?? 2011, National Ground Water Association.

Image coding of SAR imagery

NASA Technical Reports Server (NTRS)

Chang, C. Y.; Kwok, R.; Curlander, J. C.

1987-01-01

Five coding techniques in the spatial and transform domains have been evaluated for SAR image compression: linear three-point predictor (LTPP), block truncation coding (BTC), microadaptive picture sequencing (MAPS), adaptive discrete cosine transform (ADCT), and adaptive Hadamard transform (AHT). These techniques have been tested with Seasat data. Both LTPP and BTC spatial domain coding techniques provide very good performance at rates of 1-2 bits/pixel. The two transform techniques, ADCT and AHT, demonstrate the capability to compress the SAR imagery to less than 0.5 bits/pixel without visible artifacts. Tradeoffs such as the rate distortion performance, the computational complexity, the algorithm flexibility, and the controllability of compression ratios are also discussed.

Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling

PubMed Central

Punzalan, Florencio Rusty; Kunieda, Yoshitoshi; Amano, Akira

2015-01-01

Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to generate code for physiological simulations and provides a tool for studying cardiac electrophysiology. PMID:26356082

41 CFR Appendix C to Chapter 301 - Standard Data Elements for Federal Travel [Traveler Identification

Code of Federal Regulations, 2014 CFR

2014-07-01

... education, in scientific, professional, technical, mechanical, trade, clerical, fiscal, administrative, or... Data Elements for Federal Travel [Accounting & Certification] Group name Data elements Description Accounting Classification Accounting Code Agency accounting code. Non-Federal Source Indicator Per Diem...

SmaggIce User Guide. 1.0

NASA Technical Reports Server (NTRS)

Baez, Marivell; Vickerman, Mary; Choo, Yung

2000-01-01

SmaggIce (Surface Modeling And Grid Generation for Iced Airfoils) is one of NASNs aircraft icing research codes developed at the Glenn Research Center. It is a software toolkit used in the process of aerodynamic performance prediction of iced airfoils. It includes tools which complement the 2D grid-based Computational Fluid Dynamics (CFD) process: geometry probing; surface preparation for gridding: smoothing and re-discretization of geometry. Future releases will also include support for all aspects of gridding: domain decomposition; perimeter discretization; grid generation and modification.

Nonlinear static and dynamic finite element analysis of an eccentrically loaded graphite-epoxy beam

NASA Technical Reports Server (NTRS)

Fasanella, Edwin L.; Jackson, Karen E.; Jones, Lisa E.

1991-01-01

The Dynamic Crash Analysis of Structures (DYCAT) and NIKE3D nonlinear finite element codes were used to model the static and implulsive response of an eccentrically loaded graphite-epoxy beam. A 48-ply unidirectional composite beam was tested under an eccentric axial compressive load until failure. This loading configuration was chosen to highlight the capabilities of two finite element codes for modeling a highly nonlinear, large deflection structural problem which has an exact solution. These codes are currently used to perform dynamic analyses of aircraft structures under impact loads to study crashworthiness and energy absorbing capabilities. Both beam and plate element models were developed to compare with the experimental data using the DYCAST and NIKE3D codes.

MILAMIN 2 - Fast MATLAB FEM solver

NASA Astrophysics Data System (ADS)

Dabrowski, Marcin; Krotkiewski, Marcin; Schmid, Daniel W.

2013-04-01

MILAMIN is a free and efficient MATLAB-based two-dimensional FEM solver utilizing unstructured meshes [Dabrowski et al., G-cubed (2008)]. The code consists of steady-state thermal diffusion and incompressible Stokes flow solvers implemented in approximately 200 lines of native MATLAB code. The brevity makes the code easily customizable. An important quality of MILAMIN is speed - it can handle millions of nodes within minutes on one CPU core of a standard desktop computer, and is faster than many commercial solutions. The new MILAMIN 2 allows three-dimensional modeling. It is designed as a set of functional modules that can be used as building blocks for efficient FEM simulations using MATLAB. The utilities are largely implemented as native MATLAB functions. For performance critical parts we use MUTILS - a suite of compiled MEX functions optimized for shared memory multi-core computers. The most important features of MILAMIN 2 are: 1. Modular approach to defining, tracking, and discretizing the geometry of the model 2. Interfaces to external mesh generators (e.g., Triangle, Fade2d, T3D) and mesh utilities (e.g., element type conversion, fast point location, boundary extraction) 3. Efficient computation of the stiffness matrix for a wide range of element types, anisotropic materials and three-dimensional problems 4. Fast global matrix assembly using a dedicated MEX function 5. Automatic integration rules 6. Flexible prescription (spatial, temporal, and field functions) and efficient application of Dirichlet, Neuman, and periodic boundary conditions 7. Treatment of transient and non-linear problems 8. Various iterative and multi-level solution strategies 9. Post-processing tools (e.g., numerical integration) 10. Visualization primitives using MATLAB, and VTK export functions We provide a large number of examples that show how to implement a custom FEM solver using the MILAMIN 2 framework. The examples are MATLAB scripts of increasing complexity that address a given technical topic (e.g., creating meshes, reordering nodes, applying boundary conditions), a given numerical topic (e.g., using various solution strategies, non-linear iterations), or that present a fully-developed solver designed to address a scientific topic (e.g., performing Stokes flow simulations in synthetic porous medium). References: Dabrowski, M., M. Krotkiewski, and D. W. Schmid MILAMIN: MATLAB-based finite element method solver for large problems, Geochem. Geophys. Geosyst., 9, Q04030, 2008

Vibration Response Models of a Stiffened Aluminum Plate Excited by a Shaker

NASA Technical Reports Server (NTRS)

Cabell, Randolph H.

2008-01-01

Numerical models of structural-acoustic interactions are of interest to aircraft designers and the space program. This paper describes a comparison between two energy finite element codes, a statistical energy analysis code, a structural finite element code, and the experimentally measured response of a stiffened aluminum plate excited by a shaker. Different methods for modeling the stiffeners and the power input from the shaker are discussed. The results show that the energy codes (energy finite element and statistical energy analysis) accurately predicted the measured mean square velocity of the plate. In addition, predictions from an energy finite element code had the best spatial correlation with measured velocities. However, predictions from a considerably simpler, single subsystem, statistical energy analysis model also correlated well with the spatial velocity distribution. The results highlight a need for further work to understand the relationship between modeling assumptions and the prediction results.

Discrete Element Modeling (DEM) of Triboelectrically Charged Particles: Revised Experiments

NASA Technical Reports Server (NTRS)

Hogue, Michael D.; Calle, Carlos I.; Curry, D. R.; Weitzman, P. S.

2008-01-01

In a previous work, the addition of basic screened Coulombic electrostatic forces to an existing commercial discrete element modeling (DEM) software was reported. Triboelectric experiments were performed to charge glass spheres rolling on inclined planes of various materials. Charge generation constants and the Q/m ratios for the test materials were calculated from the experimental data and compared to the simulation output of the DEM software. In this paper, we will discuss new values of the charge generation constants calculated from improved experimental procedures and data. Also, planned work to include dielectrophoretic, Van der Waals forces, and advanced mechanical forces into the software will be discussed.

Analysis of passive damping in thick composite structures

NASA Technical Reports Server (NTRS)

Saravanos, D. A.

1993-01-01

Computational mechanics for the prediction of damping and other dynamic characteristics in composite structures of general thicknesses and laminations are presented. Discrete layer damping mechanics that account for the representation of interlaminar shear effects in the material are summarized. Finite element based structural mechanics for the analysis of damping are described, and a specialty finite element is developed. Applications illustrate the quality of the discrete layer damping mechanics in predicting the damped dynamic characteristics of composite structures with thicker sections and/or laminate configurations that induce interlaminar shear. The results also illustrate and quantify the significance of interlaminar shear damping in such composite structures.

Particle-based simulation of charge transport in discrete-charge nano-scale systems: the electrostatic problem

PubMed Central

2012-01-01

The fast and accurate computation of the electric forces that drive the motion of charged particles at the nanometer scale represents a computational challenge. For this kind of system, where the discrete nature of the charges cannot be neglected, boundary element methods (BEM) represent a better approach than finite differences/finite elements methods. In this article, we compare two different BEM approaches to a canonical electrostatic problem in a three-dimensional space with inhomogeneous dielectrics, emphasizing their suitability for particle-based simulations: the iterative method proposed by Hoyles et al. and the Induced Charge Computation introduced by Boda et al. PMID:22338640

Particle-based simulation of charge transport in discrete-charge nano-scale systems: the electrostatic problem.

PubMed

Berti, Claudio; Gillespie, Dirk; Eisenberg, Robert S; Fiegna, Claudio

2012-02-16

The fast and accurate computation of the electric forces that drive the motion of charged particles at the nanometer scale represents a computational challenge. For this kind of system, where the discrete nature of the charges cannot be neglected, boundary element methods (BEM) represent a better approach than finite differences/finite elements methods. In this article, we compare two different BEM approaches to a canonical electrostatic problem in a three-dimensional space with inhomogeneous dielectrics, emphasizing their suitability for particle-based simulations: the iterative method proposed by Hoyles et al. and the Induced Charge Computation introduced by Boda et al.

A discrete-element model for viscoelastic deformation and fracture of glacial ice

NASA Astrophysics Data System (ADS)

Riikilä, T. I.; Tallinen, T.; Åström, J.; Timonen, J.

2015-10-01

A discrete-element model was developed to study the behavior of viscoelastic materials that are allowed to fracture. Applicable to many materials, the main objective of this analysis was to develop a model specifically for ice dynamics. A realistic model of glacial ice must include elasticity, brittle fracture and slow viscous deformations. Here the model is described in detail and tested with several benchmark simulations. The model was used to simulate various ice-specific applications with resulting flow rates that were compatible with Glen's law, and produced under fragmentation fragment-size distributions that agreed with the known analytical and experimental results.

Discretization of the induced-charge boundary integral equation.

PubMed

Bardhan, Jaydeep P; Eisenberg, Robert S; Gillespie, Dirk

2009-07-01

Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

Discretization of the induced-charge boundary integral equation

NASA Astrophysics Data System (ADS)

Bardhan, Jaydeep P.; Eisenberg, Robert S.; Gillespie, Dirk

2009-07-01

Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

Solving transient acoustic boundary value problems with equivalent sources using a lumped parameter approach.

PubMed

Fahnline, John B

2016-12-01

An equivalent source method is developed for solving transient acoustic boundary value problems. The method assumes the boundary surface is discretized in terms of triangular or quadrilateral elements and that the solution is represented using the acoustic fields of discrete sources placed at the element centers. Also, the boundary condition is assumed to be specified for the normal component of the surface velocity as a function of time, and the source amplitudes are determined to match the known elemental volume velocity vector at a series of discrete time steps. Equations are given for marching-on-in-time schemes to solve for the source amplitudes at each time step for simple, dipole, and tripole source formulations. Several example problems are solved to illustrate the results and to validate the formulations, including problems with closed boundary surfaces where long-time numerical instabilities typically occur. A simple relationship between the simple and dipole source amplitudes in the tripole source formulation is derived so that the source radiates primarily in the direction of the outward surface normal. The tripole source formulation is shown to eliminate interior acoustic resonances and long-time numerical instabilities.

A fast solver for the Helmholtz equation based on the generalized multiscale finite-element method

NASA Astrophysics Data System (ADS)

Fu, Shubin; Gao, Kai

2017-11-01

Conventional finite-element methods for solving the acoustic-wave Helmholtz equation in highly heterogeneous media usually require finely discretized mesh to represent the medium property variations with sufficient accuracy. Computational costs for solving the Helmholtz equation can therefore be considerably expensive for complicated and large geological models. Based on the generalized multiscale finite-element theory, we develop a novel continuous Galerkin method to solve the Helmholtz equation in acoustic media with spatially variable velocity and mass density. Instead of using conventional polynomial basis functions, we use multiscale basis functions to form the approximation space on the coarse mesh. The multiscale basis functions are obtained from multiplying the eigenfunctions of a carefully designed local spectral problem with an appropriate multiscale partition of unity. These multiscale basis functions can effectively incorporate the characteristics of heterogeneous media's fine-scale variations, thus enable us to obtain accurate solution to the Helmholtz equation without directly solving the large discrete system formed on the fine mesh. Numerical results show that our new solver can significantly reduce the dimension of the discrete Helmholtz equation system, and can also obviously reduce the computational time.

A discrete element and ray framework for rapid simulation of acoustical dispersion of microscale particulate agglomerations

NASA Astrophysics Data System (ADS)

Zohdi, T. I.

2016-03-01

In industry, particle-laden fluids, such as particle-functionalized inks, are constructed by adding fine-scale particles to a liquid solution, in order to achieve desired overall properties in both liquid and (cured) solid states. However, oftentimes undesirable particulate agglomerations arise due to some form of mutual-attraction stemming from near-field forces, stray electrostatic charges, process ionization and mechanical adhesion. For proper operation of industrial processes involving particle-laden fluids, it is important to carefully breakup and disperse these agglomerations. One approach is to target high-frequency acoustical pressure-pulses to breakup such agglomerations. The objective of this paper is to develop a computational model and corresponding solution algorithm to enable rapid simulation of the effect of acoustical pulses on an agglomeration composed of a collection of discrete particles. Because of the complex agglomeration microstructure, containing gaps and interfaces, this type of system is extremely difficult to mesh and simulate using continuum-based methods, such as the finite difference time domain or the finite element method. Accordingly, a computationally-amenable discrete element/discrete ray model is developed which captures the primary physical events in this process, such as the reflection and absorption of acoustical energy, and the induced forces on the particulate microstructure. The approach utilizes a staggered, iterative solution scheme to calculate the power transfer from the acoustical pulse to the particles and the subsequent changes (breakup) of the pulse due to the particles. Three-dimensional examples are provided to illustrate the approach.

Implementation of the full viscoresistive magnetohydrodynamic equations in a nonlinear finite element code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haverkort, J.W.; Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven; Blank, H.J. de

Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. Amore » rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field. Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model. Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.« less

Implementation of a Tabulated Failure Model Into a Generalized Composite Material Model Suitable for Use in Impact Problems

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Carney, Kelly S.; Dubois, Paul; Hoffarth, Canio; Khaled, Bilal; Shyamsunder, Loukham; Rajan, Subramaniam; Blankenhorn, Gunther

2017-01-01

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased use in the aerospace and automotive communities. The aerospace community has identified several key capabilities which are currently lacking in the available material models in commercial transient dynamic finite element codes. To attempt to improve the predictive capability of composite impact simulations, a next generation material model is being developed for incorporation within the commercial transient dynamic finite element code LS-DYNA. The material model, which incorporates plasticity, damage and failure, utilizes experimentally based tabulated input to define the evolution of plasticity and damage and the initiation of failure as opposed to specifying discrete input parameters such as modulus and strength. The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. For the damage model, a strain equivalent formulation is used to allow for the uncoupling of the deformation and damage analyses. For the failure model, a tabulated approach is utilized in which a stress or strain based invariant is defined as a function of the location of the current stress state in stress space to define the initiation of failure. Failure surfaces can be defined with any arbitrary shape, unlike traditional failure models where the mathematical functions used to define the failure surface impose a specific shape on the failure surface. In the current paper, the complete development of the failure model is described and the generation of a tabulated failure surface for a representative composite material is discussed.

Verification of a non-hydrostatic dynamical core using horizontally spectral element vertically finite difference method: 2-D aspects

NASA Astrophysics Data System (ADS)

Choi, S.-J.; Giraldo, F. X.; Kim, J.; Shin, S.

2014-06-01

The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative terms and quadrature. The Euler equations used here are in a flux form based on the hydrostatic pressure vertical coordinate, which are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate is implemented in this model. We verified the model by conducting widely used standard benchmark tests: the inertia-gravity wave, rising thermal bubble, density current wave, and linear hydrostatic mountain wave. The results from those tests demonstrate that the horizontally spectral element vertically finite difference model is accurate and robust. By using the 2-D slice model, we effectively show that the combined spatial discretization method of the spectral element and finite difference method in the horizontal and vertical directions, respectively, offers a viable method for the development of a NH dynamical core.

Applications of algebraic topology to compatible spatial discretizations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bochev, Pavel Blagoveston; Hyman, James M.

We provide a common framework for compatible discretizations using algebraic topology to guide our analysis. The main concept is the natural inner product on cochains, which induces a combinatorial Hodge theory. The framework comprises of mutually consistent operations of differentiation and integration, has a discrete Stokes theorem, and preserves the invariants of the DeRham cohomology groups. The latter allows for an elementary calculation of the kernel of the discrete Laplacian. Our framework provides an abstraction that includes examples of compatible finite element, finite volume and finite difference methods. We describe how these methods result from the choice of a reconstructionmore » operator and when they are equivalent.« less

One-Dimensional Czedli-Type Islands

ERIC Educational Resources Information Center

Horvath, Eszter K.; Mader, Attila; Tepavcevic, Andreja

2011-01-01

The notion of an island has surfaced in recent algebra and coding theory research. Discrete versions provide interesting combinatorial problems. This paper presents the one-dimensional case with finitely many heights, a topic convenient for student research.