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Sample records for penalty discontinuous galerkin

  1. A discontinuous Galerkin method with a modified penalty flux for the propagation and scattering of acousto-elastic waves

    NASA Astrophysics Data System (ADS)

    Ye, Ruichao; de Hoop, Maarten V.; Petrovitch, Christopher L.; Pyrak-Nolte, Laura J.; Wilcox, Lucas C.

    2016-05-01

    We develop an approach for simulating acousto-elastic wave phenomena, including scattering from fluid-solid boundaries, where the solid is allowed to be anisotropic, with the discontinuous Galerkin method. We use a coupled first-order elastic strain-velocity, acoustic velocity-pressure formulation, and append penalty terms based on interior boundary continuity conditions to the numerical (central) flux so that the consistency condition holds for the discretized discontinuous Galerkin weak formulation. We incorporate the fluid-solid boundaries through these penalty terms and obtain a stable algorithm. Our approach avoids the diagonalization into polarized wave constituents such as in the approach based on solving elementwise Riemann problems.

  2. The Reverse Time Migration technique coupled with Interior Penalty Discontinuous Galerkin method.

    NASA Astrophysics Data System (ADS)

    Baldassari, C.; Barucq, H.; Calandra, H.; Denel, B.; Diaz, J.

    2009-04-01

    Seismic imaging is based on the seismic reflection method which produces an image of the subsurface from reflected waves recordings by using a tomography process and seismic migration is the industrial standard to improve the quality of the images. The migration process consists in replacing the recorded wavefields at their actual place by using various mathematical and numerical methods but each of them follows the same schedule, according to the pioneering idea of Claerbout: numerical propagation of the source function (propagation) and of the recorded wavefields (retropropagation) and next, construction of the image by applying an imaging condition. The retropropagation step can be realized accouting for the time reversibility of the wave equation and the resulting algorithm is currently called Reverse Time Migration (RTM). To be efficient, especially in three dimensional domain, the RTM requires the solution of the full wave equation by fast numerical methods. Finite element methods are considered as the best discretization method for solving the wave equation, even if they lead to the solution of huge systems with several millions of degrees of freedom, since they use meshes adapted to the domain topography and the boundary conditions are naturally taken into account in the variational formulation. Among the different finite element families, the spectral element one (SEM) is very interesting because it leads to a diagonal mass matrix which dramatically reduces the cost of the numerical computation. Moreover this method is very accurate since it allows the use of high order finite elements. However, SEM uses meshes of the domain made of quadrangles in 2D or hexaedra in 3D which are difficult to compute and not always suitable for complex topographies. Recently, Grote et al. applied the IPDG (Interior Penalty Discontinuous Galerkin) method to the wave equation. This approach is very interesting since it relies on meshes with triangles in 2D or tetrahedra in 3D

  3. Unstructured discontinuous Galerkin for seismic inversion.

    SciTech Connect

    van Bloemen Waanders, Bart Gustaaf; Ober, Curtis Curry; Collis, Samuel Scott

    2010-04-01

    This abstract explores the potential advantages of discontinuous Galerkin (DG) methods for the time-domain inversion of media parameters within the earth's interior. In particular, DG methods enable local polynomial refinement to better capture localized geological features within an area of interest while also allowing the use of unstructured meshes that can accurately capture discontinuous material interfaces. This abstract describes our initial findings when using DG methods combined with Runge-Kutta time integration and adjoint-based optimization algorithms for full-waveform inversion. Our initial results suggest that DG methods allow great flexibility in matching the media characteristics (faults, ocean bottom and salt structures) while also providing higher fidelity representations in target regions. Time-domain inversion using discontinuous Galerkin on unstructured meshes and with local polynomial refinement is shown to better capture localized geological features and accurately capture discontinuous-material interfaces. These approaches provide the ability to surgically refine representations in order to improve predicted models for specific geological features. Our future work will entail automated extensions to directly incorporate local refinement and adaptive unstructured meshes within the inversion process.

  4. General spline filters for discontinuous Galerkin solutions

    PubMed Central

    Peters, Jörg

    2015-01-01

    The discontinuous Galerkin (dG) method outputs a sequence of polynomial pieces. Post-processing the sequence by Smoothness-Increasing Accuracy-Conserving (SIAC) convolution not only increases the smoothness of the sequence but can also improve its accuracy and yield superconvergence. SIAC convolution is considered optimal if the SIAC kernels, in the form of a linear combination of B-splines of degree d, reproduce polynomials of degree 2d. This paper derives simple formulas for computing the optimal SIAC spline coefficients for the general case including non-uniform knots. PMID:26594090

  5. Discontinuous Galerkin methods for extended hydrodynamics

    NASA Astrophysics Data System (ADS)

    Suzuki, Yoshifumi

    This dissertation presents a step towards high-order methods for continuum-transition flows. In order to achieve maximum accuracy and efficiency for numerical methods on a distorted mesh, it is desirable that both governing equations and corresponding numerical methods are in some sense compact. We argue our preference for a physical model described solely by first-order partial differential equations called hyperbolic-relaxation equations, and, among various numerical methods, for the discontinuous Galerkin method. Hyperbolic-relaxation equations can be generated as moments of the Boltzmann equation and can describe continuum-transition flows. Two challenging properties of hyperbolic-relaxation equations are the presence of a stiff source term, which drives the system towards equilibrium, and the accompanying change of eigenstructure. The first issue can be solved by an implicit treatment of the source term. To cope with the second difficulty, we develop a space-time discontinuous Galerkin method, based on Huynh's "upwind moment scheme." It is called the DG(1)--Hancock method. The DG(1)--Hancock method for one- and two-dimensional meshes is described, and Fourier analyses for both linear advection and linear hyperbolic-relaxation equations are conducted. The analyses show that the DG(1)--Hancock method is not only accurate but efficient in terms of turnaround time in comparison to other semi- and fully discrete finite-volume and discontinuous Galerkin methods. Numerical tests confirm the analyses, and also show the properties are preserved for nonlinear equations; the efficiency is superior by an order of magnitude. Subsequently, discontinuous Galerkin and finite-volume spatial discretizations are applied to more practical equations, in particular, to the set of 10-moment equations, which are gas dynamics equations that include a full pressure/temperature tensor among the flow variables. Results for flow around a micro-airfoil are compared to experimental data and

  6. Discontinuous Galerkin Methods for Turbulence Simulation

    NASA Technical Reports Server (NTRS)

    Collis, S. Scott

    2002-01-01

    A discontinuous Galerkin (DG) method is formulated, implemented, and tested for simulation of compressible turbulent flows. The method is applied to turbulent channel flow at low Reynolds number, where it is found to successfully predict low-order statistics with fewer degrees of freedom than traditional numerical methods. This reduction is achieved by utilizing local hp-refinement such that the computational grid is refined simultaneously in all three spatial coordinates with decreasing distance from the wall. Another advantage of DG is that Dirichlet boundary conditions can be enforced weakly through integrals of the numerical fluxes. Both for a model advection-diffusion problem and for turbulent channel flow, weak enforcement of wall boundaries is found to improve results at low resolution. Such weak boundary conditions may play a pivotal role in wall modeling for large-eddy simulation.

  7. Discontinuous Galerkin computation of the Maxwell eigenvalues on simplicial meshes

    NASA Astrophysics Data System (ADS)

    Buffa, Annalisa; Houston, Paul; Perugia, Ilaria

    2007-07-01

    This paper is concerned with the discontinuous Galerkin approximation of the Maxwell eigenproblem. After reviewing the theory developed in [A. Buffa, I. Perugia, Discontinuous Galerkin approximation of the Maxwell eigenproblem, Technical Report 24-PV, IMATI-CNR, Pavia, Italy, 2005 ], we present a set of numerical experiments which both validate the theory, and provide further insight regarding the practical performance of discontinuous Galerkin methods, particularly in the case when non-conforming meshes, characterized by the presence of hanging nodes, are employed.

  8. On cell entropy inequality for discontinuous Galerkin methods

    NASA Technical Reports Server (NTRS)

    Jiang, Guangshan; Shu, Chi-Wang

    1993-01-01

    We prove a cell entropy inequality for a class of high order discontinuous Galerkin finite element methods approximating conservation laws, which implies convergence for the one dimensional scalar convex case.

  9. Discontinuous Galerkin Methods for Neutrino Radiation Transport

    NASA Astrophysics Data System (ADS)

    Endeve, Eirik; Hauck, Cory; Xing, Yulong; Mezzacappa, Anthony

    2015-04-01

    We are developing new computational methods for simulation of neutrino transport in core-collapse supernovae, which is challenging since neutrinos evolve from being diffusive in the proto-neutron star to nearly free streaming in the critical neutrino heating region. To this end, we consider conservative formulations of the Boltzmann equation, and aim to develop robust, high-order accurate methods. Runge-Kutta discontinuous Galerkin (DG) methods, offer several attractive properties, including (i) high-order accuracy on a compact stencil and (ii) correct asymptotic behavior in the diffusion limit. We have recently developed a new DG method for the advection part for the transport solve, which is high-order accurate and strictly preserves the physical bounds of the distribution function; i.e., f ∈ [ 0 , 1 ] . We summarize the main ingredients of our bound-preserving DG method and discuss ongoing work to include neutrino-matter interactions in the scheme. Research sponsored in part by Oak Ridge National Laboratory, managed by UT-Battelle, LLC for the U. S. Department of Energy

  10. A thermodynamically consistent discontinuous Galerkin formulation for interface separation

    DOE PAGESBeta

    Versino, Daniele; Mourad, Hashem M.; Dávila, Carlos G.; Addessio, Francis L.

    2015-07-31

    Our paper describes the formulation of an interface damage model, based on the discontinuous Galerkin (DG) method, for the simulation of failure and crack propagation in laminated structures. The DG formulation avoids common difficulties associated with cohesive elements. Specifically, it does not introduce any artificial interfacial compliance and, in explicit dynamic analysis, it leads to a stable time increment size which is unaffected by the presence of stiff massless interfaces. This proposed method is implemented in a finite element setting. Convergence and accuracy are demonstrated in Mode I and mixed-mode delamination in both static and dynamic analyses. Significantly, numerical resultsmore » obtained using the proposed interface model are found to be independent of the value of the penalty factor that characterizes the DG formulation. By contrast, numerical results obtained using a classical cohesive method are found to be dependent on the cohesive penalty stiffnesses. The proposed approach is shown to yield more accurate predictions pertaining to crack propagation under mixed-mode fracture because of the advantage. Furthermore, in explicit dynamic analysis, the stable time increment size calculated with the proposed method is found to be an order of magnitude larger than the maximum allowable value for classical cohesive elements.« less

  11. A thermodynamically consistent discontinuous Galerkin formulation for interface separation

    SciTech Connect

    Versino, Daniele; Mourad, Hashem M.; Dávila, Carlos G.; Addessio, Francis L.

    2015-07-31

    Our paper describes the formulation of an interface damage model, based on the discontinuous Galerkin (DG) method, for the simulation of failure and crack propagation in laminated structures. The DG formulation avoids common difficulties associated with cohesive elements. Specifically, it does not introduce any artificial interfacial compliance and, in explicit dynamic analysis, it leads to a stable time increment size which is unaffected by the presence of stiff massless interfaces. This proposed method is implemented in a finite element setting. Convergence and accuracy are demonstrated in Mode I and mixed-mode delamination in both static and dynamic analyses. Significantly, numerical results obtained using the proposed interface model are found to be independent of the value of the penalty factor that characterizes the DG formulation. By contrast, numerical results obtained using a classical cohesive method are found to be dependent on the cohesive penalty stiffnesses. The proposed approach is shown to yield more accurate predictions pertaining to crack propagation under mixed-mode fracture because of the advantage. Furthermore, in explicit dynamic analysis, the stable time increment size calculated with the proposed method is found to be an order of magnitude larger than the maximum allowable value for classical cohesive elements.

  12. Discontinuous Galerkin finite element methods for gradient plasticity.

    SciTech Connect

    Garikipati, Krishna.; Ostien, Jakob T.

    2010-10-01

    In this report we apply discontinuous Galerkin finite element methods to the equations of an incompatibility based formulation of gradient plasticity. The presentation is motivated with a brief overview of the description of dislocations within a crystal lattice. A tensor representing a measure of the incompatibility with the lattice is used in the formulation of a gradient plasticity model. This model is cast in a variational formulation, and discontinuous Galerkin machinery is employed to implement the formulation into a finite element code. Finally numerical examples of the model are shown.

  13. A Discontinuous Galerkin Chimera Overset Solver

    NASA Astrophysics Data System (ADS)

    Galbraith, Marshall Christopher

    This work summarizes the development of an accurate, efficient, and flexible Computational Fluid Dynamics computer code that is an improvement relative to the state of the art. The improved accuracy and efficiency is obtained by using a high-order discontinuous Galerkin (DG) discretization scheme. In order to maximize the computational efficiency, quadrature-free integration and numerical integration optimized as matrix-vector multiplications is employed and implemented through a pre-processor (PyDG). Using the PyDG pre-processor, a C++ polynomial library has been developed that uses overloaded operators to design an efficient Domain Specific Language (DSL) that allows expressions involving polynomials to be written as if they are scalars. The DSL, which makes the syntax of computer code legible and intuitive, promotes maintainability of the software and simplifies the development of additional capabilities. The flexibility of the code is achieved by combining the DG scheme with the Chimera overset method. The Chimera overset method produces solutions on a set of overlapping grids that communicate through an exchange of data on grid boundaries (known as artificial boundaries). Finite volume and finite difference discretizations use fringe points, which are layers of points on the artificial boundaries, to maintain the interior stencil on artificial boundaries. The fringe points receive solution values interpolated from overset grids. Proper interpolation requires fringe points to be contained in overset grids. Insufficient overlap must be corrected by modifying the grid system. The Chimera scheme can also exclude regions of grids that lie outside the computational domain; a process commonly known as hole cutting. The Chimera overset method has traditionally enabled the use of high-order finite difference and finite volume approaches such as WENO and compact differencing schemes, which require structured meshes, for modeling fluid flow associated with complex

  14. Error Analysis for Discontinuous Galerkin Method for Parabolic Problems

    NASA Technical Reports Server (NTRS)

    Kaneko, Hideaki

    2004-01-01

    In the proposal, the following three objectives are stated: (1) A p-version of the discontinuous Galerkin method for a one dimensional parabolic problem will be established. It should be recalled that the h-version in space was used for the discontinuous Galerkin method. An a priori error estimate as well as a posteriori estimate of this p-finite element discontinuous Galerkin method will be given. (2) The parameter alpha that describes the behavior double vertical line u(sub t)(t) double vertical line 2 was computed exactly. This was made feasible because of the explicitly specified initial condition. For practical heat transfer problems, the initial condition may have to be approximated. Also, if the parabolic problem is proposed on a multi-dimensional region, the parameter alpha, for most cases, would be difficult to compute exactly even in the case that the initial condition is known exactly. The second objective of this proposed research is to establish a method to estimate this parameter. This will be done by computing two discontinuous Galerkin approximate solutions at two different time steps starting from the initial time and use them to derive alpha. (3) The third objective is to consider the heat transfer problem over a two dimensional thin plate. The technique developed by Vogelius and Babuska will be used to establish a discontinuous Galerkin method in which the p-element will be used for through thickness approximation. This h-p finite element approach, that results in a dimensional reduction method, was used for elliptic problems, but the application appears new for the parabolic problem. The dimension reduction method will be discussed together with the time discretization method.

  15. A Streaming Language Implementation of the Discontinuous Galerkin Method

    NASA Technical Reports Server (NTRS)

    Barth, Timothy; Knight, Timothy

    2005-01-01

    We present a Brook streaming language implementation of the 3-D discontinuous Galerkin method for compressible fluid flow on tetrahedral meshes. Efficient implementation of the discontinuous Galerkin method using the streaming model of computation introduces several algorithmic design challenges. Using a cycle-accurate simulator, performance characteristics have been obtained for the Stanford Merrimac stream processor. The current Merrimac design achieves 128 Gflops per chip and the desktop board is populated with 16 chips yielding a peak performance of 2 Teraflops. Total parts cost for the desktop board is less than $20K. Current cycle-accurate simulations for discretizations of the 3-D compressible flow equations yield approximately 40-50% of the peak performance of the Merrimac streaming processor chip. Ongoing work includes the assessment of the performance of the same algorithm on the 2 Teraflop desktop board with a target goal of achieving 1 Teraflop performance.

  16. Analysis of the discontinuous Galerkin method applied to the European option pricing problem

    NASA Astrophysics Data System (ADS)

    Hozman, J.

    2013-12-01

    In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options. We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.

  17. High-order discontinuous Galerkin methods for coupled thermoconvective flows under gravity modulation

    NASA Astrophysics Data System (ADS)

    Papanicolaou, N. C.; Aristotelous, A. C.

    2015-10-01

    In this work, we develop a High-Order Symmetric Interior Penalty (SIP) Discontinuous Galerkin (DG) Finite Element Method (FEM) to investigate convective flows in a rectangular cavity subject to both vertical and horizontal temperature gradients. The whole cavity is subject to gravity modulation (g-jitter), simulating a microgravity environment. The sensitivity of the bifurcation problem makes the use of a high-order accurate and efficient technique essential. Our method is validated by solving the plane-parallel flow problem and the results were found to be in good agreement with published results. The numerical method was designed to be easily extendable to even more complex flows.

  18. Fluorescence lifetime optical tomography with Discontinuous Galerkin discretisation scheme

    PubMed Central

    Soloviev, Vadim Y.; D'Andrea, Cosimo; Mohan, P. Surya; Valentini, Gianluca; Cubeddu, Rinaldo; Arridge, Simon R.

    2010-01-01

    We develop discontinuous Galerkin framework for solving direct and inverse problems in fluorescence diffusion optical tomography in turbid media. We show the advantages and the disadvantages of this method by comparing it with previously developed framework based on the finite volume discretization. The reconstruction algorithm was used with time-gated experimental dataset acquired by imaging a highly scattering cylindrical phantom concealing small fluorescent tubes. Optical parameters, quantum yield and lifetime were simultaneously reconstructed. Reconstruction results are presented and discussed. PMID:21258525

  19. Discontinuous Galerkin Finite Element Method for Parabolic Problems

    NASA Technical Reports Server (NTRS)

    Kaneko, Hideaki; Bey, Kim S.; Hou, Gene J. W.

    2004-01-01

    In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of parallel ut(t) parallel Lz(omega) = parallel ut parallel2, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also included.

  20. Computing Binary Black Hole Initial Data with Discontinuous Galerkin Methods

    NASA Astrophysics Data System (ADS)

    Vincent, Trevor; Pfeiffer, Harald

    2016-03-01

    Discontinuous Galerkin (DG) finite element methods have been used to solve hyperbolic PDEs in relativistic simulations and offer advantages over traditional discretization methods. Comparatively little attention has been given towards using the DG method to solve the elliptic PDEs arising from the Einstein initial data equations. We describe how the DG method can be used to create a parallel, adaptive solver for initial data. We discuss the use of our dG code to compute puncture initial data for binary black holes.

  1. GPU-accelerated discontinuous Galerkin methods on hybrid meshes

    NASA Astrophysics Data System (ADS)

    Chan, Jesse; Wang, Zheng; Modave, Axel; Remacle, Jean-Francois; Warburton, T.

    2016-08-01

    We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto (Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions for hybrid meshes are derived by bounding the spectral radius of the DG operator using order-dependent constants in trace and Markov inequalities. Computational efficiency is achieved under a combination of element-specific kernels (including new quadrature-free operators for the pyramid), multi-rate timestepping, and acceleration using Graphics Processing Units.

  2. Local Analysis of Shock Capturing Using Discontinuous Galerkin Methodology

    NASA Technical Reports Server (NTRS)

    Atkins, H. L.

    1997-01-01

    The compact form of the discontinuous Galerkin method allows for a detailed local analysis of the method in the neighborhood of the shock for a non-linear model problem. Insight gained from the analysis leads to new flux formulas that are stable and that preserve the compactness of the method. Although developed for a model equation, the flux formulas are applicable to systems such as the Euler equations. This article presents the analysis for methods with a degree up to 5. The analysis is accompanied by supporting numerical experiments using Burgers' equation and the Euler equations.

  3. Properties of Discontinuous Galerkin Algorithms and Implications for Edge Gyrokinetics

    NASA Astrophysics Data System (ADS)

    Hammett, G. W.; Hakim, A.; Shi, E. L.; Abel, I. G.; Stoltzfus-Dueck, T.

    2015-11-01

    The continuum gyrokinetic code Gkeyll uses Discontinuous Galerkin (DG) algorithms, which have a lot of flexibility in the choice of basis functions and inner product norm that can be useful in designing algorithms for particular problems. Rather than use regular polynomial basis functions, we consider here Maxwellian-weighted basis functions (which have similarities to Gaussian radial basis functions). The standard Galerkin approach loses particle and energy conservation, but this can be restored with a particular weight for the inner product (this is equivalent to a Petrov-Galerkin method). This allows a full- F code to have some benefits similar to the Gaussian quadrature used in gyrokinetic δf codes to integrate Gaussians times some polynomials exactly. In tests of Gkeyll for electromagnetic fluctuations, we found it is important to use consistent basis functions where the potential is in a higher-order continuity subspace of the space for the vector potential A| |. A regular projection method to this subspace is a non-local operation, while we show a self-adjoint averaging operator that can preserve locality and energy conservation. This does not introduce damping, but like gyro-averaging involves only the reactive part of the dynamics. Supported by the Max-Planck/Princeton Center for Plasma Physics, the SciDAC Center for the Study of Plasma Microturbulence, and DOE Contract DE-AC02-09CH11466.

  4. A discontinuous Galerkin method for unsteady two-dimensional convective flows

    NASA Astrophysics Data System (ADS)

    Aristotelous, A. C.; Papanicolaou, N. C.

    2016-10-01

    We develop a High-Order Symmetric Interior Penalty (SIP) Discontinuous Galerkin (DG) Finite Element Method (FEM) to investigate two-dimensional in space natural convective flows in a vertical cavity. The physical problem is modeled by a coupled nonlinear system of partial differential equations and admits various solutions including stable and unstable modes in the form of traveling and/or standing waves, depending on the governing parameters. These flows are characterized by steep boundary and internal layers which evolve with time and can be well-resolved by high-order methods that also are adept to adaptive meshing. The standard no-slip boundary conditions which apply on the lateral walls, and the periodic conditions prescribed on the upper and lower boundaries, present additional challenges. The numerical scheme proposed herein is shown to successfully address these issues and furthermore, large Prandtl number values can be handled naturally. Discontinuous source terms and coefficients are an innate feature of multiphase flows involving heterogeneous fluids and will be a topic of subsequent work. Spatially adaptive Discontinuous Galerkin Finite Elements are especially suited to such problems.

  5. A discontinuous Galerkin method for studying elasticity and variable viscosity Stokes problems

    NASA Astrophysics Data System (ADS)

    Schnepp, Sascha M.; Charrier, Dominic; May, Dave

    2015-04-01

    Traditionally in the geodynamics community, staggered grid finite difference schemes and mixed Finite Elements (FE) have been utilised to discretise the variable viscosity (VV) Stokes problem. These methods have been demonstrated to be sufficiently robust and accurate for a wide range of variable viscosity problems involving both smooth viscosity structures possessing large spatial variations, and for discontinuous viscosity structures. One caveat of the aforementioned discretisations is that they tend to have inf-sup constants which are highly dependent on the cell aspect ratio. Whilst high order mixed FE approaches utilising spaces defined via Qk - Qk-2, k ≥ 3, alleviate this shortcoming, such elements are seldomly used as they are computationally expensive, the definition of multi-level preconditioners is complex, and spectral accuracy is often not obtained. Discontinuous Galerkin (DG) methods offer the advantage that spaces can be constructed which have both low order in velocity and pressure and inf-sup constants which are not sensitive to the element aspect ratio. To date, DG discretisations have not been extensively used within geodynamic applications associated with VV Stokes formulations. Here we rigorously evaluate the applicability of two Interior Penalty Discontinuous Galerkin methods, namely the Nonsymmetric and Symmetric Interior Penalty Galerkin methods (NIPG and SIPG) for compressible elasticity and incompressible, variable viscosity Stokes problems. Through a suite of numerical experiments, our evaluation considers the stability, order of accuracy and robustness of the NIPG and SIPG discretisations for cases with both smooth and discontinuous coefficients. Using manufactured solutions, we confirm that both DG formulations are stable and result in convergent solutions for displacement based elasticity formulations, even in the limit of Poisson ratio approaching 0.5. With regards to incompressible flow simulations, using the analytic solution Sol

  6. Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.

    1999-01-01

    Simplified forms of the space-time discontinuous Galerkin (DG) and discontinuous Galerkin least-squares (DGLS) finite element method are developed and analyzed. The new formulations exploit simplifying properties of entropy endowed conservation law systems while retaining the favorable energy properties associated with symmetric variable formulations.

  7. Scalable parallel Newton-Krylov solvers for discontinuous Galerkin discretizations

    SciTech Connect

    Persson, P.-O.

    2008-12-31

    We present techniques for implicit solution of discontinuous Galerkin discretizations of the Navier-Stokes equations on parallel computers. While a block-Jacobi method is simple and straight-forward to parallelize, its convergence properties are poor except for simple problems. Therefore, we consider Newton-GMRES methods preconditioned with block-incomplete LU factorizations, with optimized element orderings based on a minimum discarded fill (MDF) approach. We discuss the difficulties with the parallelization of these methods, but also show that with a simple domain decomposition approach, most of the advantages of the block-ILU over the block-Jacobi preconditioner are still retained. The convergence is further improved by incorporating the matrix connectivities into the mesh partitioning process, which aims at minimizing the errors introduced from separating the partitions. We demonstrate the performance of the schemes for realistic two- and three-dimensional flow problems.

  8. Continued Development of the Discontinuous Galerkin Method for Computational Aeroacoustic Applications

    NASA Technical Reports Server (NTRS)

    Atkins, H. L.

    1997-01-01

    The formulation and the implementation of boundary conditions within the context of the quadrature-free form of the discontinuous Galerkin method are presented for several types of boundary conditions for the Euler equations. An important feature of the discontinuous Galerkin method is that the interior point algorithm is well behaved in the neighborhood of the boundary and requires no modifications. This feature leads to a simple and accurate treatment for wall boundary conditions and simple inflow and outflow boundary conditions. Curved walls are accurately treated with only minor changes to the implementation described in earlier work. The 'perfectly matched layer' approach to nonreflecting boundary conditions is easily applied to the discontinuous Galerkin. The compactness of the discontinuous Galerkin method makes it better suited for buffer-zone-type methods than high-order finite-difference methods. Results are presented for wall, characteristic inflow and outflow, and nonreflecting boundary conditions.

  9. A Quadrature Free Discontinuous Galerkin Conservative Level Set Scheme

    NASA Astrophysics Data System (ADS)

    Czajkowski, Mark; Desjardins, Olivier

    2010-11-01

    In an effort to improve the scalability and accuracy of the Accurate Conservative Level Set (ACLS) scheme [Desjardins et al., J COMPUT PHYS 227 (2008)], a scheme based on the quadrature free discontinuous Galerkin (DG) methodology has been developed. ACLS relies on a hyperbolic tangent level set function that is transported and reinitialized using conservative schemes in order to alleviate mass conservation issues known to plague level set methods. DG allows for an arbitrarily high order representation of the interface by using a basis of high order polynomials while only using data from the faces of neighboring cells. The small stencil allows DG to have excellent parallel scalability. The diffusion term present in the conservative reinitialization equation is handled using local DG method [Cockburn et al., SIAM J NUMER ANAL 39, (2001)] while the normals are computed from a limited form of the level set function in order to avoid spurious oscillations. The resulting scheme is shown to be both robust, accurate, and highly scalable, making it a method of choice for large-scale simulations of multiphase flows with complex interfacial topology.

  10. Bound-preserving discontinuous Galerkin methods for relativistic hydrodynamics

    NASA Astrophysics Data System (ADS)

    Qin, Tong; Shu, Chi-Wang; Yang, Yang

    2016-06-01

    In this paper, we develop a discontinuous Galerkin (DG) method to solve the ideal special relativistic hydrodynamics (RHD) and design a bound-preserving (BP) limiter for this scheme by extending the idea in X. Zhang and C.-W. Shu, (2010) [56]. For RHD, the density and pressure are positive and the velocity is bounded by the speed of light. One difficulty in numerically solving the RHD in its conservative form is that the failure of preserving these physical bounds will result in ill-posedness of the problem and blowup of the code, especially in extreme relativistic cases. The standard way in dealing with this difficulty is to add extra numerical dissipation, while in doing so there is no guarantee of maintaining the high order of accuracy. Our BP limiter has the following features. It can theoretically guarantee to preserve the physical bounds for the numerical solution and maintain its designed high order accuracy. The limiter is local to the cell and hence is very easy to implement. Moreover, it renders L1-stability to the numerical scheme. Numerical experiments are performed to demonstrate the good performance of this bound-preserving DG scheme. Even though we only discuss the BP limiter for DG schemes, it can be applied to high order finite volume schemes, such as weighted essentially non-oscillatory (WENO) finite volume schemes as well.

  11. Projection of Discontinuous Galerkin Variable Distributions During Adaptive Mesh Refinement

    NASA Astrophysics Data System (ADS)

    Ballesteros, Carlos; Herrmann, Marcus

    2012-11-01

    Adaptive mesh refinement (AMR) methods decrease the computational expense of CFD simulations by increasing the density of solution cells only in areas of the computational domain that are of interest in that particular simulation. In particular, unstructured Cartesian AMR has several advantages over other AMR approaches, as it does not require the creation of numerous guard-cell blocks, neighboring cell lookups become straightforward, and the hexahedral nature of the mesh cells greatly simplifies the refinement and coarsening operations. The h-refinement from this AMR approach can be leveraged by making use of highly-accurate, but computationally costly methods, such as the Discontinuous Galerkin (DG) numerical method. DG methods are capable of high orders of accuracy while retaining stencil locality--a property critical to AMR using unstructured meshes. However, the use of DG methods with AMR requires the use of special flux and projection operators during refinement and coarsening operations in order to retain the high order of accuracy. The flux and projection operators needed for refinement and coarsening of unstructured Cartesian adaptive meshes using Legendre polynomial test functions will be discussed, and their performance will be shown using standard test cases.

  12. A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Hu, Changqing; Shu, Chi-Wang

    1998-01-01

    In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.

  13. A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS

    SciTech Connect

    Hong Luo; Yidong Xia; Robert Nourgaliev

    2011-05-01

    A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison. Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness.

  14. A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

    SciTech Connect

    Hong Luo; Luqing Luo; Robert Nourgaliev; Vincent A. Mousseau

    2010-01-01

    A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.

  15. Thermoelastic Simulations Based on Discontinuous Galerkin Methods: Formulation and Application in Gas Turbines

    NASA Astrophysics Data System (ADS)

    Hao, Zengrong; Gu, Chunwei; Song, Yin

    2016-06-01

    This study extends the discontinuous Galerkin (DG) methods to simulations of thermoelasticity. A thermoelastic formulation of interior penalty DG (IP-DG) method is presented and aspects of the numerical implementation are discussed in matrix form. The content related to thermal expansion effects is illustrated explicitly in the discretized equation system. The feasibility of the method for general thermoelastic simulations is validated through typical test cases, including tackling stress discontinuities caused by jumps of thermal expansive properties and controlling accompanied non-physical oscillations through adjusting the magnitude of IP term. The developed simulation platform upon the method is applied to the engineering analysis of thermoelastic performance for a turbine vane and a series of vanes with various types of simplified thermal barrier coating (TBC) systems. This analysis demonstrates that while TBC properties on heat conduction are generally the major consideration for protecting the alloy base vanes, the mechanical properties may have more significant effects on protections of coatings themselves. Changing characteristics of normal tractions on TBC/base interface, closely related to the occurrence of coating failures, over diverse components distributions along TBC thickness of the functional graded materials are summarized and analysed, illustrating the opposite tendencies in situations with different thermal-stress-free temperatures for coatings.

  16. A Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Unstructured Tetrahedral Grids

    SciTech Connect

    Hong Luo; Yidong Xia; Robert Nourgaliev; Chunpei Cai

    2011-06-01

    A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on unstructured tetrahedral grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on unstructured grids. The preliminary results indicate that this RDG method is stable on unstructured tetrahedral grids, and provides a viable and attractive alternative for the discretization of the viscous and heat fluxes in the Navier-Stokes equations.

  17. Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion

    NASA Astrophysics Data System (ADS)

    Lv, Yu; Ihme, Matthias

    2014-08-01

    This paper presents the development of a discontinuous Galerkin (DG) method for application to chemically reacting flows in subsonic and supersonic regimes under the consideration of variable thermo-viscous-diffusive transport properties, detailed and stiff reaction chemistry, and shock capturing. A hybrid-flux formulation is developed for treatment of the convective fluxes, combining a conservative Riemann-solver and an extended double-flux scheme. A computationally efficient splitting scheme is proposed, in which advection and diffusion operators are solved in the weak form, and the chemically stiff substep is advanced in the strong form using a time-implicit scheme. The discretization of the viscous-diffusive transport terms follows the second form of Bassi and Rebay, and the WENO-based limiter due to Zhong and Shu is extended to multicomponent systems. Boundary conditions are developed for subsonic and supersonic flow conditions, and the algorithm is coupled to thermochemical libraries to account for detailed reaction chemistry and complex transport. The resulting DG method is applied to a series of test cases of increasing physico-chemical complexity. Beginning with one- and two-dimensional multispecies advection and shock-fluid interaction problems, computational efficiency, convergence, and conservation properties are demonstrated. This study is followed by considering a series of detonation and supersonic combustion problems to investigate the convergence-rate and the shock-capturing capability in the presence of one- and multistep reaction chemistry. The DG algorithm is then applied to diffusion-controlled deflagration problems. By examining convergence properties for polynomial order and spatial resolution, and comparing these with second-order finite-volume solutions, it is shown that optimal convergence is achieved and that polynomial refinement provides advantages in better resolving the localized flame structure and complex flow-field features

  18. Discontinuous Galerkin methods for modeling Hurricane storm surge

    NASA Astrophysics Data System (ADS)

    Dawson, Clint; Kubatko, Ethan J.; Westerink, Joannes J.; Trahan, Corey; Mirabito, Christopher; Michoski, Craig; Panda, Nishant

    2011-09-01

    Storm surge due to hurricanes and tropical storms can result in significant loss of life, property damage, and long-term damage to coastal ecosystems and landscapes. Computer modeling of storm surge can be used for two primary purposes: forecasting of surge as storms approach land for emergency planning and evacuation of coastal populations, and hindcasting of storms for determining risk, development of mitigation strategies, coastal restoration and sustainability. Storm surge is modeled using the shallow water equations, coupled with wind forcing and in some events, models of wave energy. In this paper, we will describe a depth-averaged (2D) model of circulation in spherical coordinates. Tides, riverine forcing, atmospheric pressure, bottom friction, the Coriolis effect and wind stress are all important for characterizing the inundation due to surge. The problem is inherently multi-scale, both in space and time. To model these problems accurately requires significant investments in acquiring high-fidelity input (bathymetry, bottom friction characteristics, land cover data, river flow rates, levees, raised roads and railways, etc.), accurate discretization of the computational domain using unstructured finite element meshes, and numerical methods capable of capturing highly advective flows, wetting and drying, and multi-scale features of the solution. The discontinuous Galerkin (DG) method appears to allow for many of the features necessary to accurately capture storm surge physics. The DG method was developed for modeling shocks and advection-dominated flows on unstructured finite element meshes. It easily allows for adaptivity in both mesh ( h) and polynomial order ( p) for capturing multi-scale spatial events. Mass conservative wetting and drying algorithms can be formulated within the DG method. In this paper, we will describe the application of the DG method to hurricane storm surge. We discuss the general formulation, and new features which have been added to

  19. Super-convergence of Discontinuous Galerkin Method Applied to the Navier-Stokes Equations

    NASA Technical Reports Server (NTRS)

    Atkins, Harold L.

    2009-01-01

    The practical benefits of the hyper-accuracy properties of the discontinuous Galerkin method are examined. In particular, we demonstrate that some flow attributes exhibit super-convergence even in the absence of any post-processing technique. Theoretical analysis suggest that flow features that are dominated by global propagation speeds and decay or growth rates should be super-convergent. Several discrete forms of the discontinuous Galerkin method are applied to the simulation of unsteady viscous flow over a two-dimensional cylinder. Convergence of the period of the naturally occurring oscillation is examined and shown to converge at 2p+1, where p is the polynomial degree of the discontinuous Galerkin basis. Comparisons are made between the different discretizations and with theoretical analysis.

  20. The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

    NASA Technical Reports Server (NTRS)

    Cockburn, Bernardo; Shu, Chi-Wang

    1997-01-01

    In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L(sup 2)-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.

  1. Multiwavelet Discontinuous Galerkin Accelerated ELP Method for the Shallow Water Equations on the Cubed Sphere

    SciTech Connect

    White III, James B; Archibald, Richard K; Evans, Katherine J; Drake, John

    2011-01-01

    In this paper we present a new approach to increase the time-step size for an explicit discontinuous Galerkin numerical method. The attributes of this approach are demonstrated on standard tests for the shallow-water equations on the sphere. The addition of multiwavelets to discontinuous Galerkin method, which has the benefit of being scalable, flexible, and conservative, provides a hierarchical scale structure that can be exploited to improve computational efficiency in both the spatial and temporal dimensions. This paper explains how combining a multiwavelet discontinuous Galerkin method with exact linear part time-evolution schemes, which can remain stable for implicit-sized time steps, can help increase the time-step size for shallow water equations on the sphere.

  2. A High Order Discontinuous Galerkin Method for 2D Incompressible Flows

    NASA Technical Reports Server (NTRS)

    Liu, Jia-Guo; Shu, Chi-Wang

    1999-01-01

    In this paper we introduce a high order discontinuous Galerkin method for two dimensional incompressible flow in vorticity streamfunction formulation. The momentum equation is treated explicitly, utilizing the efficiency of the discontinuous Galerkin method The streamfunction is obtained by a standard Poisson solver using continuous finite elements. There is a natural matching between these two finite element spaces, since the normal component of the velocity field is continuous across element boundaries. This allows for a correct upwinding gluing in the discontinuous Galerkin framework, while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability The method is suitable for inviscid or high Reynolds number flows. Optimal error estimates are proven and verified by numerical experiments.

  3. ON THE ROLE OF INVOLUTIONS IN THE DISCONTINUOUS GALERKIN DISCRETIZATION OF MAXWELL AND MAGNETOHYDRODYNAMIC SYSTEMS

    NASA Technical Reports Server (NTRS)

    Barth, Timothy

    2005-01-01

    The role of involutions in energy stability of the discontinuous Galerkin (DG) discretization of Maxwell and magnetohydrodynamic (MHD) systems is examined. Important differences are identified in the symmetrization of the Maxwell and MHD systems that impact the construction of energy stable discretizations using the DG method. Specifically, general sufficient conditions to be imposed on the DG numerical flux and approximation space are given so that energy stability is retained These sufficient conditions reveal the favorable energy consequence of imposing continuity in the normal component of the magnetic induction field at interelement boundaries for MHD discretizations. Counterintuitively, this condition is not required for stability of Maxwell discretizations using the discontinuous Galerkin method.

  4. On the simulation of industrial gas dynamic applications with the discontinuous Galerkin spectral element method

    NASA Astrophysics Data System (ADS)

    Hempert, F.; Hoffmann, M.; Iben, U.; Munz, C.-D.

    2016-06-01

    In the present investigation, we demonstrate the capabilities of the discontinuous Galerkin spectral element method for high order accuracy computation of gas dynamics. The internal flow field of a natural gas injector for bivalent combustion engines is investigated under its operating conditions. The simulations of the flow field and the aeroacoustic noise emissions were in a good agreement with the experimental data. We tested several shock-capturing techniques for the discontinuous Galerkin scheme. Based on the validated framework, we analyzed the development of the supersonic jets during different opening procedures of a compressed natural gas injector. The results suggest that a more gradual injector opening decreases the noise emission.

  5. Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations

    SciTech Connect

    Liang, Xiao; Khaliq, Abdul Q. M.; Xing, Yulong

    2015-01-23

    In this paper, we study a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.

  6. A Parallel Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Aritrary Grids

    SciTech Connect

    Hong Luo; Amjad Ali; Robert Nourgaliev; Vincent A. Mousseau

    2010-01-01

    A reconstruction-based discontinuous Galerkin method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. In this method, an in-cell reconstruction is used to obtain a higher-order polynomial representation of the underlying discontinuous Galerkin polynomial solution and an inter-cell reconstruction is used to obtain a continuous polynomial solution on the union of two neighboring, interface-sharing cells. The in-cell reconstruction is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. The inter-cell reconstruction is devised to remove an interface discontinuity of the solution and its derivatives and thus to provide a simple, accurate, consistent, and robust approximation to the viscous and heat fluxes in the Navier-Stokes equations. A parallel strategy is also devised for the resulting reconstruction discontinuous Galerkin method, which is based on domain partitioning and Single Program Multiple Data (SPMD) parallel programming model. The RDG method is used to compute a variety of compressible flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results demonstrate that this RDG method is third-order accurate at a cost slightly higher than its underlying second-order DG method, at the same time providing a better performance than the third order DG method, in terms of both computing costs and storage requirements.

  7. A hybrid reconstructed discontinuous Galerkin and continuous Galerkin finite element method for incompressible flows on unstructured grids

    NASA Astrophysics Data System (ADS)

    Pandare, Aditya K.; Luo, Hong

    2016-10-01

    A hybrid reconstructed discontinuous Galerkin and continuous Galerkin method based on an incremental pressure projection formulation, termed rDG (PnPm) + CG (Pn) in this paper, is developed for solving the unsteady incompressible Navier-Stokes equations on unstructured grids. In this method, a reconstructed discontinuous Galerkin method (rDG (PnPm)) is used to discretize the velocity and a standard continuous Galerkin method (CG (Pn)) is used to approximate the pressure. The rDG (PnPm) + CG (Pn) method is designed to increase the accuracy of the hybrid DG (Pn) + CG (Pn) method and yet still satisfy Ladyženskaja-Babuška-Brezzi (LBB) condition, thus avoiding the pressure checkerboard instability. An upwind method is used to discretize the nonlinear convective fluxes in the momentum equations in order to suppress spurious oscillations in the velocity field. A number of incompressible flow problems for a variety of flow conditions are computed to numerically assess the spatial order of convergence of the rDG (PnPm) + CG (Pn) method. The numerical experiments indicate that both rDG (P0P1) + CG (P1) and rDG (P1P2) + CG (P1) methods can attain the designed 2nd order and 3rd order accuracy in space for the velocity respectively. Moreover, the 3rd order rDG (P1P2) + CG (P1) method significantly outperforms its 2nd order rDG (P0P1) + CG (P1) and rDG (P1P1) + CG (P1) counterparts: being able to not only increase the accuracy of the velocity by one order but also improve the accuracy of the pressure.

  8. A Runge-Kutta discontinuous Galerkin approach to solve reactive flows: The hyperbolic operator

    SciTech Connect

    Billet, G.; Ryan, J.

    2011-02-20

    A Runge-Kutta discontinuous Galerkin method to solve the hyperbolic part of reactive Navier-Stokes equations written in conservation form is presented. Complex thermodynamics laws are taken into account. Particular care has been taken to solve the stiff gaseous interfaces correctly with no restrictive hypothesis. 1D and 2D test cases are presented.

  9. A Local Discontinuous Galerkin Method for the Complex Modified KdV Equation

    SciTech Connect

    Li Wenting; Jiang Kun

    2010-09-30

    In this paper, we develop a local discontinuous Galerkin(LDG) method for solving complex modified KdV(CMKdV) equation. The LDG method has the flexibility for arbitrary h and p adaptivity. We prove the L{sup 2} stability for general solutions.

  10. Efficient high-order discontinuous Galerkin schemes with first-order hyperbolic advection-diffusion system approach

    NASA Astrophysics Data System (ADS)

    Mazaheri, Alireza; Nishikawa, Hiroaki

    2016-09-01

    We propose arbitrary high-order discontinuous Galerkin (DG) schemes that are designed based on a first-order hyperbolic advection-diffusion formulation of the target governing equations. We present, in details, the efficient construction of the proposed high-order schemes (called DG-H), and show that these schemes have the same number of global degrees-of-freedom as comparable conventional high-order DG schemes, produce the same or higher order of accuracy solutions and solution gradients, are exact for exact polynomial functions, and do not need a second-derivative diffusion operator. We demonstrate that the constructed high-order schemes give excellent quality solution and solution gradients on irregular triangular elements. We also construct a Weighted Essentially Non-Oscillatory (WENO) limiter for the proposed DG-H schemes and apply it to discontinuous problems. We also make some accuracy comparisons with conventional DG and interior penalty schemes. A relative qualitative cost analysis is also reported, which indicates that the high-order schemes produce orders of magnitude more accurate results than the low-order schemes for a given CPU time. Furthermore, we show that the proposed DG-H schemes are nearly as efficient as the DG and Interior-Penalty (IP) schemes as these schemes produce results that are relatively at the same error level for approximately a similar CPU time.

  11. Numerical Relativistic Magnetohydrodynamics with ADER Discontinuous Galerkin methods on adaptively refined meshes.

    NASA Astrophysics Data System (ADS)

    Zanotti, O.; Dumbser, M.; Fambri, F.

    2016-05-01

    We describe a new method for the solution of the ideal MHD equations in special relativity which adopts the following strategy: (i) the main scheme is based on Discontinuous Galerkin (DG) methods, allowing for an arbitrary accuracy of order N+1, where N is the degree of the basis polynomials; (ii) in order to cope with oscillations at discontinuities, an ”a-posteriori” sub-cell limiter is activated, which scatters the DG polynomials of the previous time-step onto a set of 2N+1 sub-cells, over which the solution is recomputed by means of a robust finite volume scheme; (iii) a local spacetime Discontinuous-Galerkin predictor is applied both on the main grid of the DG scheme and on the sub-grid of the finite volume scheme; (iv) adaptive mesh refinement (AMR) with local time-stepping is used. We validate the new scheme and comment on its potential applications in high energy astrophysics.

  12. Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

    NASA Technical Reports Server (NTRS)

    Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

  13. A toolbox for a class of discontinuous Petrov-Galerkin methods using trilinos.

    SciTech Connect

    Roberts, Nathaniel David; Bochev, Pavel Blagoveston; Demkowicz, Leszek D.; Ridzal, Denis

    2011-09-01

    The class of discontinuous Petrov-Galerkin finite element methods (DPG) proposed by L. Demkowicz and J. Gopalakrishnan guarantees the optimality of the solution in an energy norm and produces a symmetric positive definite stiffness matrix, among other desirable properties. In this paper, we describe a toolbox, implemented atop Sandia's Trilinos library, for rapid development of solvers for DPG methods. We use this toolbox to develop solvers for the Poisson and Stokes problems.

  14. Hydrodynamic Interaction Of Strong Shocks With Inhomogeneous Media:A Discontinuous Galerkin Approach

    NASA Astrophysics Data System (ADS)

    Kulkarni, Rohit; Shelton, A.

    2011-04-01

    HYDRODYNAMIC INTERACTION OF STRONG SHOCKS WITH INHOMOGENEOUS MEDIA: A DISCONTINUOUS GALERKIN APPROACH Rohit Kulkarni, Andrew Shelton, Department of Aerospace Engineering, Auburn University, AL 36849 Many astrophysical flows, which have been observed, occur in inhomogeneous (clumpy) media. This numerical experiment comprises a model which will analyze the hydrodynamic interaction of strong shocks with inhomogeneous media neglecting any radiative losses, heat conduction, and gravitational forces. Formulation of this numerical study considers interaction of a steady, planar shock with embedded cylindrical clouds in the two-dimensional computational space. Hydrodynamic system of non-linear hyperbolic conservation equations for single fluid system is considered to govern the underlying physical phenomenon. Emphasis will be on the development of discontinuous Galerkin finite element based code towards discretizing and then solving the physical conservation laws for the defined numerical experiment. This higher-order accurate scheme in spatial and temporal domain uses the discontinuous Galerkin method and this scheme will be compared with the Godunov-type finite volume method for accuracy and computational expense. Then the results will be obtained for the defined numerical model using the discontinuous Galerkin method, to discuss and conduct a comparative study which will provide the insights about the time evolution of a shock wave interacting with a single cloud system studied in a described computational domain. Numerical code developed will use an adaptive mesh refinement tool provided by AMRCLAW code which will allow us to achieve sufficiently high resolution both at small and large scales of simulation. Rohit Kulkarni rak0008@tigermail.auburn.edu Department of Aerospace Engineering, Auburn University .

  15. Discontinuous Galerkin finite element method applied to the 1-D spherical neutron transport equation

    SciTech Connect

    Machorro, Eric . E-mail: machorro@amath.washington.edu

    2007-04-10

    Discontinuous Galerkin finite element methods are used to estimate solutions to the non-scattering 1-D spherical neutron transport equation. Various trial and test spaces are compared in the context of a few sample problems whose exact solution is known. Certain trial spaces avoid unphysical behaviors that seem to plague other methods. Comparisons with diamond differencing and simple corner-balancing are presented to highlight these improvements.

  16. A Leap-Frog Discontinuous Galerkin Method for the Time-Domain Maxwell's Equations in Metamaterials

    SciTech Connect

    Li, J., Waters, J. W., Machorro, E. A.

    2012-06-01

    Numerical simulation of metamaterials play a very important role in the design of invisibility cloak, and sub-wavelength imaging. In this paper, we propose a leap-frog discontinuous Galerkin method to solve the time-dependent Maxwell’s equations in metamaterials. Conditional stability and error estimates are proved for the scheme. The proposed algorithm is implemented and numerical results supporting the analysis are provided.

  17. A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

    NASA Technical Reports Server (NTRS)

    Larson, Mats G.; Barth, Timothy J.

    1999-01-01

    This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

  18. A Comparative Study of Different Reconstruction Schemes for a Reconstructed Discontinuous Galerkin Method on Arbitrary Grids

    SciTech Connect

    Hong Luo; Hanping Xiao; Robert Nourgaliev; Chunpei Cai

    2011-06-01

    A comparative study of different reconstruction schemes for a reconstruction-based discontinuous Galerkin, termed RDG(P1P2) method is performed for compressible flow problems on arbitrary grids. The RDG method is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution via a reconstruction scheme commonly used in the finite volume method. Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are implemented to obtain a quadratic polynomial representation of the underlying discontinuous Galerkin linear polynomial solution on each cell. These three reconstruction/recovery methods are compared for a variety of compressible flow problems on arbitrary meshes to access their accuracy and robustness. The numerical results demonstrate that all three reconstruction methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstruction method provides the best performance in terms of both accuracy and robustness.

  19. A spectral-element discontinuous Galerkin lattice Boltzmann method for incompressible flows.

    SciTech Connect

    Min, M.; Lee, T.; Mathematics and Computer Science; City Univ. of New York

    2011-01-01

    We present a spectral-element discontinuous Galerkin lattice Boltzmann method for solving nearly incompressible flows. Decoupling the collision step from the streaming step offers numerical stability at high Reynolds numbers. In the streaming step, we employ high-order spectral-element discontinuous Galerkin discretizations using a tensor product basis of one-dimensional Lagrange interpolation polynomials based on Gauss-Lobatto-Legendre grids. Our scheme is cost-effective with a fully diagonal mass matrix, advancing time integration with the fourth-order Runge-Kutta method. We present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous Galerkin approach. We show convergence studies for Couette flows and demonstrate two benchmark cases with lid-driven cavity flows for Re = 400-5000 and flows around an impulsively started cylinder for Re = 550-9500. Computational results are compared with those of other theoretical and computational work that used a multigrid method, a vortex method, and a spectral element model.

  20. A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids

    SciTech Connect

    Hong Luo; Luqing Luo; Robert Nourgaliev

    2012-11-01

    A reconstruction-based discontinuous Galerkin (RDG(P1P2)) method, a variant of P1P2 method, is presented for the solution of the compressible Euler equations on arbitrary grids. In this method, an in-cell reconstruction, designed to enhance the accuracy of the discontinuous Galerkin method, is used to obtain a quadratic polynomial solution (P2) from the underlying linear polynomial (P1) discontinuous Galerkin solution using a least-squares method. The stencils used in the reconstruction involve only the von Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG(P1P2) method is third-order accurate, and outperforms the third-order DG method (DG(P2)) in terms of both computing costs and storage requirements.

  1. A Hierarchical WENO Reconstructed Discontinuous Galerkin Method for Computing Shock Waves

    NASA Astrophysics Data System (ADS)

    Xia, Y.; Frisbey, M.; Luo, H.

    The discontinuous Galerkin (DG) methods[1] have recently become popular for the solution of systems of conservation laws because of their several attractive features such as easy extension to and compact stencil for higher-order (> 2nd) approximation, flexibility in handling arbitrary types of grids for complex geometries, and amenability to parallelization and hp-adaptation. However, the DG Methods have their own share weaknesses. In particular, how to effectively control spurious oscillations in the presence of strong discontinuities, and how to reduce the computing costs and storage requirements for the DGM remain the two most challenging and unresolved issues in the DGM.

  2. A discontinuous Galerkin method for two-dimensional PDE models of Asian options

    NASA Astrophysics Data System (ADS)

    Hozman, J.; Tichý, T.; Cvejnová, D.

    2016-06-01

    In our previous research we have focused on the problem of plain vanilla option valuation using discontinuous Galerkin method for numerical PDE solution. Here we extend a simple one-dimensional problem into two-dimensional one and design a scheme for valuation of Asian options, i.e. options with payoff depending on the average of prices collected over prespecified horizon. The algorithm is based on the approach combining the advantages of the finite element methods together with the piecewise polynomial generally discontinuous approximations. Finally, an illustrative example using DAX option market data is provided.

  3. An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Bey, Kim S.

    1994-01-01

    This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

  4. A weighted Runge-Kutta discontinuous Galerkin method for wavefield modelling

    NASA Astrophysics Data System (ADS)

    He, Xijun; Yang, Dinghui; Wu, Hao

    2015-03-01

    In this paper, we propose a weighted Runge-Kutta (RK) discontinuous Galerkin (WRKDG) method for wavefield modelling. For this method, we first transform the seismic wave equations in 2-D heterogeneous anisotropic media into a first-order hyperbolic system, and then combine the discontinuous Galerkin method (DGM) with a weighted RK time discretization. The time discretization is based on an implicit diagonal RK method and an explicit technique, which changes the implicit RK method into an explicit one. In addition, we introduce a weighting factor in the process. Linear and quadratic polynomials for spatial basis functions are typically employed. We investigate the properties of the method in great detail, including the stability criteria and numerical dispersion relations for solving the 2-D acoustic equations. Our analysis indicates that the stability condition for the WRKDG method is more relaxed compared with the classic total variation diminishing (TVD) RK discontinuous Galerkin (RKDG) method, resulting in a 1.7 times superiority for P1 element and is about as efficient as TVD RKDG method for P2 element in computational efficiency. We also demonstrate that the WRKDG method can suppress numerical dispersion more efficiently than the staggered-grid (SG) method on the same grid. The WRKDG method is applied to simulate the wavefields in a large velocity contrast model, a 2-D homogeneous transversely isotropic (TI) model, a fluid-filled fracture model, and a 2-D SEG/EAGE salt dome model. Regular rectangular and irregular triangular elements are used. The numerical results show that the WRKDG method can effectively suppress numerical dispersion and provide accurate information on the wavefield on a coarse mesh. Therefore, the method evidently reduces the scale of the problem and increases computational efficiency. In addition, promising numerical tests show that the WRKDG method combines well with split perfectly matched layer boundary conditions.

  5. A high order Discontinuous Galerkin - Fourier incompressible 3D Navier-Stokes solver with rotating sliding meshes

    NASA Astrophysics Data System (ADS)

    Ferrer, Esteban; Willden, Richard H. J.

    2012-08-01

    We present the development of a sliding mesh capability for an unsteady high order (order ⩾ 3) h/p Discontinuous Galerkin solver for the three-dimensional incompressible Navier-Stokes equations. A high order sliding mesh method is developed and implemented for flow simulation with relative rotational motion of an inner mesh with respect to an outer static mesh, through the use of curved boundary elements and mixed triangular-quadrilateral meshes. A second order stiffly stable method is used to discretise in time the Arbitrary Lagrangian-Eulerian form of the incompressible Navier-Stokes equations. Spatial discretisation is provided by the Symmetric Interior Penalty Galerkin formulation with modal basis functions in the x-y plane, allowing hanging nodes and sliding meshes without the requirement to use mortar type techniques. Spatial discretisation in the z-direction is provided by a purely spectral method that uses Fourier series and allows computation of spanwise periodic three-dimensional flows. The developed solver is shown to provide high order solutions, second order in time convergence rates and spectral convergence when solving the incompressible Navier-Stokes equations on meshes where fixed and rotating elements coexist. In addition, an exact implementation of the no-slip boundary condition is included for curved edges; circular arcs and NACA 4-digit airfoils, where analytic expressions for the geometry are used to compute the required metrics. The solver capabilities are tested for a number of two dimensional problems governed by the incompressible Navier-Stokes equations on static and rotating meshes: the Taylor vortex problem, a static and rotating symmetric NACA0015 airfoil and flows through three bladed cross-flow turbines. In addition, three dimensional flow solutions are demonstrated for a three bladed cross-flow turbine and a circular cylinder shadowed by a pitching NACA0012 airfoil.

  6. Analysis of Preconditioning and Relaxation Operators for the Discontinuous Galerkin Method Applied to Diffusion

    NASA Technical Reports Server (NTRS)

    Atkins, H. L.; Shu, Chi-Wang

    2001-01-01

    The explicit stability constraint of the discontinuous Galerkin method applied to the diffusion operator decreases dramatically as the order of the method is increased. Block Jacobi and block Gauss-Seidel preconditioner operators are examined for their effectiveness at accelerating convergence. A Fourier analysis for methods of order 2 through 6 reveals that both preconditioner operators bound the eigenvalues of the discrete spatial operator. Additionally, in one dimension, the eigenvalues are grouped into two or three regions that are invariant with order of the method. Local relaxation methods are constructed that rapidly damp high frequencies for arbitrarily large time step.

  7. Development of a Perfectly Matched Layer Technique for a Discontinuous-Galerkin Spectral-Element Method

    NASA Technical Reports Server (NTRS)

    Garai, Anirban; Diosady, Laslo T.; Murman, Scott M.; Madavan, Nateri K.

    2016-01-01

    The perfectly matched layer (PML) technique is developed in the context of a high- order spectral-element Discontinuous-Galerkin (DG) method. The technique is applied to a range of test cases and is shown to be superior compared to other approaches, such as those based on using characteristic boundary conditions and sponge layers, for treating the inflow and outflow boundaries of computational domains. In general, the PML technique improves the quality of the numerical results for simulations of practical flow configurations, but it also exhibits some instabilities for large perturbations. A preliminary analysis that attempts to understand the source of these instabilities is discussed.

  8. Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws

    NASA Technical Reports Server (NTRS)

    Barth, Timothy; Charrier, Pierre; Mansour, Nagi N. (Technical Monitor)

    2001-01-01

    We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.

  9. Towards Robust Discontinuous Galerkin Methods for General Relativistic Neutrino Radiation Transport

    NASA Astrophysics Data System (ADS)

    Endeve, E.; Hauck, C. D.; Xing, Y.; Mezzacappa, A.

    2015-10-01

    With an eye towards simulating neutrino transport in core-collapse supernovae, we have developed a conservative, robust, and high-order numerical method for solving the general relativistic phase space advection problem in stationary spacetimes. The method achieves high-order accuracy using Discontinuous Galerkin discretization and Runge-Kutta time integration. For robustness, care is taken to ensure that the physical bounds on the phase space distribution function are preserved; i.e., f ∈ [0,1]. We briefly describe the bound-preserving scheme, and present results from numerical experiments in spherical symmetry adopting the Schwarzschild metric, which demonstrate that the method preserves the bounds on the distribution function.

  10. The ALE Discontinuous Galerkin Method for the Simulatio of Air Flow Through Pulsating Human Vocal Folds

    NASA Astrophysics Data System (ADS)

    Feistauer, Miloslav; Kučera, Václav; Prokopová, Jaroslav; Horáček, Jaromír

    2010-09-01

    The aim of this work is the simulation of viscous compressible flows in human vocal folds during phonation. The computational domain is a bounded subset of IR2, whose geometry mimics the shape of the human larynx. During phonation, parts of the solid impermeable walls are moving in a prescribed manner, thus simulating the opening and closing of the vocal chords. As the governing equations we take the compressible Navier-Stokes equations in ALE form. Space semidiscretization is carried out by the discontinuous Galerkin method combined with a linearized semi-implicit approach. Numerical experiments are performed with the resulting scheme.

  11. A discontinuous Petrov-Galerkin methodology for adaptive solutions to the incompressible Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Roberts, Nathan V.; Demkowicz, Leszek; Moser, Robert

    2015-11-01

    The discontinuous Petrov-Galerkin methodology with optimal test functions (DPG) of Demkowicz and Gopalakrishnan [18,20] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. Whereas Bubnov-Galerkin methods use identical trial and test spaces, Petrov-Galerkin methods allow these function spaces to differ. In DPG, test functions are computed on the fly and are chosen to realize the supremum in the inf-sup condition; the method is equivalent to a minimum residual method. For well-posed problems with sufficiently regular solutions, DPG can be shown to converge at optimal rates-the inf-sup constants governing the convergence are mesh-independent, and of the same order as those governing the continuous problem [48]. DPG also provides an accurate mechanism for measuring the error, and this can be used to drive adaptive mesh refinements. We employ DPG to solve the steady incompressible Navier-Stokes equations in two dimensions, building on previous work on the Stokes equations, and focusing particularly on the usefulness of the approach for automatic adaptivity starting from a coarse mesh. We apply our approach to a manufactured solution due to Kovasznay as well as the lid-driven cavity flow, backward-facing step, and flow past a cylinder problems.

  12. A Discontinuous Petrov-Galerkin Methodology for Adaptive Solutions to the Incompressible Navier-Stokes Equations

    SciTech Connect

    Roberts, Nathan V.; Demkowiz, Leszek; Moser, Robert

    2015-11-15

    The discontinuous Petrov-Galerkin methodology with optimal test functions (DPG) of Demkowicz and Gopalakrishnan [18, 20] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. Whereas Bubnov-Galerkin methods use identical trial and test spaces, Petrov-Galerkin methods allow these function spaces to differ. In DPG, test functions are computed on the fly and are chosen to realize the supremum in the inf-sup condition; the method is equivalent to a minimum residual method. For well-posed problems with sufficiently regular solutions, DPG can be shown to converge at optimal rates—the inf-sup constants governing the convergence are mesh-independent, and of the same order as those governing the continuous problem [48]. DPG also provides an accurate mechanism for measuring the error, and this can be used to drive adaptive mesh refinements. We employ DPG to solve the steady incompressible Navier-Stokes equations in two dimensions, building on previous work on the Stokes equations, and focusing particularly on the usefulness of the approach for automatic adaptivity starting from a coarse mesh. We apply our approach to a manufactured solution due to Kovasznay as well as the lid-driven cavity flow, backward-facing step, and flow past a cylinder problems.

  13. Solving 3D relativistic hydrodynamical problems with weighted essentially nonoscillatory discontinuous Galerkin methods

    NASA Astrophysics Data System (ADS)

    Bugner, Marcus; Dietrich, Tim; Bernuzzi, Sebastiano; Weyhausen, Andreas; Brügmann, Bernd

    2016-10-01

    Discontinuous Galerkin (DG) methods coupled to weighted essentially nonoscillatory (WENO) algorithms allow high order convergence for smooth problems and for the simulation of discontinuities and shocks. In this work, we investigate WENO-DG algorithms in the context of numerical general relativity, in particular for general relativistic hydrodynamics. We implement the standard WENO method at different orders, a compact (simple) WENO scheme, as well as an alternative subcell evolution algorithm. To evaluate the performance of the different numerical schemes, we study nonrelativistic, special relativistic, and general relativistic test beds. We present the first three-dimensional simulations of general relativistic hydrodynamics, albeit for a fixed spacetime background, within the framework of WENO-DG methods. The most important test bed is a single Tolman-Oppenheimer-Volkoff star in three dimensions, showing that long term stable simulations of single isolated neutron stars can be obtained with WENO-DG methods.

  14. Dynamic Rupture Modeling in Three Dimensions on Unstructured Meshes Using a Discontinuous Galerkin Method

    NASA Astrophysics Data System (ADS)

    Pelties, C.; Käser, M.

    2010-12-01

    We will present recent developments concerning the extensions of the ADER-DG method to solve three dimensional dynamic rupture problems on unstructured tetrahedral meshes. The simulation of earthquake rupture dynamics and seismic wave propagation using a discontinuous Galerkin (DG) method in 2D was recently presented by J. de la Puente et al. (2009). A considerable feature of this study regarding spontaneous rupture problems was the combination of the DG scheme and a time integration method using Arbitrarily high-order DERivatives (ADER) to provide high accuracy in space and time with the discretization on unstructured meshes. In the resulting discrete velocity-stress formulation of the elastic wave equations variables are naturally discontinuous at the interfaces between elements. The so-called Riemann problem can then be solved to obtain well defined values of the variables at the discontinuity itself. This is in particular valid for the fault at which a certain friction law has to be evaluated. Hence, the fault’s geometry is honored by the computational mesh. This way, complex fault planes can be modeled adequately with small elements while fast mesh coarsening is possible with increasing distance from the fault. Due to the strict locality of the scheme using only direct neighbor communication, excellent parallel behavior can be observed. A further advantage of the scheme is that it avoids spurious high-frequency contributions in the slip rate spectra and therefore does not require artificial Kelvin-Voigt damping or filtering of synthetic seismograms. In order to test the accuracy of the ADER-DG method the Southern California Earthquake Center (SCEC) benchmark for spontaneous rupture simulations was employed. Reference: J. de la Puente, J.-P. Ampuero, and M. Käser (2009), Dynamic rupture modeling on unstructured meshes using a discontinuous Galerkin method, JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, B10302, doi:10.1029/2008JB006271

  15. Lyapunov exponents and adaptive mesh refinement for high-speed flows using a discontinuous Galerkin scheme

    NASA Astrophysics Data System (ADS)

    Moura, R. C.; Silva, A. F. C.; Bigarella, E. D. V.; Fazenda, A. L.; Ortega, M. A.

    2016-08-01

    This paper proposes two important improvements to shock-capturing strategies using a discontinuous Galerkin scheme, namely, accurate shock identification via finite-time Lyapunov exponent (FTLE) operators and efficient shock treatment through a point-implicit discretization of a PDE-based artificial viscosity technique. The advocated approach is based on the FTLE operator, originally developed in the context of dynamical systems theory to identify certain types of coherent structures in a flow. We propose the application of FTLEs in the detection of shock waves and demonstrate the operator's ability to identify strong and weak shocks equally well. The detection algorithm is coupled with a mesh refinement procedure and applied to transonic and supersonic flows. While the proposed strategy can be used potentially with any numerical method, a high-order discontinuous Galerkin solver is used in this study. In this context, two artificial viscosity approaches are employed to regularize the solution near shocks: an element-wise constant viscosity technique and a PDE-based smooth viscosity model. As the latter approach is more sophisticated and preferable for complex problems, a point-implicit discretization in time is proposed to reduce the extra stiffness introduced by the PDE-based technique, making it more competitive in terms of computational cost.

  16. High performance computing aspects of a dimension independent semi-Lagrangian discontinuous Galerkin code

    NASA Astrophysics Data System (ADS)

    Einkemmer, Lukas

    2016-05-01

    The recently developed semi-Lagrangian discontinuous Galerkin approach is used to discretize hyperbolic partial differential equations (usually first order equations). Since these methods are conservative, local in space, and able to limit numerical diffusion, they are considered a promising alternative to more traditional semi-Lagrangian schemes (which are usually based on polynomial or spline interpolation). In this paper, we consider a parallel implementation of a semi-Lagrangian discontinuous Galerkin method for distributed memory systems (so-called clusters). Both strong and weak scaling studies are performed on the Vienna Scientific Cluster 2 (VSC-2). In the case of weak scaling we observe a parallel efficiency above 0.8 for both two and four dimensional problems and up to 8192 cores. Strong scaling results show good scalability to at least 512 cores (we consider problems that can be run on a single processor in reasonable time). In addition, we study the scaling of a two dimensional Vlasov-Poisson solver that is implemented using the framework provided. All of the simulations are conducted in the context of worst case communication overhead; i.e., in a setting where the CFL (Courant-Friedrichs-Lewy) number increases linearly with the problem size. The framework introduced in this paper facilitates a dimension independent implementation of scientific codes (based on C++ templates) using both an MPI and a hybrid approach to parallelization. We describe the essential ingredients of our implementation.

  17. A high order characteristic discontinuous Galerkin scheme for advection on unstructured meshes

    NASA Astrophysics Data System (ADS)

    Lee, D.; Lowrie, R.; Petersen, M.; Ringler, T.; Hecht, M.

    2016-11-01

    A new characteristic discontinuous Galerkin (CDG) advection scheme is presented. In contrast to standard discontinuous Galerkin schemes, the test functions themselves follow characteristics in order to ensure conservation and the edges of each element are also traced backwards along characteristics in order to create a swept region, which is integrated in order to determine the mass flux across the edge. Both the accuracy and performance of the scheme are greatly improved by the use of large Courant-Friedrichs-Lewy numbers for a shear flow test case and the scheme is shown to scale sublinearly with the number of tracers being advected, outperforming a standard flux corrected transport scheme for 10 or more tracers with a linear basis. Moreover the CDG scheme may be run to arbitrarily high order spatial accuracy and on unstructured grids, and is shown to give the correct order of error convergence for piecewise linear and quadratic bases on regular quadrilateral and hexahedral planar grids. Using a modal Taylor series basis, the scheme may be made monotone while preserving conservation with the use of a standard slope limiter, although this reduces the formal accuracy of the scheme to first order. The second order scheme is roughly as accurate as the incremental remap scheme with nonlocal gradient reconstruction at half the horizontal resolution. The scheme is being developed for implementation within the Model for Prediction Across Scales (MPAS) Ocean model, an unstructured grid finite volume ocean model.

  18. A Reconstructed Discontinuous Galerkin Method for the Compressible Euler Equations on Arbitrary Grids

    SciTech Connect

    Hong Luo; Luquing Luo; Robert Nourgaliev; Vincent Mousseau

    2009-06-01

    A reconstruction-based discontinuous Galerkin (DG) method is presented for the solution of the compressible Euler equations on arbitrary grids. By taking advantage of handily available and yet invaluable information, namely the derivatives, in the context of the discontinuous Galerkin methods, a solution polynomial of one degree higher is reconstructed using a least-squares method. The stencils used in the reconstruction involve only the van Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The resulting DG method can be regarded as an improvement of a recovery-based DG method in the sense that it shares the same nice features as the recovery-based DG method, such as high accuracy and efficiency, and yet overcomes some of its shortcomings such as a lack of flexibility, compactness, and robustness. The developed DG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate the accuracy and efficiency of the method. The numerical results indicate that this reconstructed DG method is able to obtain a third-order accurate solution at a slightly higher cost than its second-order DG method and provide an increase in performance over the third order DG method in terms of computing time and storage requirement.

  19. Elastic wave propagation in variable media using a discontinuous Galerkin method.

    SciTech Connect

    Ober, Curtis Curry; Smith, Thomas Michael; Collis, Samuel Scott; Overfelt, James Robert; Schwaiger, Hans

    2010-04-01

    Motivated by the needs of seismic inversion and building on our prior experience for fluid-dynamics systems, we present a high-order discontinuous Galerkin (DG) Runge-Kutta method applied to isotropic, linearized elasto-dynamics. Unlike other DG methods recently presented in the literature, our method allows for inhomogeneous material variations within each element that enables representation of realistic earth models - a feature critical for future use in seismic inversion. Likewise, our method supports curved elements and hybrid meshes that include both simplicial and nonsimplicial elements. We demonstrate the capabilities of this method through a series of numerical experiments including hybrid mesh discretizations of the Marmousi2 model as well as a modified Marmousi2 model with a oscillatory ocean bottom that is exactly captured by our discretization. A discontinuous Galerkin method for solving the equations of linear isotropic elasticity has been presented. The formulation is designed to accommodate variation of media parameters within elements, curved elements and unstructured heterogeneous meshes. We have demonstrated that each of these important features of the formulation can produce results that are significantly different from formulations that do not possess these capabilities suggesting that each of these capabilities may be important for effective full waveform inversion of elastic medium.

  20. Tests of Maxwellian-Weighted Basis Functions in a Discontinuous Galerkin Kinetic Code

    NASA Astrophysics Data System (ADS)

    Hammett, G. W.; Hakim, A.; Shi, E. L.

    2013-10-01

    Discontinuous Galerkin (DG) algorithms have been very actively studied and used in the applied math and computational fluid dynamics communities in the past decade. They combine certain attractive properties of finite element methods (like high accuracy per interpolation point) and finite volume methods (like locality of calculation for parallel computers and flexibility for limiters). Higher-order methods also have more floating point operations per data point, and so can be more efficient on modern computers that are often bandwidth limited. The flexibility of DG allows one to consider various types of Maxwellian-weighted basis functions while preserving important conservation properties of the underlying system. One can think of this either as a modified inner-product norm or a Petrov-Galerkin approach. Here we explore some ways of using Maxwellian-Weighted Basis functions and test them on paradigm problems using the Gkeyll code, which is being developed for edge gyrokinetic simulations. In addition to the formal order of accuracy in the asymptotic limit as a grid is refined, we are also interested in robust reasonable solutions on coarser grids. This work was supported by the Max-Planck/Princeton Center for Plasma Physics and DOE Contract DE-AC02-09CH11466.

  1. Efficient construction of unified continuous and discontinuous Galerkin formulations for the 3D Euler equations

    NASA Astrophysics Data System (ADS)

    Abdi, Daniel S.; Giraldo, Francis X.

    2016-09-01

    A unified approach for the numerical solution of the 3D hyperbolic Euler equations using high order methods, namely continuous Galerkin (CG) and discontinuous Galerkin (DG) methods, is presented. First, we examine how classical CG that uses a global storage scheme can be constructed within the DG framework using constraint imposition techniques commonly used in the finite element literature. Then, we implement and test a simplified version in the Non-hydrostatic Unified Model of the Atmosphere (NUMA) for the case of explicit time integration and a diagonal mass matrix. Constructing CG within the DG framework allows CG to benefit from the desirable properties of DG such as, easier hp-refinement, better stability etc. Moreover, this representation allows for regional mixing of CG and DG depending on the flow regime in an area. The different flavors of CG and DG in the unified implementation are then tested for accuracy and performance using a suite of benchmark problems representative of cloud-resolving scale, meso-scale and global-scale atmospheric dynamics. The value of our unified approach is that we are able to show how to carry both CG and DG methods within the same code and also offer a simple recipe for modifying an existing CG code to DG and vice versa.

  2. Discontinuous Galerkin finite element method for solving population density functions of cortical pyramidal and thalamic neuronal populations.

    PubMed

    Huang, Chih-Hsu; Lin, Chou-Ching K; Ju, Ming-Shaung

    2015-02-01

    Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons.

  3. Error Analysis of p-Version Discontinuous Galerkin Method for Heat Transfer in Built-up Structures

    NASA Technical Reports Server (NTRS)

    Kaneko, Hideaki; Bey, Kim S.

    2004-01-01

    The purpose of this paper is to provide an error analysis for the p-version of the discontinuous Galerkin finite element method for heat transfer in built-up structures. As a special case of the results in this paper, a theoretical error estimate for the numerical experiments recently conducted by James Tomey is obtained.

  4. A Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin for Diffusion

    NASA Technical Reports Server (NTRS)

    Huynh, H. T.

    2009-01-01

    We introduce a new approach to high-order accuracy for the numerical solution of diffusion problems by solving the equations in differential form using a reconstruction technique. The approach has the advantages of simplicity and economy. It results in several new high-order methods including a simplified version of discontinuous Galerkin (DG). It also leads to new definitions of common value and common gradient quantities at each interface shared by the two adjacent cells. In addition, the new approach clarifies the relations among the various choices of new and existing common quantities. Fourier stability and accuracy analyses are carried out for the resulting schemes. Extensions to the case of quadrilateral meshes are obtained via tensor products. For the two-point boundary value problem (steady state), it is shown that these schemes, which include most popular DG methods, yield exact common interface quantities as well as exact cell average solutions for nearly all cases.

  5. A Realizability-Preserving Discontinuous Galerkin Method for the $M_1$ Model of Radiative Transfer

    SciTech Connect

    Frank, Martin; Olbrant, Edgar; Hauck, Cory D

    2012-01-01

    The M{sub 1} model for radiative transfer coupled to a material energy equation in planar geometry is studied in this paper. For this model to be well-posed, its moment variables must fulfill certain realizability conditions. Our main focus is the design and implementation of an explicit Runge-Kutta discontinuous Galerkin method which, under a more restrictive CFL condition, guarantees the realizability of the moment variables and the positivity of the material temperature. An analytical proof for our realizability-preserving scheme, which also includes a slope-limiting technique, is provided and confirmed by various numerical examples. Among other things, we present accuracy tests showing convergence up to fourth-order, compare our results with an analytical solution in a Riemann problem, and consider a Marshak wave problem.

  6. A GPU-accelerated adaptive discontinuous Galerkin method for level set equation

    NASA Astrophysics Data System (ADS)

    Karakus, A.; Warburton, T.; Aksel, M. H.; Sert, C.

    2016-01-01

    This paper presents a GPU-accelerated nodal discontinuous Galerkin method for the solution of two- and three-dimensional level set (LS) equation on unstructured adaptive meshes. Using adaptive mesh refinement, computations are localised mostly near the interface location to reduce the computational cost. Small global time step size resulting from the local adaptivity is avoided by local time-stepping based on a multi-rate Adams-Bashforth scheme. Platform independence of the solver is achieved with an extensible multi-threading programming API that allows runtime selection of different computing devices (GPU and CPU) and different threading interfaces (CUDA, OpenCL and OpenMP). Overall, a highly scalable, accurate and mass conservative numerical scheme that preserves the simplicity of LS formulation is obtained. Efficiency, performance and local high-order accuracy of the method are demonstrated through distinct numerical test cases.

  7. DNS of Flows over Periodic Hills using a Discontinuous-Galerkin Spectral-Element Method

    NASA Technical Reports Server (NTRS)

    Diosady, Laslo T.; Murman, Scott M.

    2014-01-01

    Direct numerical simulation (DNS) of turbulent compressible flows is performed using a higher-order space-time discontinuous-Galerkin finite-element method. The numerical scheme is validated by performing DNS of the evolution of the Taylor-Green vortex and turbulent flow in a channel. The higher-order method is shown to provide increased accuracy relative to low-order methods at a given number of degrees of freedom. The turbulent flow over a periodic array of hills in a channel is simulated at Reynolds number 10,595 using an 8th-order scheme in space and a 4th-order scheme in time. These results are validated against previous large eddy simulation (LES) results. A preliminary analysis provides insight into how these detailed simulations can be used to improve Reynoldsaveraged Navier-Stokes (RANS) modeling

  8. A discontinuous Galerkin method for gravity-driven viscous fingering instabilities in porous media

    NASA Astrophysics Data System (ADS)

    Scovazzi, G.; Gerstenberger, A.; Collis, S. S.

    2013-01-01

    We present a new approach to the simulation of gravity-driven viscous fingering instabilities in porous media flow. These instabilities play a very important role during carbon sequestration processes in brine aquifers. Our approach is based on a nonlinear implementation of the discontinuous Galerkin method, and possesses a number of key features. First, the method developed is inherently high order, and is therefore well suited to study unstable flow mechanisms. Secondly, it maintains high-order accuracy on completely unstructured meshes. The combination of these two features makes it a very appealing strategy in simulating the challenging flow patterns and very complex geometries of actual reservoirs and aquifers. This article includes an extensive set of verification studies on the stability and accuracy of the method, and also features a number of computations with unstructured grids and non-standard geometries.

  9. A discontinuous Galerkin front tracking method for two-phase flows with surface tension

    SciTech Connect

    Nguyen, V.-T.; Peraire, J.; Cheong, K.B.; Persson, P.-O.

    2008-12-28

    A Discontinuous Galerkin method for solving hyperbolic systems of conservation laws involving interfaces is presented. The interfaces are represented by a collection of element boundaries and their position is updated using an arbitrary Lagrangian-Eulerian method. The motion of the interfaces and the numerical fluxes are obtained by solving a Riemann problem. As the interface is propagated, a simple and effective remeshing technique based on distance functions regenerates the grid to preserve its quality. Compared to other interface capturing techniques, the proposed approach avoids smearing of the jumps across the interface which leads to an improvement in accuracy. Numerical results are presented for several typical two-dimensional interface problems, including flows with surface tension.

  10. Explicit PREDICTOR-MULTICORRECTOR Time Discontinuous Galerkin Methods for Non-Linear Dynamics

    NASA Astrophysics Data System (ADS)

    Bonelli, A.; Bursi, O. S.; Mancuso, M.

    2002-09-01

    Explicit predictor-multicorrector time discontinuous Galerkin (TDG) methods developed for linear structural dynamics are formulated and implemented in a form suitable for arbitrary non-linear analysis of structural dynamics problems. The formulation is intended to inherit the accuracy properties of the exact parent implicit TDG methods. To this end, suitable predictors and correctors are designed to achieve third order accuracy, large stability limits and controllable numerical dissipation by means of an algorithmic parameter. As the study of a general non-linear case is rather complex, the analysis of the convergence properties of the resulting algorithms are restricted to conservative Duffing oscillators, for which closed-form solutions are available. It is shown that the main properties of the underlying parent scheme can be retained. Finally, results of representative numerical simulations relevant to Duffing oscillators and to a stiff spring pendulum discretized with finite elements illustrate the performance of the numerical schemes and confirm the analytical estimates.

  11. Integral equation and discontinuous Galerkin methods for the analysis of light-matter interaction

    NASA Astrophysics Data System (ADS)

    Baczewski, Andrew David

    Light-matter interaction is among the most enduring interests of the physical sciences. The understanding and control of this physics is of paramount importance to the design of myriad technologies ranging from stained glass, to molecular sensing and characterization techniques, to quantum computers. The development of complex engineered systems that exploit this physics is predicated at least partially upon in silico design and optimization that properly capture the light-matter coupling. In this thesis, the details of computational frameworks that enable this type of analysis, based upon both Integral Equation and Discontinuous Galerkin formulations will be explored. There will be a primary focus on the development of efficient and accurate software, with results corroborating both. The secondary focus will be on the use of these tools in the analysis of a number of exemplary systems.

  12. A discontinuous Galerkin finite element discretization of the Euler equations for compressible and incompressible fluids

    SciTech Connect

    Pesch, L. Vegt, J.J.W. van der

    2008-05-10

    Using the generalized variable formulation of the Euler equations of fluid dynamics, we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior: ideal and real gases can be treated with the same method as an incompressible fluid. The well-defined incompressible limit relies on using pressure primitive or entropy variables. In particular entropy variables can provide numerical methods with attractive properties, e.g. fulfillment of the second law of thermodynamics. We show how a discontinuous Galerkin finite element discretization previously used for compressible flow with an ideal gas equation of state can be extended for general fluids. We also examine which components of the numerical method have to be changed or adapted. Especially, we investigate different possibilities of solving the nonlinear algebraic system with a pseudo-time iteration. Numerical results highlight the applicability of the method for various fluids.

  13. Evaluation of shielding effectiveness of composite wall with a time domain discontinuous Galerkin method

    NASA Astrophysics Data System (ADS)

    Kameni Ntichi, Abelin; Modave, Axel; Boubekeur, Mohamed; Preault, Valentin; Pichon, Lionel; Geuzaine, Christophe

    2013-11-01

    This article presents a time domain discontinuous Galerkin method applied for solving the con-servative form of Maxwells' equations and computing the radiated fields in electromagnetic compatibility problems. The results obtained in homogeneous media for the transverse magnetic waves are validated in two cases. We compare our solution to an analytical solution of Maxwells' equations based on characteristic method. Our results on shielding effectiveness of a conducting wall are same as those obtained from analytical expression in frequency domain. The propagation in heterogeneous medium is explored. The shielding effectiveness of a composite wall partially filled by circular conductives inclusions is computed. The proposed results are in conformity with the classical predictive homogenization rules. Contribution to the Topical Issue "Numelec 2012", Edited by Adel Razek.

  14. Discontinuous Galerkin Method with Numerical Roe Flux for Spherical Shallow Water Equations

    NASA Astrophysics Data System (ADS)

    Yi, T.; Choi, S.; Kang, S.

    2013-12-01

    In developing the dynamic core of a numerical weather prediction model with discontinuous Galerkin method, a numerical flux at the boundaries of grid elements plays a vital role since it preserves the local conservation properties and has a significant impact on the accuracy and stability of numerical solutions. Due to these reasons, we developed the numerical Roe flux based on an approximate Riemann problem for spherical shallow water equations in Cartesian coordinates [1] to find out its stability and accuracy. In order to compare the performance with its counterpart flux, we used the Lax-Friedrichs flux, which has been used in many dynamic cores such as NUMA [1], CAM-DG [2] and MCore [3] because of its simplicity. The Lax-Friedrichs flux is implemented by a flux difference between left and right states plus the maximum characteristic wave speed across the boundaries of elements. It has been shown that the Lax-Friedrichs flux with the finite volume method is more dissipative and unstable than other numerical fluxes such as HLLC, AUSM+ and Roe. The Roe flux implemented in this study is based on the decomposition of flux difference over the element boundaries where the nonlinear equations are linearized. It is rarely used in dynamic cores due to its complexity and thus computational expensiveness. To compare the stability and accuracy of the Roe flux with the Lax-Friedrichs, two- and three-dimensional test cases are performed on a plane and cubed-sphere, respectively, with various numbers of element and polynomial order. For the two-dimensional case, the Gaussian bell is simulated on the plane with two different numbers of elements at the fixed polynomial orders. In three-dimensional cases on the cubed-sphere, we performed the test cases of a zonal flow over an isolated mountain and a Rossby-Haurwitz wave, of which initial conditions are the same as those of Williamson [4]. This study presented that the Roe flux with the discontinuous Galerkin method is less

  15. Direct discontinuous Galerkin method and its variations for second order elliptic equations

    DOE PAGESBeta

    Huang, Hongying; Chen, Zheng; Li, Jin; Yan, Jue

    2016-08-23

    In this study, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under L2 norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Math 31(6):638–662,more » 2013). A series of numerical examples are carried out to illustrate the accuracy and capability of the schemes. Numerically we obtain optimal (k+1)th order convergence for DDG method with interface correction and symmetric DDG method on nonuniform and unstructured triangular meshes. An interface problem with discontinuous diffusion coefficients is investigated and optimal (k+1)th order accuracy is obtained. Peak solutions with sharp transitions are captured well. Highly oscillatory wave solutions of Helmholz equation are well resolved.« less

  16. Variational space-time (dis)continuous Galerkin method for nonlinear free surface water waves

    NASA Astrophysics Data System (ADS)

    Gagarina, E.; Ambati, V. R.; van der Vegt, J. J. W.; Bokhove, O.

    2014-10-01

    A new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a finite element discretization that is continuous in space and discontinuous in time. One novel feature of this variational finite element approach is that the free surface evolution is variationally dependent on the mesh deformation vis-à-vis the mesh deformation being geometrically dependent on free surface evolution. Another key feature is the use of a variational (dis)continuous Galerkin finite element discretization in time. Moreover, in the absence of a wave maker, it is shown to be equivalent to the second order symplectic Störmer-Verlet time stepping scheme for the free-surface degrees of freedom. These key features add to the stability of the numerical method. Finally, the resulting numerical scheme is verified against nonlinear analytical solutions with long time simulations and validated against experimental measurements of driven wave solutions in a wave basin of the Maritime Research Institute Netherlands.

  17. A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates

    NASA Astrophysics Data System (ADS)

    Läuter, Matthias; Giraldo, Francis X.; Handorf, Dörthe; Dethloff, Klaus

    2008-12-01

    A global model of the atmosphere is presented governed by the shallow water equations and discretized by a Runge-Kutta discontinuous Galerkin method on an unstructured triangular grid. The shallow water equations on the sphere, a two-dimensional surface in R3, are locally represented in terms of spherical triangular coordinates, the appropriate local coordinate mappings on triangles. On every triangular grid element, this leads to a two-dimensional representation of tangential momentum and therefore only two discrete momentum equations. The discontinuous Galerkin method consists of an integral formulation which requires both area (elements) and line (element faces) integrals. Here, we use a Rusanov numerical flux to resolve the discontinuous fluxes at the element faces. A strong stability-preserving third-order Runge-Kutta method is applied for the time discretization. The polynomial space of order k on each curved triangle of the grid is characterized by a Lagrange basis and requires high-order quadature rules for the integration over elements and element faces. For the presented method no mass matrix inversion is necessary, except in a preprocessing step. The validation of the atmospheric model has been done considering standard tests from Williamson et al. [D.L. Williamson, J.B. Drake, J.J. Hack, R. Jakob, P.N. Swarztrauber, A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys. 102 (1992) 211-224], unsteady analytical solutions of the nonlinear shallow water equations and a barotropic instability caused by an initial perturbation of a jet stream. A convergence rate of O(Δx) was observed in the model experiments. Furthermore, a numerical experiment is presented, for which the third-order time-integration method limits the model error. Thus, the time step Δt is restricted by both the CFL-condition and accuracy demands. Conservation of mass was shown up to machine precision and energy conservation

  18. A high order discontinuous Galerkin method for elastic wave propagation in arbitrary heterogeneous media

    NASA Astrophysics Data System (ADS)

    Glinsky, Nathalie; Mercerat, Diego

    2013-04-01

    High-order numerical methods allow accurate simulations of ground motion using unstructured and relatively coarse meshes. In realistic media (sedimentary basins for example), we have to include strong variations of the material properties. For such configurations, the hypothesis that material properties are set constant in each element of the mesh can be a severe limitation since we need to use very fine meshes resulting in very small time steps for explicit time integration schemes. Moreover, smooth models are approximated by piecewise constant materials. For these reasons, we present an improvement of a nodal discontinuous Galerkin method (DG) allowing non constant material properties in the elements of the mesh for a better approximation of arbitrary heterogeneous media. We consider an isotropic, linearly elastic two-dimensional medium (characterized by ?, ? and μ) and solve the first-order velocity-stress system. As the stress tensor is symmetrical, let W? = (?V,?-?)t contain the velocity vector ?-V = (vx,vy)t and the stress components ?-? = (?xx,?yy,?xy)t, then, the system writes t ?-W + Ax (?,?,μ) ^xW?- + Ay(?,?,μ) ^yW ?- = 0, where Ax and Ay are 5x5 matrices depending of the material properties. We apply a discontinuous Galerkin method based on centered fluxes and a leap-frog time scheme to this system. We consider a bounded polyhedral domain discretized by triangles. The approximation of W?- is defined locally on each element by considering the Lagrange nodal interpolants. The system is multiplied by a test function t and integrated on each element Ti. To avoid computing extra terms, related to the variable properties within Ti, we introduce a change of variables on the stress components ( )t ?-? = (?xx,?yy,?xy)t ? ??? = 1(?xx + ?yy), 1 (?xx - ?yy),?xy 2 2 which allows writing the system in a pseudo-conservative form in the variable ?-W? = (?-V,???)t ? (?,?,μ) ^tW ?? + ?Ax x ??W + A?y y ??W = 0 , where the constant matrices Ãx and Ãy do not depend

  19. High-order Hybridized Discontinuous Galerkin (HDG) method for wave propagation simulation in complex geophysical media (elastic, acoustic and hydro-acoustic); an unifying framework to couple continuous Spectral Element and Discontinuous Galerkin Methods

    NASA Astrophysics Data System (ADS)

    Terrana, Sebastien; Vilotte, Jean-Pierre; Guillot, Laurent; Mariotti, Christian

    2015-04-01

    Today seismological observation systems combine broadband seismic receivers, hydrophones and micro-barometers antenna that provide complementary observations of source-radiated waves in heterogeneous and complex geophysical media. Exploiting these observations requires accurate and multi-physics - elastic, hydro-acoustic, infrasonic - wave simulation methods. A popular approach is the Spectral Element Method (SEM) (Chaljub et al, 2006) which is high-order accurate (low dispersion error), very flexible to parallelization and computationally attractive due to efficient sum factorization technique and diagonal mass matrix. However SEMs suffer from lack of flexibility in handling complex geometry and multi-physics wave propagation. High-order Discontinuous Galerkin Methods (DGMs), i.e. Dumbser et al (2006), Etienne et al. (2010), Wilcox et al (2010), are recent alternatives that can handle complex geometry, space-and-time adaptativity, and allow efficient multi-physics wave coupling at interfaces. However, DGMs are more memory demanding and less computationally attractive than SEMs, especially when explicit time stepping is used. We propose a new class of higher-order Hybridized Discontinuous Galerkin Spectral Elements (HDGSEM) methods for spatial discretization of wave equations, following the unifying framework for hybridization of Cockburn et al (2009) and Nguyen et al (2011), which allows for a single implementation of conforming and non-conforming SEMs. When used with energy conserving explicit time integration schemes, HDGSEM is flexible to handle complex geometry, computationally attractive and has significantly less degrees of freedom than classical DGMs, i.e., the only coupled unknowns are the single-valued numerical traces of the velocity field on the element's faces. The formulation can be extended to model fractional energy loss at interfaces between elastic, acoustic and hydro-acoustic media. Accuracy and performance of the HDGSEM are illustrated and

  20. A mass and momentum flux-form high-order discontinuous Galerkin shallow water model on the cubed-sphere

    NASA Astrophysics Data System (ADS)

    Bao, Lei; Nair, Ramachandran D.; Tufo, Henry M.

    2014-08-01

    A well-balanced discontinuous Galerkin (DG) flux-form shallow-water (SW) model on the sphere is developed and compared with a nodal DG SW model cast in the vector-invariant form for accuracy and conservation properties. A second-order diffusion scheme based on the local discontinuous Galerkin (LDG) method is added to the viscous version of the SW model and tested for conservation behaviors. The inviscid flux-form SW model is found to have better conservation of total energy and zonal angular momentum while the vector-invariant form provides better ability of conserving potential enstrophy. The inviscid flux-form tends to generate spurious vorticity but the LDG scheme combined with a well-balanced treatment can effectively eliminate the small-scale noise and generate smooth and accurate results.

  1. A priori error estimates for an hp-version of the discontinuous Galerkin method for hyperbolic conservation laws

    NASA Technical Reports Server (NTRS)

    Bey, Kim S.; Oden, J. Tinsley

    1993-01-01

    A priori error estimates are derived for hp-versions of the finite element method for discontinuous Galerkin approximations of a model class of linear, scalar, first-order hyperbolic conservation laws. These estimates are derived in a mesh dependent norm in which the coefficients depend upon both the local mesh size h(sub K) and a number p(sub k) which can be identified with the spectral order of the local approximations over each element.

  2. Kershaw closures for linear transport equations in slab geometry II: High-order realizability-preserving discontinuous-Galerkin schemes

    NASA Astrophysics Data System (ADS)

    Schneider, Florian

    2016-10-01

    This paper provides a generalization of the realizability-preserving discontinuous-Galerkin scheme given in [3] to general full-moment models that can be closed analytically. It is applied to the class of Kershaw closures, which are able to provide a cheap closure of the moment problem. This results in an efficient algorithm for the underlying linear transport equation. The efficiency of high-order methods is demonstrated using numerical convergence tests and non-smooth benchmark problems.

  3. An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes - IV. Anisotropy

    NASA Astrophysics Data System (ADS)

    de la Puente, Josep; Käser, Martin; Dumbser, Michael; Igel, Heiner

    2007-06-01

    We present a new numerical method to solve the heterogeneous elastic anisotropic wave equation with arbitrary high-order accuracy in space and time on unstructured tetrahedral meshes. Using the most general Hooke's tensor we derive the velocity-stress formulation leading to a linear hyperbolic system which accounts for the variation of the material properties depending on direction. This approach allows for the accurate modelling even of the most general crystalline symmetry class, the triclinic anisotropy, as no interpolation of material properties to particular mesh vertices is necessary. The proposed method combines the Discontinuous Galerkin method with the arbitrary high-order derivatives (ADER) time integration approach using arbitrary high-order derivatives of the piecewise polynomial representation of the unknown solution. The discontinuities of this piecewise polynomial approximation at element interfaces permit the application of the well-established theory of finite volumes and numerical fluxes across element interfaces obtained by the solution of derivative Riemann problems. Due to the novel ADER time integration technique the scheme provides the same approximation order in space and time automatically. A numerical convergence study confirms that the new scheme achieves the desired arbitrary high-order accuracy even for anisotropic material on unstructured tetrahedral meshes. Furthermore, it shows that higher accuracy can be reached with higher-order schemes while reducing computational cost and storage space. To this end, we also present a new Godunov-type numerical flux for anisotropic material and compare its accuracy with a computationally simpler Rusanov flux. As a further extension, we include the coupling of anisotropy and viscoelastic attenuation based on the Generalized Maxwell Body rheology and the mean and deviatoric stress concepts. Finally, we validate the new scheme by comparing the results of our simulations to an analytic solution as

  4. A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media

    NASA Astrophysics Data System (ADS)

    Wilcox, Lucas C.; Stadler, Georg; Burstedde, Carsten; Ghattas, Omar

    2010-12-01

    We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic-acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic-acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.

  5. A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media

    SciTech Connect

    Wilcox, Lucas C.; Stadler, Georg; Burstedde, Carsten; Ghattas, Omar

    2010-12-10

    We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic-acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic-acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.

  6. Equivalence between the Energy Stable Flux Reconstruction and Filtered Discontinuous Galerkin Schemes

    NASA Astrophysics Data System (ADS)

    Zwanenburg, Philip; Nadarajah, Siva

    2016-02-01

    The aim of this paper is to demonstrate the equivalence between filtered Discontinuous Galerkin (DG) schemes and the Energy Stable Flux Reconstruction (ESFR) schemes, expanding on previous demonstrations in 1D [1] and for straight-sided elements in 3D [2]. We first derive the DG and ESFR schemes in strong form and compare the respective flux penalization terms while highlighting the implications of the fundamental assumptions for stability in the ESFR formulations, notably that all ESFR scheme correction fields can be interpreted as modally filtered DG correction fields. We present the result in the general context of all higher dimensional curvilinear element formulations. Through a demonstration that there exists a weak form of the ESFR schemes which is both discretely and analytically equivalent to the strong form, we then extend the results obtained for the strong formulations to demonstrate that ESFR schemes can be interpreted as a DG scheme in weak form where discontinuous edge flux is substituted for numerical edge flux correction. Theoretical derivations are then verified with numerical results obtained from a 2D Euler testcase with curved boundaries. Given the current choice of high-order DG-type schemes and the question as to which might be best to use for a specific application, the main significance of this work is the bridge that it provides between them. Clearly outlining the similarities between the schemes results in the important conclusion that it is always less efficient to use ESFR schemes, as opposed to the weak DG scheme, when solving problems implicitly.

  7. Fully-Implicit Reconstructed Discontinuous Galerkin Method for Stiff Multiphysics Problems

    NASA Astrophysics Data System (ADS)

    Nourgaliev, Robert

    2015-11-01

    A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method's capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing. We focus on the method's accuracy (in both space and time), as well as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver. 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 at LLNL under project tracking code 13-SI-002.

  8. On Formulations of Discontinuous Galerkin and Related Methods for Conservation Laws

    NASA Technical Reports Server (NTRS)

    Huynh, H. T.

    2014-01-01

    A formulation for the discontinuous Galerkin (DG) method that leads to solutions using the differential form of the equation (as opposed to the standard integral form) is presented. The formulation includes (a) a derivative calculation that involves only data within each cell with no data interaction among cells, and (b) for each cell, corrections to this derivative that deal with the jumps in fluxes at the cell boundaries and allow data across cells to interact. The derivative with no interaction is obtained by a projection, but for nodal-type methods, evaluating this derivative by interpolation at the nodal points is more economical. The corrections are derived using the approximate (Dirac) delta functions. The formulation results in a family of schemes: different approximate delta functions give rise to different methods. It is shown that the current formulation is essentially equivalent to the flux reconstruction (FR) formulation. Due to the use of approximate delta functions, an energy stability proof simpler than that of Vincent, Castonguay, and Jameson (2011) for a family of schemes is derived. Accuracy and stability of resulting schemes are discussed via Fourier analyses. Similar to FR, the current formulation provides a unifying framework for high-order methods by recovering the DG, spectral difference (SD), and spectral volume (SV) schemes. It also yields stable, accurate, and economical methods.

  9. A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Hybrid Grids

    SciTech Connect

    Xiaodong Liu; Lijun Xuan; Hong Luo; Yidong Xia

    2001-01-01

    A reconstructed discontinuous Galerkin (rDG(P1P2)) method, originally introduced for the compressible Euler equations, is developed for the solution of the compressible Navier- Stokes equations on 3D hybrid grids. In this method, a piecewise quadratic polynomial solution is obtained from the underlying piecewise linear DG solution using a hierarchical Weighted Essentially Non-Oscillatory (WENO) reconstruction. The reconstructed quadratic polynomial solution is then used for the computation of the inviscid fluxes and the viscous fluxes using the second formulation of Bassi and Reay (Bassi-Rebay II). The developed rDG(P1P2) method is used to compute a variety of flow problems to assess its accuracy, efficiency, and robustness. The numerical results demonstrate that the rDG(P1P2) method is able to achieve the designed third-order of accuracy at a cost slightly higher than its underlying second-order DG method, outperform the third order DG method in terms of both computing costs and storage requirements, and obtain reliable and accurate solutions to the large eddy simulation (LES) and direct numerical simulation (DNS) of compressible turbulent flows.

  10. DG-FTLE: Lagrangian coherent structures with high-order discontinuous-Galerkin methods

    NASA Astrophysics Data System (ADS)

    Nelson, Daniel A.; Jacobs, Gustaaf B.

    2015-08-01

    We present an algorithm for the computation of finite-time Lyapunov exponent (FTLE) fields using discontinuous-Galerkin (dG) methods in two dimensions. The algorithm is designed to compute FTLE fields simultaneously with the time integration of dG-based flow solvers of conservation laws. Fluid tracers are initialized at Gauss-Lobatto quadrature nodes within an element. The deformation gradient tensor, defined by the deformation of the Lagrangian flow map in finite time, is determined per element with high-order dG operators. Multiple flow maps are constructed from a particle trace that is released at a single initial time by mapping and interpolating the flow map formed by the locations of the fluid tracers after finite time integration to a unit square master element and to the quadrature nodes within the element, respectively. The interpolated flow maps are used to compute forward-time and backward-time FTLE fields at several times using dG operators. For a large finite integration time, the interpolation is increasingly poorly conditioned because of the excessive subdomain deformation. The conditioning can be used in addition to the FTLE to quantify the deformation of the flow field and identify subdomains with material lines that define Lagrangian coherent structures. The algorithm is tested on three benchmarks: an analytical spatially periodic gyre flow, a vortex advected by a uniform inviscid flow, and the viscous flow around a square cylinder. In these cases, the algorithm is shown to have spectral convergence.

  11. Recovery Discontinuous Galerkin Jacobian-free Newton-Krylov Method for all-speed flows

    SciTech Connect

    HyeongKae Park; Robert Nourgaliev; Vincent Mousseau; Dana Knoll

    2008-07-01

    There is an increasing interest to develop the next generation simulation tools for the advanced nuclear energy systems. These tools will utilize the state-of-art numerical algorithms and computer science technology in order to maximize the predictive capability, support advanced reactor designs, reduce uncertainty and increase safety margins. In analyzing nuclear energy systems, we are interested in compressible low-Mach number, high heat flux flows with a wide range of Re, Ra, and Pr numbers. Under these conditions, the focus is placed on turbulent heat transfer, in contrast to other industries whose main interest is in capturing turbulent mixing. Our objective is to develop singlepoint turbulence closure models for large-scale engineering CFD code, using Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES) tools, requireing very accurate and efficient numerical algorithms. The focus of this work is placed on fully-implicit, high-order spatiotemporal discretization based on the discontinuous Galerkin method solving the conservative form of the compressible Navier-Stokes equations. The method utilizes a local reconstruction procedure derived from weak formulation of the problem, which is inspired by the recovery diffusion flux algorithm of van Leer and Nomura [?] and by the piecewise parabolic reconstruction [?] in the finite volume method. The developed methodology is integrated into the Jacobianfree Newton-Krylov framework [?] to allow a fully-implicit solution of the problem.

  12. Validation of an Adaptive Triangular Discontinuous Galerkin Shallow Water Model for the 2011 Tohoku Tsunami

    NASA Astrophysics Data System (ADS)

    Vater, Stefan; Behrens, Jörn

    2016-04-01

    We apply a tsunami simulation framework, which is based on depth-integrated hydrodynamic model equations, to the 2011 Tohoku tsunami event. While this model has been previously validated for analytic test cases and laboratory experiments, here it is applied to earthquake sources which are based on seismic inversion. Simulated wave heights and runup at the coast are compared to actual measurements. The discretization is based on a second-order Runge-Kutta discontinuous Galerkin (RKDG) scheme on triangular grids and features a robust wetting and drying scheme for the simulation of inundation events at the coast. Adaptive mesh refinement enables the efficient computation of large domains, while at the same time it allows for high local resolution and geometric accuracy. This work is part of the ASCETE (Advanced Simulation of Coupled Earthquake and Tsunami Events) project, which aims at an improved understanding of the coupling between the earthquake and the generated tsunami event. In this course, a coupled simulation framework has been developed which couples physics-based rupture generation with the presented hydrodynamic tsunami propagation and inundation model.

  13. An h-adaptive local discontinuous Galerkin method for the Navier-Stokes-Korteweg equations

    NASA Astrophysics Data System (ADS)

    Tian, Lulu; Xu, Yan; Kuerten, J. G. M.; van der Vegt, J. J. W.

    2016-08-01

    In this article, we develop a mesh adaptation algorithm for a local discontinuous Galerkin (LDG) discretization of the (non)-isothermal Navier-Stokes-Korteweg (NSK) equations modeling liquid-vapor flows with phase change. This work is a continuation of our previous research, where we proposed LDG discretizations for the (non)-isothermal NSK equations with a time-implicit Runge-Kutta method. To save computing time and to capture the thin interfaces more accurately, we extend the LDG discretization with a mesh adaptation method. Given the current adapted mesh, a criterion for selecting candidate elements for refinement and coarsening is adopted based on the locally largest value of the density gradient. A strategy to refine and coarsen the candidate elements is then provided. We emphasize that the adaptive LDG discretization is relatively simple and does not require additional stabilization. The use of a locally refined mesh in combination with an implicit Runge-Kutta time method is, however, non-trivial, but results in an efficient time integration method for the NSK equations. Computations, including cases with solid wall boundaries, are provided to demonstrate the accuracy, efficiency and capabilities of the adaptive LDG discretizations.

  14. A Kinetic Vlasov Model for Plasma Simulation Using Discontinuous Galerkin Method on Many-Core Architectures

    NASA Astrophysics Data System (ADS)

    Reddell, Noah

    Advances are reported in the three pillars of computational science achieving a new capability for understanding dynamic plasma phenomena outside of local thermodynamic equilibrium. A continuum kinetic model for plasma based on the Vlasov-Maxwell system for multiple particle species is developed. Consideration is added for boundary conditions in a truncated velocity domain and supporting wall interactions. A scheme to scale the velocity domain for multiple particle species with different temperatures and particle mass while sharing one computational mesh is described. A method for assessing the degree to which the kinetic solution differs from a Maxwell-Boltzmann distribution is introduced and tested on a thoroughly studied test case. The discontinuous Galerkin numerical method is extended for efficient solution of hyperbolic conservation laws in five or more particle phase-space dimensions using tensor-product hypercube elements with arbitrary polynomial order. A scheme for velocity moment integration is integrated as required for coupling between the plasma species and electromagnetic waves. A new high performance simulation code WARPM is developed to efficiently implement the model and numerical method on emerging many-core supercomputing architectures. WARPM uses the OpenCL programming model for computational kernels and task parallelism to overlap computation with communication. WARPM single-node performance and parallel scaling efficiency are analyzed with bottlenecks identified guiding future directions for the implementation. The plasma modeling capability is validated against physical problems with analytic solutions and well established benchmark problems.

  15. Discontinuous Galerkin Methods for the Two-Moment Model of Radiation Transport

    NASA Astrophysics Data System (ADS)

    Endeve, Eirik; Hauck, Cory

    2016-03-01

    We are developing computational methods for simulation of radiation transport in astrophysical systems (e.g., neutrino transport in core-collapse supernovae). Here we consider the two-moment model of radiation transport, where the energy density E and flux F - angular moments of a phase space distribution function - approximates the radiation field in a computationally tractable manner. We aim to develop multi-dimensional methods that are (i) high-order accurate for computational efficiency, and (ii) robust in the sense that the solution remains in the realizable set R = { (E , F) | E >= 0 and E - | F | >= 0 } (i.e., E and F are consistent with moments of an underlying distribution). Our approach is based on the Runge-Kutta discontinuous Galerkin method, which has many attractive properties, including high-order accuracy on a compact stencil. We present the physical model and numerical method, and show results from a multi-dimensional implementation. Tests show that the method is high-order accurate and strictly preserves realizability of the moments.

  16. A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flows

    NASA Astrophysics Data System (ADS)

    Owkes, Mark; Desjardins, Olivier

    2013-09-01

    The accurate conservative level set (ACLS) method of Desjardins et al. [O. Desjardins, V. Moureau, H. Pitsch, An accurate conservative level set/ghost fluid method for simulating turbulent atomization, J. Comput. Phys. 227 (18) (2008) 8395-8416] is extended by using a discontinuous Galerkin (DG) discretization. DG allows for the scheme to have an arbitrarily high order of accuracy with the smallest possible computational stencil resulting in an accurate method with good parallel scaling. This work includes a DG implementation of the level set transport equation, which moves the level set with the flow field velocity, and a DG implementation of the reinitialization equation, which is used to maintain the shape of the level set profile to promote good mass conservation. A near second order converging interface curvature is obtained by following a height function methodology (common amongst volume of fluid schemes) in the context of the conservative level set. Various numerical experiments are conducted to test the properties of the method and show excellent results, even on coarse meshes. The tests include Zalesak’s disk, two-dimensional deformation of a circle, time evolution of a standing wave, and a study of the Kelvin-Helmholtz instability. Finally, this novel methodology is employed to simulate the break-up of a turbulent liquid jet.

  17. An efficient parallel implementation of explicit multirate Runge–Kutta schemes for discontinuous Galerkin computations

    SciTech Connect

    Seny, Bruno Lambrechts, Jonathan; Toulorge, Thomas; Legat, Vincent; Remacle, Jean-François

    2014-01-01

    Although explicit time integration schemes require small computational efforts per time step, their efficiency is severely restricted by their stability limits. Indeed, the multi-scale nature of some physical processes combined with highly unstructured meshes can lead some elements to impose a severely small stable time step for a global problem. Multirate methods offer a way to increase the global efficiency by gathering grid cells in appropriate groups under local stability conditions. These methods are well suited to the discontinuous Galerkin framework. The parallelization of the multirate strategy is challenging because grid cells have different workloads. The computational cost is different for each sub-time step depending on the elements involved and a classical partitioning strategy is not adequate any more. In this paper, we propose a solution that makes use of multi-constraint mesh partitioning. It tends to minimize the inter-processor communications, while ensuring that the workload is almost equally shared by every computer core at every stage of the algorithm. Particular attention is given to the simplicity of the parallel multirate algorithm while minimizing computational and communication overheads. Our implementation makes use of the MeTiS library for mesh partitioning and the Message Passing Interface for inter-processor communication. Performance analyses for two and three-dimensional practical applications confirm that multirate methods preserve important computational advantages of explicit methods up to a significant number of processors.

  18. Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation

    NASA Astrophysics Data System (ADS)

    Kompenhans, Moritz; Rubio, Gonzalo; Ferrer, Esteban; Valero, Eusebio

    2016-02-01

    In this paper three p-adaptation strategies based on the minimization of the truncation error are presented for high order discontinuous Galerkin methods. The truncation error is approximated by means of a τ-estimation procedure and enables the identification of mesh regions that require adaptation. Three adaptation strategies are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. All strategies require fine solutions, which are obtained by enriching the polynomial order, but while the former needs time converged solutions, the last two rely on non-converged solutions, which lead to faster computations. In addition, the high order method permits the spatial decoupling for the estimated errors and enables anisotropic p-adaptation. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier-Stokes equations. It is shown that the two quasi-a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively.

  19. A Spalart-Allmaras turbulence model implementation in a discontinuous Galerkin solver for incompressible flows

    NASA Astrophysics Data System (ADS)

    Crivellini, Andrea; D'Alessandro, Valerio; Bassi, Francesco

    2013-05-01

    In this paper the artificial compressibility flux Discontinuous Galerkin (DG) method for the solution of the incompressible Navier-Stokes equations has been extended to deal with the Reynolds-Averaged Navier-Stokes (RANS) equations coupled with the Spalart-Allmaras (SA) turbulence model. DG implementations of the RANS and SA equations for compressible flows have already been reported in the literature, including the description of limiting or stabilization techniques adopted in order to prevent the turbulent viscosity ν˜ from becoming negative. In this paper we introduce an SA model implementation that deals with negative ν˜ values by modifying the source and diffusion terms in the SA model equation only when the working variable or one of the model closure functions become negative. This results in an efficient high-order implementation where either stabilization terms or even additional equations are avoided. We remark that the proposed implementation is not DG specific and it is well suited for any numerical discretization of the RANS-SA governing equations. The reliability, robustness and accuracy of the proposed implementation have been assessed by computing several high Reynolds number turbulent test cases: the flow over a flat plate (Re=107), the flow past a backward-facing step (Re=37400) and the flow around a NACA 0012 airfoil at different angles of attack (α=0°, 10°, 15°) and Reynolds numbers (Re=2.88×106,6×106).

  20. A nodal discontinuous Galerkin method for reverse-time migration on GPU clusters

    NASA Astrophysics Data System (ADS)

    Modave, A.; St-Cyr, A.; Mulder, W. A.; Warburton, T.

    2015-11-01

    Improving both accuracy and computational performance of numerical tools is a major challenge for seismic imaging and generally requires specialized implementations to make full use of modern parallel architectures. We present a computational strategy for reverse-time migration (RTM) with accelerator-aided clusters. A new imaging condition computed from the pressure and velocity fields is introduced. The model solver is based on a high-order discontinuous Galerkin time-domain (DGTD) method for the pressure-velocity system with unstructured meshes and multirate local time stepping. We adopted the MPI+X approach for distributed programming where X is a threaded programming model. In this work we chose OCCA, a unified framework that makes use of major multithreading languages (e.g. CUDA and OpenCL) and offers the flexibility to run on several hardware architectures. DGTD schemes are suitable for efficient computations with accelerators thanks to localized element-to-element coupling and the dense algebraic operations required for each element. Moreover, compared to high-order finite-difference schemes, the thin halo inherent to DGTD method reduces the amount of data to be exchanged between MPI processes and storage requirements for RTM procedures. The amount of data to be recorded during simulation is reduced by storing only boundary values in memory rather than on disk and recreating the forward wavefields. Computational results are presented that indicate that these methods are strong scalable up to at least 32 GPUs for a three-dimensional RTM case.

  1. A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flows

    SciTech Connect

    Owkes, Mark Desjardins, Olivier

    2013-09-15

    The accurate conservative level set (ACLS) method of Desjardins et al. [O. Desjardins, V. Moureau, H. Pitsch, An accurate conservative level set/ghost fluid method for simulating turbulent atomization, J. Comput. Phys. 227 (18) (2008) 8395–8416] is extended by using a discontinuous Galerkin (DG) discretization. DG allows for the scheme to have an arbitrarily high order of accuracy with the smallest possible computational stencil resulting in an accurate method with good parallel scaling. This work includes a DG implementation of the level set transport equation, which moves the level set with the flow field velocity, and a DG implementation of the reinitialization equation, which is used to maintain the shape of the level set profile to promote good mass conservation. A near second order converging interface curvature is obtained by following a height function methodology (common amongst volume of fluid schemes) in the context of the conservative level set. Various numerical experiments are conducted to test the properties of the method and show excellent results, even on coarse meshes. The tests include Zalesak’s disk, two-dimensional deformation of a circle, time evolution of a standing wave, and a study of the Kelvin–Helmholtz instability. Finally, this novel methodology is employed to simulate the break-up of a turbulent liquid jet.

  2. Robust and Accurate Shock Capturing Method for High-Order Discontinuous Galerkin Methods

    NASA Technical Reports Server (NTRS)

    Atkins, Harold L.; Pampell, Alyssa

    2011-01-01

    A simple yet robust and accurate approach for capturing shock waves using a high-order discontinuous Galerkin (DG) method is presented. The method uses the physical viscous terms of the Navier-Stokes equations as suggested by others; however, the proposed formulation of the numerical viscosity is continuous and compact by construction, and does not require the solution of an auxiliary diffusion equation. This work also presents two analyses that guided the formulation of the numerical viscosity and certain aspects of the DG implementation. A local eigenvalue analysis of the DG discretization applied to a shock containing element is used to evaluate the robustness of several Riemann flux functions, and to evaluate algorithm choices that exist within the underlying DG discretization. A second analysis examines exact solutions to the DG discretization in a shock containing element, and identifies a "model" instability that will inevitably arise when solving the Euler equations using the DG method. This analysis identifies the minimum viscosity required for stability. The shock capturing method is demonstrated for high-speed flow over an inviscid cylinder and for an unsteady disturbance in a hypersonic boundary layer. Numerical tests are presented that evaluate several aspects of the shock detection terms. The sensitivity of the results to model parameters is examined with grid and order refinement studies.

  3. Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

    NASA Technical Reports Server (NTRS)

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

    2006-01-01

    We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

  4. Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change

    DOE PAGESBeta

    Nourgaliev, R.; Luo, H.; Weston, B.; Anderson, A.; Schofield, S.; Dunn, T.; Delplanque, J. -P.

    2015-11-11

    A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as wellmore » as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.« less

  5. An efficient, unconditionally energy stable local discontinuous Galerkin scheme for the Cahn-Hilliard-Brinkman system

    NASA Astrophysics Data System (ADS)

    Guo, Ruihan; Xu, Yan

    2015-10-01

    In this paper, we present an efficient and unconditionally energy stable fully-discrete local discontinuous Galerkin (LDG) method for approximating the Cahn-Hilliard-Brinkman (CHB) system, which is comprised of a Cahn-Hilliard type equation and a generalized Brinkman equation modeling fluid flow. The semi-discrete energy stability of the LDG method is proved firstly. Due to the strict time step restriction (Δt = O (Δx4)) of explicit time discretization methods for stability, we introduce a semi-implicit scheme which consists of the implicit Euler method combined with a convex splitting of the discrete Cahn-Hilliard energy strategy for the temporal discretization. The unconditional energy stability of this fully-discrete convex splitting scheme is also proved. Obviously, the fully-discrete equations at the implicit time level are nonlinear, and to enhance the efficiency of the proposed approach, the nonlinear Full Approximation Scheme (FAS) multigrid method has been employed to solve this system of algebraic equations. We also show the nearly optimal complexity numerically. Numerical experiments based on the overall solution method of combining the proposed LDG method, convex splitting scheme and the nonlinear multigrid solver are given to validate the theoretical results and to show the effectiveness of the proposed approach for the CHB system.

  6. Edge reconstruction in armchair phosphorene nanoribbons revealed by discontinuous Galerkin density functional theory.

    PubMed

    Hu, Wei; Lin, Lin; Yang, Chao

    2015-12-21

    With the help of our recently developed massively parallel DGDFT (Discontinuous Galerkin Density Functional Theory) methodology, we perform large-scale Kohn-Sham density functional theory calculations on phosphorene nanoribbons with armchair edges (ACPNRs) containing a few thousands to ten thousand atoms. The use of DGDFT allows us to systematically achieve a conventional plane wave basis set type of accuracy, but with a much smaller number (about 15) of adaptive local basis (ALB) functions per atom for this system. The relatively small number of degrees of freedom required to represent the Kohn-Sham Hamiltonian, together with the use of the pole expansion the selected inversion (PEXSI) technique that circumvents the need to diagonalize the Hamiltonian, results in a highly efficient and scalable computational scheme for analyzing the electronic structures of ACPNRs as well as their dynamics. The total wall clock time for calculating the electronic structures of large-scale ACPNRs containing 1080-10,800 atoms is only 10-25 s per self-consistent field (SCF) iteration, with accuracy fully comparable to that obtained from conventional planewave DFT calculations. For the ACPNR system, we observe that the DGDFT methodology can scale to 5000-50,000 processors. We use DGDFT based ab initio molecular dynamics (AIMD) calculations to study the thermodynamic stability of ACPNRs. Our calculations reveal that a 2 × 1 edge reconstruction appears in ACPNRs at room temperature.

  7. De-Aliasing Through Over-Integration Applied to the Flux Reconstruction and Discontinuous Galerkin Methods

    NASA Technical Reports Server (NTRS)

    Spiegel, Seth C.; Huynh, H. T.; DeBonis, James R.

    2015-01-01

    High-order methods are quickly becoming popular for turbulent flows as the amount of computer processing power increases. The flux reconstruction (FR) method presents a unifying framework for a wide class of high-order methods including discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV). It offers a simple, efficient, and easy way to implement nodal-based methods that are derived via the differential form of the governing equations. Whereas high-order methods have enjoyed recent success, they have been known to introduce numerical instabilities due to polynomial aliasing when applied to under-resolved nonlinear problems. Aliasing errors have been extensively studied in reference to DG methods; however, their study regarding FR methods has mostly been limited to the selection of the nodal points used within each cell. Here, we extend some of the de-aliasing techniques used for DG methods, primarily over-integration, to the FR framework. Our results show that over-integration does remove aliasing errors but may not remove all instabilities caused by insufficient resolution (for FR as well as DG).

  8. Discontinuous Galerkin methods for plasma physics in the scrape-off layer of tokamaks

    SciTech Connect

    Michoski, C.; Meyerson, D.; Isaac, T.; Waelbroeck, F.

    2014-10-01

    A new parallel discontinuous Galerkin solver, called ArcOn, is developed to describe the intermittent turbulent transport of filamentary blobs in the scrape-off layer (SOL) of fusion plasma. The model is comprised of an elliptic subsystem coupled to two convection-dominated reaction–diffusion–convection equations. Upwinding is used for a class of numerical fluxes developed to accommodate cross product driven convection, and the elliptic solver uses SIPG, NIPG, IIPG, Brezzi, and Bassi–Rebay fluxes to formulate the stiffness matrix. A novel entropy sensor is developed for this system, designed for a space–time varying artificial diffusion/viscosity regularization algorithm. Some numerical experiments are performed to show convergence order on manufactured solutions, regularization of blob/streamer dynamics in the SOL given unstable parameterizations, long-time stability of modon (or dipole drift vortex) solutions arising in simulations of drift-wave turbulence, and finally the formation of edge mode turbulence in the scrape-off layer under turbulent saturation conditions.

  9. GPU performance analysis of a nodal discontinuous Galerkin method for acoustic and elastic models

    NASA Astrophysics Data System (ADS)

    Modave, A.; St-Cyr, A.; Warburton, T.

    2016-06-01

    Finite element schemes based on discontinuous Galerkin methods possess features amenable to massively parallel computing accelerated with general purpose graphics processing units (GPUs). However, the computational performance of such schemes strongly depends on their implementation. In the past, several implementation strategies have been proposed. They are based exclusively on specialized compute kernels tuned for each operation, or they can leverage BLAS libraries that provide optimized routines for basic linear algebra operations. In this paper, we present and analyze up-to-date performance results for different implementations, tested in a unified framework on a single NVIDIA GTX980 GPU. We show that specialized kernels written with a one-node-per-thread strategy are competitive for polynomial bases up to the fifth and seventh degrees for acoustic and elastic models, respectively. For higher degrees, a strategy that makes use of the NVIDIA cuBLAS library provides better results, able to reach a net arithmetic throughput 35.7% of the theoretical peak value.

  10. A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation

    NASA Astrophysics Data System (ADS)

    Liu, Hailiang; Yi, Nianyu

    2016-09-01

    The invariant preserving property is one of the guiding principles for numerical algorithms in solving wave equations, in order to minimize phase and amplitude errors after long time simulation. In this paper, we design, analyze and numerically validate a Hamiltonian preserving discontinuous Galerkin method for solving the Korteweg-de Vries (KdV) equation. For the generalized KdV equation, the semi-discrete formulation is shown to preserve both the first and the third conserved integrals, and approximately preserve the second conserved integral; for the linearized KdV equation, all the first three conserved integrals are preserved, and optimal error estimates are obtained for polynomials of even degree. The preservation properties are also maintained by the fully discrete DG scheme. Our numerical experiments demonstrate both high accuracy of convergence and preservation of all three conserved integrals for the generalized KdV equation. We also show that the shape of the solution, after long time simulation, is well preserved due to the Hamiltonian preserving property.

  11. Three discontinuous Galerkin schemes for the anisotropic heat conduction equation on non-aligned grids

    NASA Astrophysics Data System (ADS)

    Held, M.; Wiesenberger, M.; Stegmeir, A.

    2016-02-01

    We present and discuss three discontinuous Galerkin (dG) discretizations for the anisotropic heat conduction equation on non-aligned cylindrical grids. Our non-aligned scheme relies on a self-adjoint local dG (LDG) discretization of the elliptic operator. It conserves the energy exactly and converges with arbitrary order. The pollution by numerical perpendicular heat fluxes decreases with superconvergence rates. We compare this scheme with aligned schemes that are based on the flux-coordinate independent approach for the discretization of parallel derivatives. Here, the dG method provides the necessary interpolation. The first aligned discretization can be used in an explicit time-integrator. However, the scheme violates conservation of energy and shows up stagnating convergence rates for very high resolutions. We overcome this partly by using the adjoint of the parallel derivative operator to construct a second self-adjoint aligned scheme. This scheme preserves energy, but reveals unphysical oscillations in the numerical tests, which result in a decreased order of convergence. Both aligned schemes exhibit low numerical heat fluxes into the perpendicular direction and are superior for flute-modes with finite parallel gradients. We build our argumentation on various numerical experiments on all three schemes for a general axisymmetric magnetic field, which is closed by a comparison to the aligned finite difference (FD) schemes of Stegmeir et al. (2014) and Stegmeir et al. (submitted for publication).

  12. An efficient parallel implementation of explicit multirate Runge-Kutta schemes for discontinuous Galerkin computations

    NASA Astrophysics Data System (ADS)

    Seny, Bruno; Lambrechts, Jonathan; Toulorge, Thomas; Legat, Vincent; Remacle, Jean-François

    2014-01-01

    Although explicit time integration schemes require small computational efforts per time step, their efficiency is severely restricted by their stability limits. Indeed, the multi-scale nature of some physical processes combined with highly unstructured meshes can lead some elements to impose a severely small stable time step for a global problem. Multirate methods offer a way to increase the global efficiency by gathering grid cells in appropriate groups under local stability conditions. These methods are well suited to the discontinuous Galerkin framework. The parallelization of the multirate strategy is challenging because grid cells have different workloads. The computational cost is different for each sub-time step depending on the elements involved and a classical partitioning strategy is not adequate any more. In this paper, we propose a solution that makes use of multi-constraint mesh partitioning. It tends to minimize the inter-processor communications, while ensuring that the workload is almost equally shared by every computer core at every stage of the algorithm. Particular attention is given to the simplicity of the parallel multirate algorithm while minimizing computational and communication overheads. Our implementation makes use of the MeTiS library for mesh partitioning and the Message Passing Interface for inter-processor communication. Performance analyses for two and three-dimensional practical applications confirm that multirate methods preserve important computational advantages of explicit methods up to a significant number of processors.

  13. Bound-preserving discontinuous Galerkin methods for conservative phase space advection in curvilinear coordinates

    NASA Astrophysics Data System (ADS)

    Endeve, Eirik; Hauck, Cory D.; Xing, Yulong; Mezzacappa, Anthony

    2015-04-01

    We extend the positivity-preserving method of Zhang and Shu [49] to simulate the advection of neutral particles in phase space using curvilinear coordinates. The ability to utilize these coordinates is important for non-equilibrium transport problems in general relativity and also in science and engineering applications with specific geometries. The method achieves high-order accuracy using Discontinuous Galerkin (DG) discretization of phase space and strong stability-preserving, Runge-Kutta (SSP-RK) time integration. Special care is taken to ensure that the method preserves strict bounds for the phase space distribution function f; i.e., f ∈ [ 0 , 1 ]. The combination of suitable CFL conditions and the use of the high-order limiter proposed in [49] is sufficient to ensure positivity of the distribution function. However, to ensure that the distribution function satisfies the upper bound, the discretization must, in addition, preserve the divergence-free property of the phase space flow. Proofs that highlight the necessary conditions are presented for general curvilinear coordinates, and the details of these conditions are worked out for some commonly used coordinate systems (i.e., spherical polar spatial coordinates in spherical symmetry and cylindrical spatial coordinates in axial symmetry, both with spherical momentum coordinates). Results from numerical experiments - including one example in spherical symmetry adopting the Schwarzschild metric - demonstrate that the method achieves high-order accuracy and that the distribution function satisfies the maximum principle.

  14. A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction

    DOE PAGESBeta

    Sheldon, Jason P.; Miller, Scott T.; Pitt, Jonathan S.

    2016-08-31

    This study presents a novel application of the hybridizable discontinuous Galerkin (HDG) finite element method to the multi-physics simulation of coupled fluid–structure interaction (FSI) problems. Recent applications of the HDG method have primarily been for single-physics problems including both solids and fluids, which are necessary building blocks for FSI modeling. Utilizing these established models, HDG formulations for linear elastostatics, a nonlinear elastodynamic model, and arbitrary Lagrangian–Eulerian Navier–Stokes are derived. The elasticity formulations are written in a Lagrangian reference frame, with the nonlinear formulation restricted to hyperelastic materials. With these individual solid and fluid formulations, the remaining challenge in FSI modelingmore » is coupling together their disparate mathematics on the fluid–solid interface. This coupling is presented, along with the resultant HDG FSI formulation. Verification of the component models, through the method of manufactured solutions, is performed and each model is shown to converge at the expected rate. The individual components, along with the complete FSI model, are then compared to the benchmark problems proposed by Turek and Hron [1]. The solutions from the HDG formulation presented in this work trend towards the benchmark as the spatial polynomial order and the temporal order of integration are increased.« less

  15. Discontinuous Galerkin solution of the Navier-Stokes equations on deformable domains

    SciTech Connect

    Persson, P.-O.; Bonet, J.; Peraire, J.

    2009-01-13

    We describe a method for computing time-dependent solutions to the compressible Navier-Stokes equations on variable geometries. We introduce a continuous mapping between a fixed reference configuration and the time varying domain, By writing the Navier-Stokes equations as a conservation law for the independent variables in the reference configuration, the complexity introduced by variable geometry is reduced to solving a transformed conservation law in a fixed reference configuration, The spatial discretization is carried out using the Discontinuous Galerkin method on unstructured meshes of triangles, while the time integration is performed using an explicit Runge-Kutta method, For general domain changes, the standard scheme fails to preserve exactly the free-stream solution which leads to some accuracy degradation, especially for low order approximations. This situation is remedied by adding an additional equation for the time evolution of the transformation Jacobian to the original conservation law and correcting for the accumulated metric integration errors. A number of results are shown to illustrate the flexibility of the approach to handle high order approximations on complex geometries.

  16. Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change

    SciTech Connect

    Nourgaliev, R.; Luo, H.; Weston, B.; Anderson, A.; Schofield, S.; Dunn, T.; Delplanque, J. -P.

    2015-11-11

    A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as well as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.

  17. Hamiltonian discontinuous Galerkin FEM for linear, rotating incompressible Euler equations: Inertial waves

    SciTech Connect

    Nurijanyan, S.; Vegt, J.J.W. van der; Bokhove, O.

    2013-05-15

    A discontinuous Galerkin finite element method (DGFEM) has been developed and tested for the linear, three-dimensional, rotating incompressible Euler equations. These equations admit complicated wave solutions, which poses numerical challenges. These challenges concern: (i) discretisation of a divergence-free velocity field; (ii) discretisation of geostrophic boundary conditions combined with no-normal flow at solid walls; (iii) discretisation of the conserved, Hamiltonian dynamics of the inertial-waves; and, (iv) large-scale computational demands owing to the three-dimensional nature of inertial-wave dynamics and possibly its narrow zones of chaotic attraction. These issues have been resolved, for example: (i) by employing Dirac’s method of constrained Hamiltonian dynamics to our DGFEM for linear, compressible flows, thus enforcing the incompressibility constraints; (ii) by enforcing no-normal flow at solid walls in a weak form and geostrophic tangential flow along the wall; and, (iii) by applying a symplectic time discretisation. We compared our simulations with exact solutions of three-dimensional incompressible flows, in (non) rotating periodic and partly periodic cuboids (Poincaré waves). Additional verifications concerned semi-analytical eigenmode solutions in rotating cuboids with solid walls. Finally, a simulation in a tilted rotating tank, yielding more complicated wave dynamics, demonstrates the potential of our new method.

  18. Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations

    NASA Astrophysics Data System (ADS)

    Jiang, Zhen-Hua; Yan, Chao; Yu, Jian

    2013-08-01

    Two types of implicit algorithms have been improved for high order discontinuous Galerkin (DG) method to solve compressible Navier-Stokes (NS) equations on triangular grids. A block lower-upper symmetric Gauss-Seidel (BLU-SGS) approach is implemented as a nonlinear iterative scheme. And a modified LU-SGS (LLU-SGS) approach is suggested to reduce the memory requirements while retain the good convergence performance of the original LU-SGS approach. Both implicit schemes have the significant advantage that only the diagonal block matrix is stored. The resulting implicit high-order DG methods are applied, in combination with Hermite weighted essentially non-oscillatory (HWENO) limiters, to solve viscous flow problems. Numerical results demonstrate that the present implicit methods are able to achieve significant efficiency improvements over explicit counterparts and for viscous flows with shocks, and the HWENO limiters can be used to achieve the desired essentially non-oscillatory shock transition and the designed high-order accuracy simultaneously.

  19. A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws

    NASA Astrophysics Data System (ADS)

    Dumbser, Michael; Zanotti, Olindo; Loubère, Raphaël; Diot, Steven

    2014-12-01

    The purpose of this work is to propose a novel a posteriori finite volume subcell limiter technique for the Discontinuous Galerkin finite element method for nonlinear systems of hyperbolic conservation laws in multiple space dimensions that works well for arbitrary high order of accuracy in space and time and that does not destroy the natural subcell resolution properties of the DG method. High order time discretization is achieved via a one-step ADER approach that uses a local space-time discontinuous Galerkin predictor method to evolve the data locally in time within each cell. Our new limiting strategy is based on the so-called MOOD paradigm, which a posteriori verifies the validity of a discrete candidate solution against physical and numerical detection criteria after each time step. Here, we employ a relaxed discrete maximum principle in the sense of piecewise polynomials and the positivity of the numerical solution as detection criteria. Within the DG scheme on the main grid, the discrete solution is represented by piecewise polynomials of degree N. For those troubled cells that need limiting, our new limiter approach recomputes the discrete solution by scattering the DG polynomials at the previous time step onto a set of Ns=2N+1 finite volume subcells per space dimension. A robust but accurate ADER-WENO finite volume scheme then updates the subcell averages of the conservative variables within the detected troubled cells. The recomputed subcell averages are subsequently gathered back into high order cell-centered DG polynomials on the main grid via a subgrid reconstruction operator. The choice of Ns=2N+1 subcells is optimal since it allows to match the maximum admissible time step of the finite volume scheme on the subgrid with the maximum admissible time step of the DG scheme on the main grid, minimizing at the same time also the local truncation error of the subcell finite volume scheme. It furthermore provides an excellent subcell resolution of

  20. Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang

    2004-01-01

    This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier

  1. Almost Optimal Interior Penalty Discontinuous Approximations of Symmetric Elliptic Problems on Non-Matching Grids

    SciTech Connect

    Lazarov, R D; Pasciak, J E; Schoberl, J; Vassilevski, P S

    2001-08-08

    We consider an interior penalty discontinuous approximation for symmetric elliptic problems of second order on non-matching grids in this paper. The main result is an almost optimal error estimate for the interior penalty approximation of the original problem based on the partition of the domain into a finite number of subdomains. Further, an error analysis for the finite element approximation of the penalty formulation is given. Finally, numerical experiments on a series of model second order problems are presented.

  2. An entropy-residual shock detector for solving conservation laws using high-order discontinuous Galerkin methods

    NASA Astrophysics Data System (ADS)

    Lv, Yu; See, Yee Chee; Ihme, Matthias

    2016-10-01

    This manuscript is concerned with the detection of shock discontinuities in the solution of conservation laws for high-order discontinuous Galerkin methods. A shock detector based on the entropy residual is proposed to distinguish smooth and non-smooth parts of the solution. The numerical analysis shows that the proposed entropy residual converges if the true solution is smooth and sufficiently regularized in space and time. To precisely localize discontinuities of different natures, an approach is developed that dynamically sets the threshold on the detection function, such that the detection criterion retains its sensitivity to the characteristics of the local solution. The implementation is conducted in an entropy-bounded discontinuous Galerkin framework, and numerical tests confirm the convergence property of the entropy-residual formulation and the effectiveness of the thresholding procedure. This shock detector is combined with an artificial viscosity scheme for shock stabilization. Comparison with other detectors is performed to demonstrate the excellent performance of the entropy-residual based shock detector for a wide range of problems on regular and triangular grids.

  3. A GPU Accelerated Discontinuous Galerkin Conservative Level Set Method for Simulating Atomization

    NASA Astrophysics Data System (ADS)

    Jibben, Zechariah J.

    This dissertation describes a process for interface capturing via an arbitrary-order, nearly quadrature free, discontinuous Galerkin (DG) scheme for the conservative level set method (Olsson et al., 2005, 2008). The DG numerical method is utilized to solve both advection and reinitialization, and executed on a refined level set grid (Herrmann, 2008) for effective use of processing power. Computation is executed in parallel utilizing both CPU and GPU architectures to make the method feasible at high order. Finally, a sparse data structure is implemented to take full advantage of parallelism on the GPU, where performance relies on well-managed memory operations. With solution variables projected into a kth order polynomial basis, a k + 1 order convergence rate is found for both advection and reinitialization tests using the method of manufactured solutions. Other standard test cases, such as Zalesak's disk and deformation of columns and spheres in periodic vortices are also performed, showing several orders of magnitude improvement over traditional WENO level set methods. These tests also show the impact of reinitialization, which often increases shape and volume errors as a result of level set scalar trapping by normal vectors calculated from the local level set field. Accelerating advection via GPU hardware is found to provide a 30x speedup factor comparing a 2.0GHz Intel Xeon E5-2620 CPU in serial vs. a Nvidia Tesla K20 GPU, with speedup factors increasing with polynomial degree until shared memory is filled. A similar algorithm is implemented for reinitialization, which relies on heavier use of shared and global memory and as a result fills them more quickly and produces smaller speedups of 18x.

  4. Discontinuous Galerkin methodology for Large-Eddy Simulations of wind turbine airfoils

    NASA Astrophysics Data System (ADS)

    Frére, A.; Sørensen, N. N.; Hillewaert, K.; Winckelmans, G.

    2016-09-01

    This paper aims at evaluating the potential of the Discontinuous Galerkin (DG) methodology for Large-Eddy Simulation (LES) of wind turbine airfoils. The DG method has shown high accuracy, excellent scalability and capacity to handle unstructured meshes. It is however not used in the wind energy sector yet. The present study aims at evaluating this methodology on an application which is relevant for that sector and focuses on blade section aerodynamics characterization. To be pertinent for large wind turbines, the simulations would need to be at low Mach numbers (M ≤ 0.3) where compressible approaches are often limited and at large Reynolds numbers (Re ≥ 106) where wall-resolved LES is still unaffordable. At these high Re, a wall-modeled LES (WMLES) approach is thus required. In order to first validate the LES methodology, before the WMLES approach, this study presents airfoil flow simulations at low and high Reynolds numbers and compares the results to state-of-the-art models used in industry, namely the panel method (XFOIL with boundary layer modeling) and Reynolds Averaged Navier-Stokes (RANS). At low Reynolds number (Re = 6 x 104), involving laminar boundary layer separation and transition in the detached shear layer, the Eppler 387 airfoil is studied at two angles of attack. The LES results agree slightly better with the experimental chordwise pressure distribution than both XFOIL and RANS results. At high Reynolds number (Re = 1.64 x 106), the NACA4412 airfoil is studied close to stall condition. In this case, although the wall model approach used for the WMLES is very basic and not supposed to handle separation nor adverse pressure gradients, all three methods provide equivalent accuracy on averaged quantities. The present work is hence considered as a strong step forward in the use of LES at high Reynolds numbers.

  5. High order asymptotic preserving nodal discontinuous Galerkin IMEX schemes for the BGK equation

    NASA Astrophysics Data System (ADS)

    Xiong, Tao; Jang, Juhi; Li, Fengyan; Qiu, Jing-Mei

    2015-03-01

    In this paper, we develop high-order asymptotic preserving (AP) schemes for the BGK equation in a hyperbolic scaling, which leads to the macroscopic models such as the Euler and compressible Navier-Stokes equations in the asymptotic limit. Our approaches are based on the so-called micro-macro formulation of the kinetic equation which involves a natural decomposition of the problem to the equilibrium and the non-equilibrium parts. The proposed methods are formulated for the BGK equation with constant or spatially variant Knudsen number. The new ingredients for the proposed methods to achieve high order accuracy are the following: we introduce discontinuous Galerkin (DG) discretization of arbitrary order of accuracy with nodal Lagrangian basis functions in space; we employ a high order globally stiffly accurate implicit-explicit (IMEX) Runge-Kutta (RK) scheme as time discretization. Two versions of the schemes are proposed: Scheme I is a direct formulation based on the micro-macro decomposition of the BGK equation, while Scheme II, motivated by the asymptotic analysis for the continuous problem, utilizes certain properties of the projection operator. Compared with Scheme I, Scheme II not only has better computational efficiency (the computational cost is reduced by half roughly), but also allows the establishment of a formal asymptotic analysis. Specifically, it is demonstrated that when 0 < ε ≪ 1, Scheme II, up to O (ε2), becomes a local DG discretization with an explicit RK method for the macroscopic compressible Navier-Stokes equations, a method in a similar spirit to the ones in Bassi and Rebay (1997) [3], Cockburn and Shu (1998) [16]. Numerical results are presented for a wide range of Knudsen number to illustrate the effectiveness and high order accuracy of the methods.

  6. Fast discontinuous Galerkin lattice-Boltzmann simulations on GPUs via maximal kernel fusion

    NASA Astrophysics Data System (ADS)

    Mazzeo, Marco D.

    2013-03-01

    A GPU implementation of the discontinuous Galerkin lattice-Boltzmann method with square spectral elements, and highly optimised for speed and precision of calculations is presented. An extensive analysis of the numerous variants of the fluid solver unveils that best performance is obtained by maximising CUDA kernel fusion and by arranging the resulting kernel tasks so as to trigger memory coherent and scattered loads in a specific manner, albeit at the cost of introducing cross-thread load unbalancing. Surprisingly, any attempt to vanish this, to maximise thread occupancy and to adopt conventional work tiling or distinct custom kernels highly tuned via ad hoc data and computation layouts invariably deteriorate performance. As such, this work sheds light into the possibility to hide fetch latencies of workloads involving heterogeneous loads in a way that is more effective than what is achieved with frequently suggested techniques. When simulating the lid-driven cavity on a NVIDIA GeForce GTX 480 via a 5-stage 4th-order Runge-Kutta (RK) scheme, the first four digits of the obtained centreline velocity values, or more, converge to those of the state-of-the-art literature data at a simulation speed of 7.0G primitive variable updates per second during the collision stage and 4.4G ones during each RK step of the advection by employing double-precision arithmetic (DPA) and a computational grid of 642 4×4-point elements only. The new programming engine leads to about 2× performance w.r.t. the best programming guidelines in the field. The new fluid solver on the above GPU is also 20-30 times faster than a highly optimised version running on a single core of a Intel Xeon X5650 2.66 GHz.

  7. Multicomponent gas flow computations by a discontinuous Galerkin scheme using L2-projection of perfect gas EOS

    NASA Astrophysics Data System (ADS)

    Franchina, N.; Savini, M.; Bassi, F.

    2016-06-01

    A new formulation of multicomponent gas flow computation, suited to a discontinuous Galerkin discretization, is here presented and discussed. The original key feature is the use of L2-projection form of the (perfect gas) equation of state that allows all thermodynamic variables to span the same functional space. This choice greatly mitigates problems encountered by the front-capturing schemes in computing discontinuous flow field, retaining at the same time their conservation properties at the discrete level and ease of use. This new approach, combined with an original residual-based artificial dissipation technique, shows itself capable, through a series of tests illustrated in the paper, to both control the spurious oscillations of flow variables occurring in high-order accurate computations and reduce them increasing the degree of the polynomial representation of the solution. This result is of great importance in computing reacting gaseous flows, where the local accuracy of temperature and species mass fractions is crucial to the correct evaluation of the chemical source terms contained in the equations, even if the presence of the physical diffusivities somewhat brings relief to these problems. The present work can therefore also be considered, among many others already presented in the literature, as the authors' first step toward the construction of a new discontinuous Galerkin scheme for reacting gas mixture flows.

  8. Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations

    NASA Astrophysics Data System (ADS)

    Banerjee, Amartya S.; Lin, Lin; Hu, Wei; Yang, Chao; Pask, John E.

    2016-10-01

    The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials' simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale two-dimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. Employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.

  9. Quantum hydrodynamics with trajectories: The nonlinear conservation form mixed/discontinuous Galerkin method with applications in chemistry

    SciTech Connect

    Michoski, C. Evans, J.A.; Schmitz, P.G.; Vasseur, A.

    2009-12-10

    We present a solution to the conservation form (Eulerian form) of the quantum hydrodynamic equations which arise in chemical dynamics by implementing a mixed/discontinuous Galerkin (MDG) finite element numerical scheme. We show that this methodology is stable, showing good accuracy and a remarkable scale invariance in its solution space. In addition the MDG method is robust, adapting well to various initial-boundary value problems of particular significance in a range of physical and chemical applications. We further show explicitly how to recover the Lagrangian frame (or pathline) solutions.

  10. 3D Discontinuous Galerkin elastic seismic wave modeling based upon a grid injection method

    NASA Astrophysics Data System (ADS)

    Monteiller, V.

    2015-12-01

    Full waveform inversion (FWI) is a seismic imaging method that estimates thesub-surface physical properties with a spatial resolution of the order of thewavelength. FWI is generally recast as the iterative optimization of anobjective function that measures the distance between modeled and recordeddata. In the framework of local descent methods, FWI requires to perform atleast two seismic modelings per source and per FWI iteration.Due to the resulting computational burden, applications of elastic FWI have been usuallyrestricted to 2D geometries. Despite the continuous growth of high-performancecomputing facilities, application of 3D elastic FWI to real-scale problemsremain computationally too expensive. To perform elastic seismic modeling with a reasonable amount of time, weconsider a reduced computational domain embedded in a larger background modelin which seismic sources are located. Our aim is to compute repeatedly thefull wavefield in the targeted domain after model alteration, once theincident wavefield has been computed once for all in the background model. Toachieve this goal, we use a grid injection method referred to as the Total-Field/Scattered-Field (TF/SF) technique in theelectromagnetic community. We implemented the Total-Field/Scattered-Field approach in theDiscontinuous Galerkin Finite Element method (DG-FEM) that is used to performmodeling in the local domain. We show how to interface the DG-FEM with any modeling engine (analytical solution, finite difference or finite elements methods) that is suitable for the background simulation. One advantage of the Total-Field/Scattered-Field approach is related to thefact that the scattered wavefield instead of the full wavefield enter thePMLs, hence making more efficient the absorption of the outgoing waves at theouter edges of the computational domain. The domain reduction in which theDG-FEM is applied allows us to use modest computational resources opening theway for high-resolution imaging by full

  11. High-Fidelity Lagrangian Coherent Structures Analysis and DNS with Discontinuous-Galerkin Methods

    NASA Astrophysics Data System (ADS)

    Nelson, Daniel Alan Wendell

    High-fidelity numerical tools based on high-order Discontinuous-Galerkin (DG) methods and Lagrangian Coherent Structure (LCS) theory are developed and validated for the study of separated, vortex-dominated flows over complex geometry. The numerical framework couples prediction of separated turbulent flows using DG with time-dependent analysis of the flow through LCS and is intended for the development of separation control strategies for aerodynamic surfaces. The compressible viscous flow over a NACA 65-(1)412 airfoil is solved with a DG based Navier-Stokes solver in two and three dimensions. A method is presented in which high-order polynomial element edges adjacent to curved boundaries are matched to boundaries defined by non-smooth splines. Artificial surface roughness introduced by the piecewise-linear boundary approximation of straight-sided meshes results in the simulation of incorrect physics, including wake instabilities and spurious time-dependent modes. Spectral accuracy in the boundary approximation is not achieved for non-analytic boundary functions, particularly in high curvature regions. An algorithm is developed for the high-order computation of Finite-Time Lyapunov Exponent (FTLE) fields simultaneously and efficiently with two and three dimensional DG-based flow solvers. Fluid tracers are initialized at Gauss-Lobatto quadrature nodes within an element and form the high-order basis for a flow map at later time. Gradients of the flow map and FTLE are evaluated with DG operators. Multiple flow maps are determined from a single particle trace by remapping the flow map to the quadrature nodes on deformed mesh elements. For large integration times, excessive subdomain deformation deteriorates the interpolating conditioning. The conditioning provides information on the fluid deformation and identifies subdomains that contain LCS. An exponential filter smooths the flow map in highly deformed areas. The algorithm is tested on several benchmarks and is shown

  12. A 3D discontinuous Galerkin finite-element method for teleseismic modelling.

    NASA Astrophysics Data System (ADS)

    monteiller, vadim; Beller, Stephen; Nolet, Guust; Operto, Stephane; Virieux, Jean

    2014-05-01

    The massive development of dense seismic arrays and the rapide increase in computing capacity allow today to consider application of full waveform inversion of teleseismic data for high-resolution lithospheric imaging. We present an hybrid numerical method that allows for the modelling of short period telesismic waves in 3D lithospheric target with the discontinuous Galerkin finite elements method, opennig the possibility to perform waveform inversion of seismograms recorded by dense regional broadband arrays. In order to reduce the computational cost of the forward-problem, we developed a method that relies on multi-core parallel computing and computational-domain reduction. We defined two nested levels for parallelism based on MPI library, which are managed by two MPI communicators. Firstly, we use a domain partitionning strategy, assigning one subdomain to one cpu and, secondly we distribute telesismic sources on different copies of the partitioned domain. However, despite the supercomputer ability, the forward-problem remains expensive for telesismic configuration especially when 3D numerical methods are considered. In order to perform the forward problem in a reasonable amount of time, we reduce the computational domain in which full waveform modelling is performed. We defined a 3D regional domain located below the seismological network that is embeded in a background homogeneous or axisymetric model, in which the seismic wavefield can be computed efficiently. The background wavefield is used to compute the full wavefield in the 3D regional domain using the so-called total-field/scattered-field technique (Alterman & Karal (1968),Taflove & Hagness (2005)), which relies on the decomposition of the wavefield into a background and a scattered wavefields. The computational domain is subdivided intro three subdomains: an outer domain formed by the perfectly-mathed absorbing layers, an intermediate zone in which only the outgoing wavefield scattered by the

  13. Solving the problem of non-stationary filtration of substance by the discontinuous Galerkin method on unstructured grids

    NASA Astrophysics Data System (ADS)

    Zhalnin, R. V.; Ladonkina, M. E.; Masyagin, V. F.; Tishkin, V. F.

    2016-06-01

    A numerical algorithm is proposed for solving the problem of non-stationary filtration of substance in anisotropic media by the Galerkin method with discontinuous basis functions on unstructured triangular grids. A characteristic feature of this method is that the flux variables are considered on the dual grid. The dual grid comprises median control volumes around the nodes of the original triangular grid. The flux values of the quantities on the boundary of an element are calculated with the help of stabilizing additions. For averaging the permeability tensor over the cells of the dual grid, the method of support operators is applied. The method is studied on the example of a two-dimensional boundary value problem. The convergence and approximation of the numerical method are analyzed, and results of mathematical modeling are presented. The numerical results demonstrate the applicability of this approach for solving problems of non-stationary filtration of substance in anisotropic media by the discontinuous Galerkin method on unstructured triangular grids.

  14. 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.

  15. A Dynamic Eddy Viscosity Model for the Shallow Water Equations Solved by Spectral Element and Discontinuous Galerkin Methods

    NASA Astrophysics Data System (ADS)

    Marras, Simone; Suckale, Jenny; Giraldo, Francis X.; Constantinescu, Emil

    2016-04-01

    We present the solution of the viscous shallow water equations where viscosity is built as a residual-based subgrid scale model originally designed for large eddy simulation of compressible [1] and stratified flows [2]. The necessity of viscosity for a shallow water model not only finds motivation from mathematical analysis [3], but is supported by physical reasoning as can be seen by an analysis of the energetics of the solution. We simulated the flow of an idealized wave as it hits a set of obstacles. The kinetic energy spectrum of this flow shows that, although the inviscid Galerkin solutions -by spectral elements and discontinuous Galerkin [4]- preserve numerical stability in spite of the spurious oscillations in the proximity of the wave fronts, the slope of the energy cascade deviates from the theoretically expected values. We show that only a sufficiently small amount of dynamically adaptive viscosity removes the unwanted high-frequency modes while preserving the overall sharpness of the solution. In addition, it yields a physically plausible energy decay. This work is motivated by a larger interest in the application of a shallow water model to the solution of tsunami triggered coastal flows. In particular, coastal flows in regions around the world where coastal parks made of mitigation hills of different sizes and configurations are considered as a means to deviate the power of the incoming wave. References [1] M. Nazarov and J. Hoffman (2013) "Residual-based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods" Int. J. Numer. Methods Fluids, 71:339-357 [2] S. Marras, M. Nazarov, F. X. Giraldo (2015) "Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES" J. Comput. Phys. 301:77-101 [3] J. F. Gerbeau and B. Perthame (2001) "Derivation of the viscous Saint-Venant system for laminar shallow water; numerical validation" Discrete Contin. Dyn. Syst. Ser. B, 1:89?102 [4] F

  16. A high-order discontinuous Galerkin method for fluid–structure interaction with efficient implicit–explicit time stepping

    SciTech Connect

    Froehle, Bradley Persson, Per-Olof

    2014-09-01

    We present a high-order accurate scheme for coupled fluid–structure interaction problems. The fluid is discretized using a discontinuous Galerkin method on unstructured tetrahedral meshes, and the structure uses a high-order volumetric continuous Galerkin finite element method. Standard radial basis functions are used for the mesh deformation. The time integration is performed using a partitioned approach based on implicit–explicit Runge–Kutta methods. The resulting scheme fully decouples the implicit solution procedures for the fluid and the solid parts, which we perform using two separate efficient parallel solvers. We demonstrate up to fifth order accuracy in time on a non-trivial test problem, on which we also show that additional subiterations are not required. We solve a benchmark problem of a cantilever beam in a shedding flow, and show good agreement with other results in the literature. Finally, we solve for the flow around a thin membrane at a high angle of attack in both 2D and 3D, and compare with the results obtained with a rigid plate.

  17. hp discontinuous Galerkin methods for the vertical extent of the water column in coastal settings part I: Barotropic forcing

    NASA Astrophysics Data System (ADS)

    Conroy, Colton J.; Kubatko, Ethan J.

    2016-01-01

    In this article, we present novel, high-order, discontinuous Galerkin (DG) methods for the vertical extent of the water column in coastal settings. We examine the shallow water equations (SWE) in the context of DG spatial discretizations coupled with explicit Runge-Kutta (RK) time stepping. All the primary variables, including the free surface elevation, are discretized using discontinuous polynomial spaces of arbitrary order. The difficulty of mismatched lateral boundary faces that accompanies the use of a discontinuous free surface is overcome through the use of a so-called sigma-coordinate system in the vertical, which transforms the bottom boundary and free surface into coordinate surfaces. We develop high-order methods for the SWE that exhibit optimal orders of convergence for all the primary variables via two distinct paths: the first involves the use of a convolution kernel made up of B-splines to filter out errors in the DG discretization of the surface elevation and the corresponding pressure flux. The second involves a method that evaluates the discrete depth-integrated velocity exactly, eliminating the need to solve the depth-integrated momentum equation altogether. The result is a simple and efficient high-order scheme that can be extended to the full three-dimensional SWE.

  18. DNS of Flow in a Low-Pressure Turbine Cascade Using a Discontinuous-Galerkin Spectral-Element Method

    NASA Technical Reports Server (NTRS)

    Garai, Anirban; Diosady, Laslo Tibor; Murman, Scott; Madavan, Nateri

    2015-01-01

    A new computational capability under development for accurate and efficient high-fidelity direct numerical simulation (DNS) and large eddy simulation (LES) of turbomachinery is described. This capability is based on an entropy-stable Discontinuous-Galerkin spectral-element approach that extends to arbitrarily high orders of spatial and temporal accuracy and is implemented in a computationally efficient manner on a modern high performance computer architecture. A validation study using this method to perform DNS of flow in a low-pressure turbine airfoil cascade are presented. Preliminary results indicate that the method captures the main features of the flow. Discrepancies between the predicted results and the experiments are likely due to the effects of freestream turbulence not being included in the simulation and will be addressed in the final paper.

  19. Simulation of near-field plasmonic interactions with a local approximation order discontinuous Galerkin time-domain method

    NASA Astrophysics Data System (ADS)

    Viquerat, Jonathan; Lanteri, Stéphane

    2016-01-01

    During the last ten years, the discontinuous Galerkin time-domain (DGTD) method has progressively emerged as a viable alternative to well established finite-difference time-domain (FDTD) and finite-element time-domain (FETD) methods for the numerical simulation of electromagnetic wave propagation problems in the time-domain. The method is now actively studied in various application contexts including those requiring to model light/matter interactions on the nanoscale. Several recent works have demonstrated the viability of the DGDT method for nanophotonics. In this paper we further demonstrate the capabilities of the method for the simulation of near-field plasmonic interactions by considering more particularly the possibility of combining the use of a locally refined conforming tetrahedral mesh with a local adaptation of the approximation order.

  20. Third order maximum-principle-satisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes

    DOE PAGESBeta

    Chen, Zheng; Huang, Hongying; Yan, Jue

    2015-12-21

    We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair (β0,β1) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried out to demonstratemore » the accuracy and capability of the maximum-principle-satisfying limiter.« less

  1. Simulation of underresolved turbulent flows by adaptive filtering using the high order discontinuous Galerkin spectral element method

    NASA Astrophysics Data System (ADS)

    Flad, David; Beck, Andrea; Munz, Claus-Dieter

    2016-05-01

    Scale-resolving simulations of turbulent flows in complex domains demand accurate and efficient numerical schemes, as well as geometrical flexibility. For underresolved situations, the avoidance of aliasing errors is a strong demand for stability. For continuous and discontinuous Galerkin schemes, an effective way to prevent aliasing errors is to increase the quadrature precision of the projection operator to account for the non-linearity of the operands (polynomial dealiasing, overintegration). But this increases the computational costs extensively. In this work, we present a novel spatially and temporally adaptive dealiasing strategy by projection filtering. We show this to be more efficient for underresolved turbulence than the classical overintegration strategy. For this novel approach, we discuss the implementation strategy and the indicator details, show its accuracy and efficiency for a decaying homogeneous isotropic turbulence and the transitional Taylor-Green vortex and compare it to the original overintegration approach and a state of the art variational multi-scale eddy viscosity formulation.

  2. Third order maximum-principle-satisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes

    SciTech Connect

    Chen, Zheng; Huang, Hongying; Yan, Jue

    2015-12-21

    We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair (β01) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried out to demonstrate the accuracy and capability of the maximum-principle-satisfying limiter.

  3. Development of a Perfectly Matched Layer Technique for a Discontinuous-Galerkin Spectral-Element Method

    NASA Technical Reports Server (NTRS)

    Garai, Anirban; Murman, Scott M.; Madavan, Nateri K.

    2016-01-01

    used involves modeling the pressure fluctuations as acoustic waves propagating in the far-field relative to a single noise-source inside the buffer region. This approach treats vorticity-induced pressure fluctuations the same as acoustic waves. Another popular approach, often referred to as the "sponge layer," attempts to dampen the flow perturbations by introducing artificial dissipation in the buffer region. Although the artificial dissipation removes all perturbations inside the sponge layer, incoming waves are still reflected from the interface boundary between the computational domain and the sponge layer. The effect of these refkections can be somewhat mitigated by appropriately selecting the artificial dissipation strength and the extent of the sponge layer. One of the most promising variants on the buffer region approach is the Perfectly Matched Layer (PML) technique. The PML technique mitigates spurious reflections from boundaries and interfaces by dampening the perturbation modes inside the buffer region such that their eigenfunctions remain unchanged. The technique was first developed by Berenger for application to problems involving electromagnetic wave propagation. It was later extended to the linearized Euler, Euler and Navier-Stokes equations by Hu and his coauthors. The PML technique ensures the no-reflection property for all waves, irrespective of incidence angle, wavelength, and propagation direction. Although the technique requires the solution of a set of auxiliary equations, the computational overhead is easily justified since it allows smaller domain sizes and can provide better accuracy, stability, and convergence of the numerical solution. In this paper, the PML technique is developed in the context of a high-order spectral-element Discontinuous Galerkin (DG) method. The technique is compared to other approaches to treating the in flow and out flow boundary, such as those based on using characteristic boundary conditions and sponge layers. The

  4. Mixed-hybrid and vertex-discontinuous-Galerkin finite element modeling of multiphase compositional flow on 3D unstructured grids

    NASA Astrophysics Data System (ADS)

    Moortgat, Joachim; Firoozabadi, Abbas

    2016-06-01

    Problems of interest in hydrogeology and hydrocarbon resources involve complex heterogeneous geological formations. Such domains are most accurately represented in reservoir simulations by unstructured computational grids. Finite element methods accurately describe flow on unstructured meshes with complex geometries, and their flexible formulation allows implementation on different grid types. In this work, we consider for the first time the challenging problem of fully compositional three-phase flow in 3D unstructured grids, discretized by any combination of tetrahedra, prisms, and hexahedra. We employ a mass conserving mixed hybrid finite element (MHFE) method to solve for the pressure and flux fields. The transport equations are approximated with a higher-order vertex-based discontinuous Galerkin (DG) discretization. We show that this approach outperforms a face-based implementation of the same polynomial order. These methods are well suited for heterogeneous and fractured reservoirs, because they provide globally continuous pressure and flux fields, while allowing for sharp discontinuities in compositions and saturations. The higher-order accuracy improves the modeling of strongly non-linear flow, such as gravitational and viscous fingering. We review the literature on unstructured reservoir simulation models, and present many examples that consider gravity depletion, water flooding, and gas injection in oil saturated reservoirs. We study convergence rates, mesh sensitivity, and demonstrate the wide applicability of our chosen finite element methods for challenging multiphase flow problems in geometrically complex subsurface media.

  5. A New Runge-Kutta Discontinuous Galerkin Method with Conservation Constraint to Improve CFL Condition for Solving Conservation Laws

    PubMed Central

    Xu, Zhiliang; Chen, Xu-Yan; Liu, Yingjie

    2014-01-01

    We present a new formulation of the Runge-Kutta discontinuous Galerkin (RKDG) method [9, 8, 7, 6] for solving conservation Laws with increased CFL numbers. The new formulation requires the computed RKDG solution in a cell to satisfy additional conservation constraint in adjacent cells and does not increase the complexity or change the compactness of the RKDG method. Numerical computations for solving one-dimensional and two-dimensional scalar and systems of nonlinear hyperbolic conservation laws are performed with approximate solutions represented by piecewise quadratic and cubic polynomials, respectively. The hierarchical reconstruction [17, 33] is applied as a limiter to eliminate spurious oscillations in discontinuous solutions. From both numerical experiments and the analytic estimate of the CFL number of the newly formulated method, we find that: 1) this new formulation improves the CFL number over the original RKDG formulation by at least three times or more and thus reduces the overall computational cost; and 2) the new formulation essentially does not compromise the resolution of the numerical solutions of shock wave problems compared with ones computed by the RKDG method. PMID:25414520

  6. High-Order Discontinuous Galerkin Level Set Method for Interface Tracking and Re-Distancing on Unstructured Meshes

    NASA Astrophysics Data System (ADS)

    Greene, Patrick; Nourgaliev, Robert; Schofield, Sam

    2015-11-01

    A new sharp high-order interface tracking method for multi-material flow problems on unstructured meshes is presented. The method combines the marker-tracking algorithm with a discontinuous Galerkin (DG) level set method to implicitly track interfaces. DG projection is used to provide a mapping from the Lagrangian marker field to the Eulerian level set field. For the level set re-distancing, we developed a novel marching method that takes advantage of the unique features of the DG representation of the level set. The method efficiently marches outward from the zero level set with values in the new cells being computed solely from cell neighbors. Results are presented for a number of different interface geometries including ones with sharp corners and multiple hierarchical level sets. The method can robustly handle the level set discontinuities without explicit utilization of solution limiters. Results show that the expected high order (3rd and higher) of convergence for the DG representation of the level set is obtained for smooth solutions on unstructured meshes. High-order re-distancing on irregular meshes is a must for applications were the interfacial curvature is important for underlying physics, such as surface tension, wetting and detonation shock dynamics. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Information management release number LLNL-ABS-675636.

  7. A New Runge-Kutta Discontinuous Galerkin Method with Conservation Constraint to Improve CFL Condition for Solving Conservation Laws.

    PubMed

    Xu, Zhiliang; Chen, Xu-Yan; Liu, Yingjie

    2014-12-01

    We present a new formulation of the Runge-Kutta discontinuous Galerkin (RKDG) method [9, 8, 7, 6] for solving conservation Laws with increased CFL numbers. The new formulation requires the computed RKDG solution in a cell to satisfy additional conservation constraint in adjacent cells and does not increase the complexity or change the compactness of the RKDG method. Numerical computations for solving one-dimensional and two-dimensional scalar and systems of nonlinear hyperbolic conservation laws are performed with approximate solutions represented by piecewise quadratic and cubic polynomials, respectively. The hierarchical reconstruction [17, 33] is applied as a limiter to eliminate spurious oscillations in discontinuous solutions. From both numerical experiments and the analytic estimate of the CFL number of the newly formulated method, we find that: 1) this new formulation improves the CFL number over the original RKDG formulation by at least three times or more and thus reduces the overall computational cost; and 2) the new formulation essentially does not compromise the resolution of the numerical solutions of shock wave problems compared with ones computed by the RKDG method.

  8. High-Order Hybridized Discontinuous Galerkin (HDG) Method for Wave Propagation Simulation in Complex Geophysical Media - Elastic, Acoustic and Hydro-Acoustic - an Unifying Framework to Couple Continuous Spectral Element and Discontinuous Galerkin Methods.

    NASA Astrophysics Data System (ADS)

    Sébastien, T.; Vilotte, J. P.; Guillot, L.; Mariotti, C.

    2014-12-01

    Today seismological observation systems combine broadband seismic receivers, hydrophones and micro-barometers antenna that provide complementary observations of source-radiated waves in heterogeneous and complex geophysical media. Exploiting these observations requires accurate and multi-physics - elastic, hydro-acoustic, infrasonic - wave simulation methods. A popular approach is the Spectral Element Method (SEM) (Chaljub et al, 2006) which is high-order accurate (low dispersion error), very flexible to parallelization and computationally attractive due to efficient sum factorization technique and diagonal mass matrix. However SEMs suffer from lack of flexibility in handling complex geometry and multi-physics wave propagation. High-order Discontinuous Galerkin Methods (DGMs), i.e. Dumbser et al (2006), Etienne et al. (2010), Wilcox et al (2010), are recent alternatives that can handle complex geometry, space-and-time adaptativity, and allow efficient multi-physics wave coupling at interfaces. However, DGMs are more memory demanding and less computationally attractive than SEMs, especially when explicit time stepping is used. We propose a new class of higher-order Hybridized Discontinuous Galerkin Spectral Elements (HDGSEM) methods for spatial discretization of wave equations, following the unifying framework for hybridization of Cockburn et al (2009) and Nguyen et al (2011), which allows for a single implementation of conforming and non-conforming SEMs. When used with energy conserving explicit time integration schemes, HDGSEM is flexible to handle complex geometry, computationally attractive and has significantly less degrees of freedom than classical DGMs, i.e., the only coupled unknowns are the single-valued numerical traces of the velocity field on the element's faces. The formulation can be extended to model fractional energy loss at interfaces between elastic, acoustic and hydro-acoustic media. Accuracy and performance of the HDGSEM are illustrated and

  9. Recent development of a hydrostatic dynamical cores using the spectral element and the discontinuous Galerkin method at KIAPS (Invited)

    NASA Astrophysics Data System (ADS)

    Choi, S.; Giraldo, F. X.; Park, J.; Jun, S.; Yi, T.; Kang, S.; Oh, T.

    2013-12-01

    Korea Institute of Atmospheric Prediction Systems (KIAPS) was founded in 2011 by Korea Meteorological Administration (KMA) as a non-profit foundation to develop Korea's own global NWP system including it's framework, data assimilation, coupler and so on. The final goal of KIAPS is to develop a global non-hydrostatic NWP system by 2019 for operational use at KMA. In the first stage (2011-2013), we have developed a dynamical core for the Eulerian hydrostatic primitive equation as a initial effort. At the meeting, the progress and status of the core will be presented. The core is based on spectral element (SE; or continuous Galerkin method) and discontinuous Galerkin methods (DG). It is expected to take the advantages that the horizontal operators can be approximated by local high-order elements while scaling efficiently on multiprocessor computers with such high processor counts, since the properties of the methods are local in nature and have a small communication footprint. In order to overcome polar singularities and retain flexibility of the grid, we consider the hydrostatic primitive equations in 3D Cartesian space. This approach is used in Giraldo and Rosmond (MWR 2004). For the horizontal discretization, the cubed sphere grid is used for the sake of isotropy and due to the simplicity with which to use quadrilateral elements. For the vertical discretization, a Lorenz staggered grid is implemented with the terrain following σ-p coordinate. Currently, explicit time integrators, such as strong stability preserving Runge-Kutta (SSPRK) are implemented. In order to validate the developed core, some results are presented for test cases such as the Rossby-Haurwitz wavenumber 4 and the Jablonowski-Williamson balanced initial state and baroclinic instability test.

  10. A 3D hp-Discontinuous Galerkin Method: Revisiting the M7.3 Landers Earthquake Dynamics

    NASA Astrophysics Data System (ADS)

    Tago, J.; Cruz-Atienza, V. M.; Virieux, J.; Etienne, V.; Sanchez-Sesma, F. J.

    2011-12-01

    Reliable dynamic source models should account of both fault geometry and heterogeneities in the surrounding medium. In this work we introduce a novel numerical method for modeling the dynamic rupture based on a 3D hp-Discontinuous Galerkin (DG) scheme. Our method is derived from the scheme proposed by Benjemaa et al. (2009), which is based on a Finite Volume (FV) approach. Migrating from such approach to the hp-Discontinuous Galerkin philosophy is somehow straightforward since the FV method can be seen as the DG method with its lowest order or approximation (i.e. P0 element). We present a novel approach for treating dynamic rupture boundary conditions using an hp-Discontinuous Galerkin method for unstructured tetrahedral meshes. Although the theory we have developed holds for fault elements with arbitrary order, we show that second order (P2) elements yield a very good convergence. Since the DG method does not impose continuity between elements, our strategy consists in the way we compute the fluxes across the fault elements. During rupture propagation, the fluxes in the elements where the shear traction overcomes the fault strength are such that continuity of every wavefield is imposed except for the tangential fault velocities, while in the unbroken elements tangential continuity is also imposed. Because the fault nodes of a given element are coupled through the Mass and Flux matrices, when a fault node breaks we impose the shear traction on that node and need to recompute the values throughout the rest, to avoid any violation of the friction law throughout the element. This procedure repeats itself iteratively following a predictor-corrector scheme for a given time step until the element solutions stabilize. We point out that our scheme for the fault fluxes in the case of P0 elements is exactly the same as the one proposed by Benjemaa et al. who compute them through energy balance considerations. To verify our mathematical and computational model we have solved

  11. OpenACC acceleration of an unstructured CFD solver based on a reconstructed discontinuous Galerkin method for compressible flows

    SciTech Connect

    Xia, Yidong; Lou, Jialin; Luo, Hong; Edwards, Jack; Mueller, Frank

    2015-02-09

    Here, an OpenACC directive-based graphics processing unit (GPU) parallel scheme is presented for solving the compressible Navier–Stokes equations on 3D hybrid unstructured grids with a third-order reconstructed discontinuous Galerkin method. The developed scheme requires the minimum code intrusion and algorithm alteration for upgrading a legacy solver with the GPU computing capability at very little extra effort in programming, which leads to a unified and portable code development strategy. A face coloring algorithm is adopted to eliminate the memory contention because of the threading of internal and boundary face integrals. A number of flow problems are presented to verify the implementation of the developed scheme. Timing measurements were obtained by running the resulting GPU code on one Nvidia Tesla K20c GPU card (Nvidia Corporation, Santa Clara, CA, USA) and compared with those obtained by running the equivalent Message Passing Interface (MPI) parallel CPU code on a compute node (consisting of two AMD Opteron 6128 eight-core CPUs (Advanced Micro Devices, Inc., Sunnyvale, CA, USA)). Speedup factors of up to 24× and 1.6× for the GPU code were achieved with respect to one and 16 CPU cores, respectively. The numerical results indicate that this OpenACC-based parallel scheme is an effective and extensible approach to port unstructured high-order CFD solvers to GPU computing.

  12. OpenACC acceleration of an unstructured CFD solver based on a reconstructed discontinuous Galerkin method for compressible flows

    DOE PAGESBeta

    Xia, Yidong; Lou, Jialin; Luo, Hong; Edwards, Jack; Mueller, Frank

    2015-02-09

    Here, an OpenACC directive-based graphics processing unit (GPU) parallel scheme is presented for solving the compressible Navier–Stokes equations on 3D hybrid unstructured grids with a third-order reconstructed discontinuous Galerkin method. The developed scheme requires the minimum code intrusion and algorithm alteration for upgrading a legacy solver with the GPU computing capability at very little extra effort in programming, which leads to a unified and portable code development strategy. A face coloring algorithm is adopted to eliminate the memory contention because of the threading of internal and boundary face integrals. A number of flow problems are presented to verify the implementationmore » of the developed scheme. Timing measurements were obtained by running the resulting GPU code on one Nvidia Tesla K20c GPU card (Nvidia Corporation, Santa Clara, CA, USA) and compared with those obtained by running the equivalent Message Passing Interface (MPI) parallel CPU code on a compute node (consisting of two AMD Opteron 6128 eight-core CPUs (Advanced Micro Devices, Inc., Sunnyvale, CA, USA)). Speedup factors of up to 24× and 1.6× for the GPU code were achieved with respect to one and 16 CPU cores, respectively. The numerical results indicate that this OpenACC-based parallel scheme is an effective and extensible approach to port unstructured high-order CFD solvers to GPU computing.« less

  13. Effect of boundary representation on viscous, separated flows in a discontinuous-Galerkin Navier-Stokes solver

    NASA Astrophysics Data System (ADS)

    Nelson, Daniel A.; Jacobs, Gustaaf B.; Kopriva, David A.

    2016-08-01

    The effect of curved-boundary representation on the physics of the separated flow over a NACA 65(1)-412 airfoil is thoroughly investigated. A method is presented to approximate curved boundaries with a high-order discontinuous-Galerkin spectral element method for the solution of the Navier-Stokes equations. Multiblock quadrilateral element meshes are constructed with the grid generation software GridPro. The boundary of a NACA 65(1)-412 airfoil, defined by a cubic natural spline, is piecewise-approximated by isoparametric polynomial interpolants that represent the edges of boundary-fitted elements. Direct numerical simulation of the airfoil is performed on a coarse mesh and fine mesh with polynomial orders ranging from four to twelve. The accuracy of the curve fitting is investigated by comparing the flows computed on curved-sided meshes with those given by straight-sided meshes. Straight-sided meshes yield irregular wakes, whereas curved-sided meshes produce a regular Karman street wake. Straight-sided meshes also produce lower lift and higher viscous drag as compared with curved-sided meshes. When the mesh is refined by reducing the sizes of the elements, the lift decrease and viscous drag increase are less pronounced. The differences in the aerodynamic performance between the straight-sided meshes and the curved-sided meshes are concluded to be the result of artificial surface roughness introduced by the piecewise-linear boundary approximation provided by the straight-sided meshes.

  14. A nodal discontinuous Galerkin method for site effects assessment in viscoelastic media—verification and validation in the Nice basin

    NASA Astrophysics Data System (ADS)

    Peyrusse, Fabien; Glinsky, Nathalie; Gélis, Céline; Lanteri, Stéphane

    2014-10-01

    We present a discontinuous Galerkin method for site effects assessment. The P-SV seismic wave propagation is studied in 2-D space heterogeneous media. The first-order velocity-stress system is obtained by assuming that the medium is linear, isotropic and viscoelastic, thus considering intrinsic attenuation. The associated stress-strain relation in the time domain being a convolution, which is numerically intractable, we consider the rheology of a generalized Maxwell body replacing the convolution by a set of differential equations. This results in a velocity-stress system which contains additional equations for the anelastic functions expressing the strain history of the material. Our numerical method, suitable for complex triangular unstructured meshes, is based on centred numerical fluxes and a leap-frog time-discretization. The method is validated through numerical simulations including comparisons with a finite-difference scheme. We study the influence of the geological structures of the Nice basin on the surface ground motion through the comparison of 1-D and 2-D soil response in homogeneous and heterogeneous soil. At last, we compare numerical results with real recordings data. The computed multiple-sediment basin response allows to reproduce the shape of the recorded amplification in the basin. This highlights the importance of knowing the lithological structures of a basin, layers properties and interface geometry.

  15. Seismic small-scale discontinuity sparsity-constraint inversion method using a penalty decomposition algorithm

    NASA Astrophysics Data System (ADS)

    Zhao, Jingtao; Peng, Suping; Du, Wenfeng

    2016-02-01

    We consider sparsity-constraint inversion method for detecting seismic small-scale discontinuities, such as edges, faults and cavities, which provide rich information about petroleum reservoirs. However, where there is karstification and interference caused by macro-scale fault systems, these seismic small-scale discontinuities are hard to identify when using currently available discontinuity-detection methods. In the subsurface, these small-scale discontinuities are separately and sparsely distributed and their seismic responses occupy a very small part of seismic image. Considering these sparsity and non-smooth features, we propose an effective L 2-L 0 norm model for improvement of their resolution. First, we apply a low-order plane-wave destruction method to eliminate macro-scale smooth events. Then, based the residual data, we use a nonlinear structure-enhancing filter to build a L 2-L 0 norm model. In searching for its solution, an efficient and fast convergent penalty decomposition method is employed. The proposed method can achieve a significant improvement in enhancing seismic small-scale discontinuities. Numerical experiment and field data application demonstrate the effectiveness and feasibility of the proposed method in studying the relevant geology of these reservoirs.

  16. Local Discontinuous Galerkin (LDG) Method for Advection of Active Compositional Fields with Discontinuous Boundaries: Demonstration and Comparison with Other Methods in the Mantle Convection Code ASPECT

    NASA Astrophysics Data System (ADS)

    He, Y.; Billen, M. I.; Puckett, E. G.

    2015-12-01

    Flow in the Earth's mantle is driven by thermo-chemical convection in which the properties and geochemical signatures of rocks vary depending on their origin and composition. For example, tectonic plates are composed of compositionally-distinct layers of crust, residual lithosphere and fertile mantle, while in the lower-most mantle there are large compositionally distinct "piles" with thinner lenses of different material. Therefore, tracking of active or passive fields with distinct compositional, geochemical or rheologic properties is important for incorporating physical realism into mantle convection simulations, and for investigating the long term mixing properties of the mantle. The difficulty in numerically advecting fields arises because they are non-diffusive and have sharp boundaries, and therefore require different methods than usually used for temperature. Previous methods for tracking fields include the marker-chain, tracer particle, and field-correction (e.g., the Lenardic Filter) methods: each of these has different advantages or disadvantages, trading off computational speed with accuracy in tracking feature boundaries. Here we present a method for modeling active fields in mantle dynamics simulations using a new solver implemented in the deal.II package that underlies the ASPECT software. The new solver for the advection-diffusion equation uses a Local Discontinuous Galerkin (LDG) algorithm, which combines features of both finite element and finite volume methods, and is particularly suitable for problems with a dominant first-order term and discontinuities. Furthermore, we have applied a post-processing technique to insure that the solution satisfies a global maximum/minimum. One potential drawback for the LDG method is that the total number of degrees of freedom is larger than the finite element method. To demonstrate the capabilities of this new method we present results for two benchmarks used previously: a falling cube with distinct buoyancy and

  17. Local Discontinuous Galerkin (LDG) Method for Advection of Active Compositional Fields with Discontinuous Boundaries: Demonstration and Comparison with Other Methods in the Mantle Convection Code ASPECT

    NASA Astrophysics Data System (ADS)

    Hsu, S. K.; Armada, L. T.; Yeh, Y. C.; Bacolcol, T. C.; Dimalanta, C. B.; Doo, W. B.; Liang, C. W.

    2014-12-01

    Flow in the Earth's mantle is driven by thermo-chemical convection in which the properties and geochemical signatures of rocks vary depending on their origin and composition. For example, tectonic plates are composed of compositionally-distinct layers of crust, residual lithosphere and fertile mantle, while in the lower-most mantle there are large compositionally distinct "piles" with thinner lenses of different material. Therefore, tracking of active or passive fields with distinct compositional, geochemical or rheologic properties is important for incorporating physical realism into mantle convection simulations, and for investigating the long term mixing properties of the mantle. The difficulty in numerically advecting fields arises because they are non-diffusive and have sharp boundaries, and therefore require different methods than usually used for temperature. Previous methods for tracking fields include the marker-chain, tracer particle, and field-correction (e.g., the Lenardic Filter) methods: each of these has different advantages or disadvantages, trading off computational speed with accuracy in tracking feature boundaries. Here we present a method for modeling active fields in mantle dynamics simulations using a new solver implemented in the deal.II package that underlies the ASPECT software. The new solver for the advection-diffusion equation uses a Local Discontinuous Galerkin (LDG) algorithm, which combines features of both finite element and finite volume methods, and is particularly suitable for problems with a dominant first-order term and discontinuities. Furthermore, we have applied a post-processing technique to insure that the solution satisfies a global maximum/minimum. One potential drawback for the LDG method is that the total number of degrees of freedom is larger than the finite element method. To demonstrate the capabilities of this new method we present results for two benchmarks used previously: a falling cube with distinct buoyancy and

  18. NEXD: A Software Package for High Order Simulation of Seismic Waves using the Nodal Discontinuous Galerkin Method

    NASA Astrophysics Data System (ADS)

    Schumacher, F.; Lambrecht, L.; Friederich, W.

    2015-12-01

    In geophysics numerical simulations are a key tool to understand the processes of earth. For example, global simulations of seismic waves excited by earthquakes are essential to infer the velocity structure within the earth. Furthermore, numerical investigations can be helpful on local scales in order to find and characterize oil and gas reservoirs. Moreover, simulations enable a better understanding of wave propagation in borehole and tunnel seismic applications. Even on microscopic scales, numerical simulations of elastic waves can help to increase knowledge about the behaviour of materials, e.g. to understand the mechanism of crack propagation in rocks. To deal with highly complex heterogeneous models, here the Nodal Discontinuous Galerkin Method (NDG) is used to calculate synthetic seismograms. The advantage of this method is that complex mesh geometries can be computed by using triangular or tetrahedral elements for domain discretization together with a high order spatial approximation of the wave field. The simulation tool NEXD is presented which has the capability of simulating elastic and anelastic wave fields for seismic experiments for one-, two- and three- dimensional settings. The implementation of poroelasticity and simulation of slip interfaces are currently in progress and are working for the one dimensional part. External models provided by e.g. Trelis/Cubit can be used for parallelized computations on triangular or tetrahedral meshes. For absorbing boundary conditions either a fluxes based approach or a Nearly Perfectly Matched Layer (NPML) can be used. Examples are presented to validate the method and to show the capability of the software for complex models such as the simulation of a tunnel seismic experiment.

  19. Implicit finite volume and discontinuous Galerkin methods for multicomponent flow in unstructured 3D fractured porous media

    NASA Astrophysics Data System (ADS)

    Moortgat, Joachim; Amooie, Mohammad Amin; Soltanian, Mohamad Reza

    2016-10-01

    We present a new implicit higher-order finite element (FE) approach to efficiently model compressible multicomponent fluid flow on unstructured grids and in fractured porous subsurface formations. The scheme is sequential implicit: pressures and fluxes are updated with an implicit Mixed Hybrid Finite Element (MHFE) method, and the transport of each species is approximated with an implicit second-order Discontinuous Galerkin (DG) FE method. Discrete fractures are incorporated with a cross-flow equilibrium approach. This is the first investigation of all-implicit higher-order MHFE-DG for unstructured triangular, quadrilateral (2D), and hexahedral (3D) grids and discrete fractures. A lowest-order implicit finite volume (FV) transport update is also developed for the same grid types. The implicit methods are compared to an Implicit-Pressure-Explicit-Composition (IMPEC) scheme. For fractured domains, the unconditionally stable implicit transport update is shown to increase computational efficiency by orders of magnitude as compared to IMPEC, which has a time-step constraint proportional to the pore volume of discrete fracture grid cells. However, when lowest-order Euler time-discretizations are used, numerical errors increase linearly with the larger implicit time-steps, resulting in high numerical dispersion. Second-order Crank-Nicolson implicit MHFE-DG and MHFE-FV are therefore presented as well. Convergence analyses show twice the convergence rate for the DG methods as compared to FV, resulting in two to three orders of magnitude higher computational efficiency. Numerical experiments demonstrate the efficiency and robustness in modeling compressible multicomponent flow on irregular and fractured 2D and 3D grids, even in the presence of fingering instabilities.

  20. A New Ice-sheet / Ocean Interaction Model for Greenland Fjords using High-Order Discontinuous Galerkin Methods

    NASA Astrophysics Data System (ADS)

    Kopera, M. A.; Maslowski, W.; Giraldo, F.

    2015-12-01

    One of the key outstanding challenges in modeling of climate change and sea-level rise is the ice-sheet/ocean interaction in narrow, elongated and geometrically complicated fjords around Greenland. To address this challenge we propose a new approach, a separate fjord model using discontinuous Galerkin (DG) methods, or FDG. The goal of this project is to build a separate, high-resolution module for use in Earth System Models (ESMs) to realistically represent the fjord bathymetry, coastlines, exchanges with the outside ocean, circulation and fine-scale processes occurring within the fjord and interactions at the ice shelf interface. FDG is currently at the first stage of development. The DG method provides FDG with high-order accuracy as well as geometrical flexibility, including the capacity to handle non-conforming adaptive mesh refinement to resolve the processes occurring near the ice-sheet/ocean interface without introducing prohibitive computational costs. Another benefit of this method is its excellent performance on multi- and many-core architectures, which allows for utilizing modern high performance computing systems for high-resolution simulations. The non-hydrostatic model of the incompressible Navier-Stokes equation will account for the stationary ice-shelf with sub-shelf ocean interaction, basal melting and subglacial meltwater influx and with boundary conditions at the surface to account for floating sea ice. The boundary conditions will be provided to FDG via a flux coupler to emulate the integration with an ESM. Initially, FDG will be tested for the Sermilik Fjord settings, using real bathymetry, boundary and initial conditions, and evaluated against available observations and other model results for this fjord. The overarching goal of the project is to be able to resolve the ice-sheet/ocean interactions around the entire coast of Greenland and two-way coupling with regional and global climate models such as the Regional Arctic System Model (RASM

  1. Discontinuous Galerkin discretization of the Reynolds-averaged Navier-Stokes equations with the shear-stress transport model

    NASA Astrophysics Data System (ADS)

    Schoenawa, Stefan; Hartmann, Ralf

    2014-04-01

    In this article we consider the development of Discontinuous Galerkin (DG) methods for the numerical approximation of the Reynolds-averaged Navier-Stokes (RANS) equations with the shear-stress transport (SST) model by Menter. This turbulence model is based on a blending of the Wilcox k-ω model used near the wall and the k-ɛ model used in the rest of the domain where the blending functions depend on the distance to the nearest wall. For the computation of the distance of each quadrature point in the domain to the nearest of the curved, piecewise polynomial wall boundaries, we propose a stabilized continuous finite element (FE) discretization of the eikonal equation. Furthermore, we propose a new wall boundary condition for the dissipation rate ω based on the projection of the analytic near-wall behavior of ω onto the discrete ansatz space of the DG discretization. Finally, we introduce an artificial viscosity to the discretization of the turbulence kinetic energy (k-)equation to suppress oscillations of k near the underresolved boundary layer edge. The wall distance computation based on the continuous FE discretization of the eikonal equation is demonstrated for an internal and three external/aerodynamic flow geometries including a three-element high-lift configuration. The DG discretization of the RANS equations with the SST model is demonstrated for turbulent flows past a flat plate and the RAE2822 airfoil (Cases 9 and 10). The results are compared to the underlying k-ω model and experimental data.

  2. Second order discontinuous Galerkin scheme for compound natural channels with movable bed. Applications for the computation of rating curves

    NASA Astrophysics Data System (ADS)

    Minatti, Lorenzo; De Cicco, Pina Nicoletta; Solari, Luca

    2016-07-01

    A new higher order 1D numerical scheme for the propagation of flood waves in compound channels with a movable bed is presented. The model equations are solved by means of an ADER Discontinuous Galerkin explicit scheme which can, in principle, reach any order of space-time accuracy. The higher order nature of the scheme allows the numerical coupling between flux and source terms appearing in the governing equations and, importantly, to handle moderately stiff and stiff source terms. Stiff source terms arise in the case of abrupt changes of river geometry such as in the case of hydraulic structures like bridges and weirs. Hydraulic interpretation of these conditions with 1D numerical modelling requires particular attention; for instance, a 1st order scheme might either lead to inaccurate solutions or impossibility to simulate these complex conditions. Validation is carried out with several test cases with the aim to check the scheme capability to deal with abrupt geometric changes and to capture the direction and celerity of propagation of bed and water surface disturbances. Validation is done also in a real case by using stage-discharge field measurements in the Ombrone river (Tuscany). The proposed scheme is further employed for the computation of flow rating curves in cross-sections just upstream of an abrupt narrowing, considering both fixed and movable bed conditions and different ratios of contraction for cross-section width. This problem is of particular relevance as, in common engineering practice, rating curves are derived from stage-measuring gauges installed on bridges with flow conditions that are likely to be influenced by local width narrowing. Results show that a higher order scheme is needed in order to deal with stiff source terms and reproduce realistic flow rating curves, unless a strong refinement of the computational grid is performed. This capability appears to be crucial for the computation of rating curves on coarse grids as it allows the

  3. One-sided Post-processing for the Discontinuous Galerkin Method Using ENO Type Stencil Choosing and the Local Edge Detection Method

    SciTech Connect

    Archibald, Richard K; Gelb, Anne; Gottlieb, Sigal; Ryan, Jennifer

    2006-01-01

    In a previous paper by Ryan and Shu [Ryan, J. K., and Shu, C.-W. (2003). Methods Appl. Anal. 10(2), 295-307], a one-sided post-processing technique for the discontinuous Galerkin method was introduced for reconstructing solutions near computational boundaries and discontinuities in the boundaries, as well as for changes in mesh size. This technique requires prior knowledge of the discontinuity location in order to determine whether to use centered, partially one-sided, or one-sided post-processing. We now present two alternative stencil choosing schemes to automate the choice of post-processing stencil. The first is an ENO type stencil choosing procedure, which is designed to choose centered post-processing in smooth regions and one-sided or partially one-sided post-processing near a discontinuity, and the second method is based on the edge detection method designed by Archibald, Gelb, and Yoon [Archibald, R., Gelb, A., and Yoon, J. (2005). SIAM J. Numeric. Anal. 43, 259-279; Archibald, R., Gelb, A., and Yoon, J. (2006). Appl. Numeric. Math. (submitted)]. We compare these stencil choosing techniques and analyze their respective strengths and weaknesses. Finally, the automated stencil choices are applied in conjunction with the appropriate post-processing procedures and it is determine that the resulting numerical solutions are of the correct order.

  4. A staggered space-time discontinuous Galerkin method for the three-dimensional incompressible Navier-Stokes equations on unstructured tetrahedral meshes

    NASA Astrophysics Data System (ADS)

    Tavelli, Maurizio; Dumbser, Michael

    2016-08-01

    In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As is typical for space-time DG schemes, the discrete solution is represented in terms of space-time basis functions. This allows to achieve very high order of accuracy also in time, which is not easy to obtain for the incompressible Navier-Stokes equations. Similarly to staggered finite difference schemes, in our approach the discrete pressure is defined on the primary tetrahedral grid, while the discrete velocity is defined on a face-based staggered dual grid. While staggered meshes are state of the art in classical finite difference schemes for the incompressible Navier-Stokes equations, their use in high order DG schemes is still quite rare. A very simple and efficient Picard iteration is used in order to derive a space-time pressure correction algorithm that achieves also high order of accuracy in time and that avoids the direct solution of global nonlinear systems. Formal substitution of the discrete momentum equation on the dual grid into the discrete continuity equation on the primary grid yields a very sparse five-point block system for the scalar pressure, which is conveniently solved with a matrix-free GMRES algorithm. From numerical experiments we find that the linear system seems to be reasonably well conditioned, since all simulations shown in this paper could be run without the use of any preconditioner, even up to very high polynomial degrees. For a piecewise constant polynomial approximation in time and if pressure boundary conditions are specified at least in one point, the resulting system is, in addition, symmetric and positive definite. This allows us to use even faster iterative solvers, like the conjugate gradient method. The flexibility and accuracy of high order space-time DG methods on curved

  5. Development of high order numerical methods for particle-laden flows on unstructured grids: A realizability-preserving Discontinuous Galerkin method for moderate Stokes number flows

    NASA Astrophysics Data System (ADS)

    Larat, Adam; Sabat, Macole; Vié, Aymeric; Chalons, Christophe; Massot, Marc

    2014-11-01

    The simulation of particle-laden flows is of primary importance for several industrial applications, like sprays in aeronautical combustors or particles in fluidized beds. Our focus is on Moment methods that describes the disperse phase as a continuum. The accuracy and performance of such approaches highly depends on the number of controlled moments for correctly describing the physics of the flow, but also on the numerics that are used to solve the continuous system of equations at a discrete level. In the present work, we investigate the use of Discontinuous Galerkin methods to solve for the convective part of the moment equations. By deriving realizability conditions on the moment system that are associated to a convex space, a projection strategy is used to maintain the solution in the realizable space. This method is applied to the resolution of the pressure less gas dynamics and the Anisotropic Gaussian moment approach, the former solving for low Stokes number flows where no Particle Trajectory Crossing occurs, while the latter is solving for moderate Stokes number flows and can handle PTC through a pressure tensor in the convective term. The strategy is assessed on turbulent flows through comparisons with Lagrangian results.

  6. A non-linear discontinuous Petrov-Galerkin method for removing oscillations in the solution of the time-dependent transport equation

    SciTech Connect

    Merton, S. R.; Smedley-Stevenson, R. P.; Pain, C. C.

    2012-07-01

    This paper describes a Non-Linear Discontinuous Petrov-Galerkin method and its application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The added dissipation is calculated at each node of the finite element mesh based on local behaviour of the transport solution on both the spatial and temporal axes of the problem. Thus a different dissipation is used in different elements. The magnitude of dissipation that is used is obtained from a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is implemented within a very general finite element Riemann framework. This makes it completely independent of choice of angular basis function allowing one to use different descriptions of the angular variation. Results show the non-linear scheme performs consistently well in demanding time-dependent multi-dimensional neutron transport problems. (authors)

  7. Experiences on p-Version Time-Discontinuous Galerkin's Method for Nonlinear Heat Transfer Analysis and Sensitivity Analysis

    NASA Technical Reports Server (NTRS)

    Hou, Gene

    2004-01-01

    The focus of this research is on the development of analysis and sensitivity analysis equations for nonlinear, transient heat transfer problems modeled by p-version, time discontinuous finite element approximation. The resulting matrix equation of the state equation is simply in the form ofA(x)x = c, representing a single step, time marching scheme. The Newton-Raphson's method is used to solve the nonlinear equation. Examples are first provided to demonstrate the accuracy characteristics of the resultant finite element approximation. A direct differentiation approach is then used to compute the thermal sensitivities of a nonlinear heat transfer problem. The report shows that only minimal coding effort is required to enhance the analysis code with the sensitivity analysis capability.

  8. New high-order, semi-implicit Hybridized Discontinuous Galerkin - Spectral Element Method (HDG-SEM) for simulation of complex wave propagation involving coupling between seismic, hydro-acoustic and infrasonic waves: numerical analysis and case studies.

    NASA Astrophysics Data System (ADS)

    Terrana, S.; Vilotte, J. P.; Guillot, L.

    2015-12-01

    New seismological monitoring networks combine broadband seismic receivers, hydrophones and micro-barometers antenna, providing complementary observation of source-radiated waves. Exploiting these observations requires accurate and multi-media - elastic, hydro-acoustic, infrasound - wave simulation methods, in order to improve our physical understanding of energy exchanges at material interfaces.We present here a new development of a high-order Hybridized Discontinuous Galerkin (HDG) method, for the simulation of coupled seismic and acoustic wave propagation, within a unified framework ([1],[2]) allowing for continuous and discontinuous Spectral Element Methods (SEM) to be used in the same simulation, with conforming and non-conforming meshes. The HDG-SEM approximation leads to differential - algebraic equations, which can be solved implicitly using energy-preserving time-schemes.The proposed HDG-SEM is computationally attractive, when compared with classical Discontinuous Galerkin methods, involving only the approximation of the single-valued traces of the velocity field along the element interfaces as globally coupled unknowns. The formulation is based on a variational approximation of the physical fluxes, which are shown to be the explicit solution of an exact Riemann problem at each element boundaries. This leads to a highly parallel and efficient unstructured and high-order accurate method, which can be space-and-time adaptive.A numerical study of the accuracy and convergence of the HDG-SEM is performed through a number of case studies involving elastic-acoustic (infrasound) coupling with geometries of increasing complexity. Finally, the performance of the method is illustrated through realistic case studies involving ground wave propagation associated to topography effects.In conclusion, we outline some on-going extensions of the method.References:[1] Cockburn, B., Gopalakrishnan, J., Lazarov, R., Unified hybridization of discontinuous Galerkin, mixed and

  9. A simple robust and accurate a posteriori sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes

    NASA Astrophysics Data System (ADS)

    Dumbser, Michael; Loubère, Raphaël

    2016-08-01

    In this paper we propose a simple, robust and accurate nonlinear a posteriori stabilization of the Discontinuous Galerkin (DG) finite element method for the solution of nonlinear hyperbolic PDE systems on unstructured triangular and tetrahedral meshes in two and three space dimensions. This novel a posteriori limiter, which has been recently proposed for the simple Cartesian grid case in [62], is able to resolve discontinuities at a sub-grid scale and is substantially extended here to general unstructured simplex meshes in 2D and 3D. It can be summarized as follows: At the beginning of each time step, an approximation of the local minimum and maximum of the discrete solution is computed for each cell, taking into account also the vertex neighbors of an element. Then, an unlimited discontinuous Galerkin scheme of approximation degree N is run for one time step to produce a so-called candidate solution. Subsequently, an a posteriori detection step checks the unlimited candidate solution at time t n + 1 for positivity, absence of floating point errors and whether the discrete solution has remained within or at least very close to the bounds given by the local minimum and maximum computed in the first step. Elements that do not satisfy all the previously mentioned detection criteria are flagged as troubled cells. For these troubled cells, the candidate solution is discarded as inappropriate and consequently needs to be recomputed. Within these troubled cells the old discrete solution at the previous time tn is scattered onto small sub-cells (Ns = 2 N + 1 sub-cells per element edge), in order to obtain a set of sub-cell averages at time tn. Then, a more robust second order TVD finite volume scheme is applied to update the sub-cell averages within the troubled DG cells from time tn to time t n + 1. The new sub-grid data at time t n + 1 are finally gathered back into a valid cell-centered DG polynomial of degree N by using a classical conservative and higher order

  10. Asynchronous communication in spectral-element and discontinuous Galerkin methods for atmospheric dynamics - a case study using the High-Order Methods Modeling Environment (HOMME-homme_dg_branch)

    NASA Astrophysics Data System (ADS)

    Jamroz, Benjamin F.; Klöfkorn, Robert

    2016-08-01

    The scalability of computational applications on current and next-generation supercomputers is increasingly limited by the cost of inter-process communication. We implement non-blocking asynchronous communication in the High-Order Methods Modeling Environment for the time integration of the hydrostatic fluid equations using both the spectral-element and discontinuous Galerkin methods. This allows the overlap of computation with communication, effectively hiding some of the costs of communication. A novel detail about our approach is that it provides some data movement to be performed during the asynchronous communication even in the absence of other computations. This method produces significant performance and scalability gains in large-scale simulations.

  11. Collocation and Galerkin Time-Stepping Methods

    NASA Technical Reports Server (NTRS)

    Huynh, H. T.

    2011-01-01

    We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods.

  12. Meshless Local Petrov-Galerkin Method for Bending Problems

    NASA Technical Reports Server (NTRS)

    Phillips, Dawn R.; Raju, Ivatury S.

    2002-01-01

    Recent literature shows extensive research work on meshless or element-free methods as alternatives to the versatile Finite Element Method. One such meshless method is the Meshless Local Petrov-Galerkin (MLPG) method. In this report, the method is developed for bending of beams - C1 problems. A generalized moving least squares (GMLS) interpolation is used to construct the trial functions, and spline and power weight functions are used as the test functions. The method is applied to problems for which exact solutions are available to evaluate its effectiveness. The accuracy of the method is demonstrated for problems with load discontinuities and continuous beam problems. A Petrov-Galerkin implementation of the method is shown to greatly reduce computational time and effort and is thus preferable over the previously developed Galerkin approach. The MLPG method for beam problems yields very accurate deflections and slopes and continuous moment and shear forces without the need for elaborate post-processing techniques.

  13. A stable interface element scheme for the p-adaptive lifting collocation penalty formulation

    NASA Astrophysics Data System (ADS)

    Cagnone, J. S.; Nadarajah, S. K.

    2012-02-01

    This paper presents a procedure for adaptive polynomial refinement in the context of the lifting collocation penalty (LCP) formulation. The LCP scheme is a high-order unstructured discretization method unifying the discontinuous Galerkin, spectral volume, and spectral difference schemes in single differential formulation. Due to the differential nature of the scheme, the treatment of inter-cell fluxes for spatially varying polynomial approximations is not straightforward. Specially designed elements are proposed to tackle non-conforming polynomial approximations. These elements are constructed such that a conforming interface between polynomial approximations of different degrees is recovered. The stability and conservation properties of the scheme are analyzed and various inviscid compressible flow calculations are performed to demonstrate the potential of the proposed approach.

  14. Time-stepping stability of continuous and discontinuous finite-element methods for 3-D wave propagation

    NASA Astrophysics Data System (ADS)

    Mulder, W. A.; Zhebel, E.; Minisini, S.

    2014-02-01

    We analyse the time-stepping stability for the 3-D acoustic wave equation, discretized on tetrahedral meshes. Two types of methods are considered: mass-lumped continuous finite elements and the symmetric interior-penalty discontinuous Galerkin method. Combining the spatial discretization with the leap-frog time-stepping scheme, which is second-order accurate and conditionally stable, leads to a fully explicit scheme. We provide estimates of its stability limit for simple cases, namely, the reference element with Neumann boundary conditions, its distorted version of arbitrary shape, the unit cube that can be partitioned into six tetrahedra with periodic boundary conditions and its distortions. The Courant-Friedrichs-Lewy stability limit contains an element diameter for which we considered different options. The one based on the sum of the eigenvalues of the spatial operator for the first-degree mass-lumped element gives the best results. It resembles the diameter of the inscribed sphere but is slightly easier to compute. The stability estimates show that the mass-lumped continuous and the discontinuous Galerkin finite elements of degree 2 have comparable stability conditions, whereas the mass-lumped elements of degree one and three allow for larger time steps.

  15. MIB Galerkin method for elliptic interface problems.

    PubMed

    Xia, Kelin; Zhan, Meng; Wei, Guo-Wei

    2014-12-15

    Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm the

  16. MIB Galerkin method for elliptic interface problems

    PubMed Central

    Xia, Kelin; Zhan, Meng; Wei, Guo-Wei

    2014-01-01

    Summary Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm

  17. Application of the Galerkin/least-squares formulation to the analysis of hypersonic flows. II - Flow past a double ellipse

    NASA Technical Reports Server (NTRS)

    Chalot, F.; Hughes, T. J. R.; Johan, Z.; Shakib, F.

    1991-01-01

    A finite element method for the compressible Navier-Stokes equations is introduced. The discretization is based on entropy variables. The methodology is developed within the framework of a Galerkin/least-squares formulation to which a discontinuity-capturing operator is added. Results for four test cases selected among those of the Workshop on Hypersonic Flows for Reentry Problems are presented.

  18. Galerkin Method for Nonlinear Dynamics

    NASA Astrophysics Data System (ADS)

    Noack, Bernd R.; Schlegel, Michael; Morzynski, Marek; Tadmor, Gilead

    A Galerkin method is presented for control-oriented reduced-order models (ROM). This method generalizes linear approaches elaborated by M. Morzyński et al. for the nonlinear Navier-Stokes equation. These ROM are used as plants for control design in the chapters by G. Tadmor et al., S. Siegel, and R. King in this volume. Focus is placed on empirical ROM which compress flow data in the proper orthogonal decomposition (POD). The chapter shall provide a complete description for construction of straight-forward ROM as well as the physical understanding and teste

  19. Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Liu, Yen; Vinokur, Marcel; Wang, Z. J.

    2004-01-01

    A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. A discussion on the Discontinuous Spectral Difference (SD) Method, locations of the unknowns and flux points and numerical results are also presented.

  20. Application of the Galerkin/least-squares formulation to the analysis of hypersonic flows. I - Flow over a two-dimensional ramp

    NASA Technical Reports Server (NTRS)

    Chalot, F.; Hughes, T. J. R.; Johan, Z.; Shakib, F.

    1991-01-01

    An FEM for the compressible Navier-Stokes equations is introduced. The discretization is based on entropy variables. The methodology is developed within the framework of a Galerkin/least-squares formulation to which a discontinuity-capturing operator is added. Results for three test cases selected among those of the Workshop on Hypersonic Flows for Reentry Problems are presented.

  1. Symmetric Galerkin boundary formulations employing curved elements

    NASA Technical Reports Server (NTRS)

    Kane, J. H.; Balakrishna, C.

    1993-01-01

    Accounts of the symmetric Galerkin approach to boundary element analysis (BEA) have recently been published. This paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency. A new symmetric Galerkin theoretical formulation for both the (harmonic) heat conduction and the (biharmonic) elasticity problem that employs regularized singular and hypersingular boundary integral equations (BIEs) is presented. The novel use of regularized BIEs in the Galerkin context is shown to allow straightforward incorporation of curved, isoparametric elements. A symmetric reusable intrinsic sample point (RISP) numerical integration algorithm is shown to produce a Galerkin (i.e., double) integration strategy that is competitive with its counterpart (i.e., singular) integration procedure in the collocation BEA approach when the time saved in the symmetric equation solution phase is also taken into account. This new formulation is shown to be capable of employing hypersingular BIEs while obviating the requirement of C 1 continuity, a fact that allows the employment of the popular continuous element technology. The behavior of the symmetric Galerkin BEA method with regard to both direct and iterative equation solution operations is also addressed. A series of example problems are presented to quantify the performance of this symmetric approach, relative to the more conventional unsymmetric BEA, in terms of both accuracy and efficiency. It is concluded that appropriate implementations of the symmetric Galerkin approach to BEA indeed have the potential to be competitive with, if not superior to, collocation-based BEA, for large-scale problems.

  2. Towards Exascale Computing with NUMA: an Element-based Galerkin Nonhydrostatic Global and Mesoscale Atmospheric Modeling

    NASA Astrophysics Data System (ADS)

    Giraldo, F.; Mueller, A.; Kopera, M. A.; Abdi, D. S.; Wilcox, L.

    2015-12-01

    In this talk, we shall describe the NUMA atmospheric model, focusing in particular on its unified continuous/discontinuous (CG and DG) Galerkin numerical methods that are used to represent the spatial derivatives. We shall describe how these two methods are formulated in a unified approach and the advantages that this brings. We will also report on the progress in extending NUMA to using adaptive mesh refinement. Lastly, we will report on the scalability and performance of NUMA on the leadership computing facilities (LCF) of the Department of Energy where we have scaled NUMA to over 3 million MPI threads achieving a 90% efficiency.

  3. A new family of stable elements for the Stokes problem based on a mixed Galerkin/least-squares finite element formulation

    NASA Technical Reports Server (NTRS)

    Franca, Leopoldo P.; Loula, Abimael F. D.; Hughes, Thomas J. R.; Miranda, Isidoro

    1989-01-01

    Adding to the classical Hellinger-Reissner formulation, a residual form of the equilibrium equation, a new Galerkin/least-squares finite element method is derived. It fits within the framework of a mixed finite element method and is stable for rather general combinations of stress and velocity interpolations, including equal-order discontinuous stress and continuous velocity interpolations which are unstable within the Galerkin approach. Error estimates are presented based on a generalization of the Babuska-Brezzi theory. Numerical results (not presented herein) have confirmed these estimates as well as the good accuracy and stability of the method.

  4. The Problem with Penalties

    ERIC Educational Resources Information Center

    Dueck, Myron

    2014-01-01

    Imposing a penalty for late or incomplete homework assignments, Dueck says, neither inspires learning nor provides accurate grades. Dueck lists four rules that a teacher must follow if penalties for inadequate homework are to be efficient in prodding students to do that work. The usual homework penalty structures violate each of these four rules.…

  5. A tessellated continuum approach to thermal analysis: discontinuity networks

    NASA Astrophysics Data System (ADS)

    Jiang, C.; Davey, K.; Prosser, R.

    2016-08-01

    Tessellated continuum mechanics is an approach for the representation of thermo-mechanical behaviour of porous media on tessellated continua. It involves the application of iteration function schemes using affine contraction and expansion maps, respectively, for the creation of porous fractal materials and associated tessellated continua. Highly complex geometries can be produced using a modest number of contraction mappings. The associated tessellations form the mesh in a numerical procedure. This paper tests the hypothesis that thermal analysis of porous structures can be achieved using a discontinuous Galerkin finite element method on a tessellation. Discontinuous behaviour is identified at a discontinuity network in a tessellation; its use is shown to provide a good representation of the physics relating to cellular heat exchanger designs. Results for different cellular designs (with corresponding tessellations) are contrasted against those obtained from direct analysis and very high accuracy is observed.

  6. Cultural Discontinuities and Schooling.

    ERIC Educational Resources Information Center

    Ogbu, John U.

    1982-01-01

    Attempts to define the cultural discontinuity (between schools and students) hypothesis by distinguishing between universal, primary, and secondary discontinuities. Suggests that each of these is associated with a distinct type of school problem, and that secondary cultural discontinuities commonly affect minority students in the United States.…

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

    SciTech Connect

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

    2014-10-11

    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.

  8. A well-posed and stable stochastic Galerkin formulation of the incompressible Navier-Stokes equations with random data

    NASA Astrophysics Data System (ADS)

    Pettersson, Per; Nordström, Jan; Doostan, Alireza

    2016-02-01

    We present a well-posed stochastic Galerkin formulation of the incompressible Navier-Stokes equations with uncertainty in model parameters or the initial and boundary conditions. The stochastic Galerkin method involves representation of the solution through generalized polynomial chaos expansion and projection of the governing equations onto stochastic basis functions, resulting in an extended system of equations. A relatively low-order generalized polynomial chaos expansion is sufficient to capture the stochastic solution for the problem considered. We derive boundary conditions for the continuous form of the stochastic Galerkin formulation of the velocity and pressure equations. The resulting problem formulation leads to an energy estimate for the divergence. With suitable boundary data on the pressure and velocity, the energy estimate implies zero divergence of the velocity field. Based on the analysis of the continuous equations, we present a semi-discretized system where the spatial derivatives are approximated using finite difference operators with a summation-by-parts property. With a suitable choice of dissipative boundary conditions imposed weakly through penalty terms, the semi-discrete scheme is shown to be stable. Numerical experiments in the laminar flow regime corroborate the theoretical results and we obtain high-order accurate results for the solution variables and the velocity divergence converges to zero as the mesh is refined.

  9. Reduced order models based on local POD plus Galerkin projection

    NASA Astrophysics Data System (ADS)

    Rapún, María-Luisa; Vega, José M.

    2010-04-01

    A method is presented to accelerate numerical simulations on parabolic problems using a numerical code and a Galerkin system (obtained via POD plus Galerkin projection) on a sequence of interspersed intervals. The lengths of these intervals are chosen according to several basic ideas that include an a priori estimate of the error of the Galerkin approximation. Several improvements are introduced that reduce computational complexity and deal with: (a) updating the POD manifold (instead of calculating it) at the end of each Galerkin interval; (b) using only a limited number of mesh points to calculate the right hand side of the Galerkin system; and (c) introducing a second error estimate based on a second Galerkin system to account for situations in which qualitative changes in the dynamics occur during the application of the Galerkin system. The resulting method, called local POD plus Galerkin projection method, turns out to be both robust and efficient. For illustration, we consider a time-dependent Fisher-like equation and a complex Ginzburg-Landau equation.

  10. A Galerkin formulation of the MIB method for three dimensional elliptic interface problems

    PubMed Central

    Xia, Kelin; Wei, Guo-Wei

    2014-01-01

    We develop a three dimensional (3D) Galerkin formulation of the matched interface and boundary (MIB) method for solving elliptic partial differential equations (PDEs) with discontinuous coefficients, i.e., the elliptic interface problem. The present approach builds up two sets of elements respectively on two extended subdomains which both include the interface. As a result, two sets of elements overlap each other near the interface. Fictitious solutions are defined on the overlapping part of the elements, so that the differentiation operations of the original PDEs can be discretized as if there was no interface. The extra coefficients of polynomial basis functions, which furnish the overlapping elements and solve the fictitious solutions, are determined by interface jump conditions. Consequently, the interface jump conditions are rigorously enforced on the interface. The present method utilizes Cartesian meshes to avoid the mesh generation in conventional finite element methods (FEMs). We implement the proposed MIB Galerkin method with three different elements, namely, rectangular prism element, five-tetrahedron element and six-tetrahedron element, which tile the Cartesian mesh without introducing any new node. The accuracy, stability and robustness of the proposed 3D MIB Galerkin are extensively validated over three types of elliptic interface problems. In the first type, interfaces are analytically defined by level set functions. These interfaces are relatively simple but admit geometric singularities. In the second type, interfaces are defined by protein surfaces, which are truly arbitrarily complex. The last type of interfaces originates from multiprotein complexes, such as molecular motors. Near second order accuracy has been confirmed for all of these problems. To our knowledge, it is the first time for an FEM to show a near second order convergence in solving the Poisson equation with realistic protein surfaces. Additionally, the present work offers the

  11. Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces

    NASA Technical Reports Server (NTRS)

    Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.

    2013-01-01

    Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.

  12. Discontinuous dual-primal mixed finite elements for elliptic problems

    NASA Technical Reports Server (NTRS)

    Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo

    2000-01-01

    We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

  13. Penalty Inflation Adjustments for Civil Money Penalties. Interim Final Rule.

    PubMed

    2016-06-27

    In accordance with the Federal Civil Penalties Inflation Adjustment Act of 1990, as amended by the Debt Collection Improvement Act of 1996, and further amended by the Bipartisan Budget Act of 2015, section 701: Federal Civil Penalties Inflation Adjustment Act Improvements Act of 2015, this interim final rule incorporates the penalty inflation adjustments for the civil money penalties contained in the Social Security Act

  14. Numerically Tracking Contact Discontinuities with an Introduction for GPU Programming

    SciTech Connect

    Davis, Sean L

    2012-08-17

    We review some of the classic numerical techniques used to analyze contact discontinuities and compare their effectiveness. Several finite difference methods (the Lax-Wendroff method, a Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) method and a Monotone Upstream Scheme for Conservation Laws (MUSCL) scheme with an Artificial Compression Method (ACM)) as well as the finite element Streamlined Upwind Petrov-Galerkin (SUPG) method were considered. These methods were applied to solve the 2D advection equation. Based on our results we concluded that the MUSCL scheme produces the sharpest interfaces but can inappropriately steepen the solution. The SUPG method seems to represent a good balance between stability and interface sharpness without any inappropriate steepening. However, for solutions with discontinuities, the MUSCL scheme is superior. In addition, a preliminary implementation in a GPU program is discussed.

  15. A new high-order accurate continuous Galerkin method for linear elastodynamics problems

    NASA Astrophysics Data System (ADS)

    Idesman, Alexander V.

    2007-07-01

    A new high-order accurate time-continuous Galerkin (TCG) method for elastodynamics is suggested. The accuracy of the new implicit TCG method is increased by a factor of two in comparison to that of the standard TCG method and is one order higher than the accuracy of the standard time-discontinuous Galerkin (TDG) method at the same number of degrees of freedom. The new method is unconditionally stable and has controllable numerical dissipation at high frequencies. An iterative predictor/multi-corrector solver that includes the factorization of the effective mass matrix of the same dimension as that of the mass matrix for the second-order methods is developed for the new TCG method. A new strategy combining numerical methods with small and large numerical dissipation is developed for elastodynamics. Simple numerical tests show a significant reduction in the computation time (by 5 25 times) for the new TCG method in comparison to that for second-order methods, and the suppression of spurious high-frequency oscillations.

  16. Teaching about the Death Penalty.

    ERIC Educational Resources Information Center

    Ryan, John Paul; Eden, John Michael

    1998-01-01

    Examines the reasons for the death penalty, the reasons why the death penalty attracts so much attention, whether the death penalty is applied consistently, and the evidence that the application of the death penalty may be racially biased. Provides an accompanying article on "Teaching Ideas" by Ronald A. Banaszak. (CMK)

  17. 77 FR 70710 - Civil Penalties

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-11-27

    ...,000. 75 FR 5246. Also on February 10, 2010, NHTSA last adjusted the maximum civil penalty for a... civil penalty policy when determining the appropriate civil penalty amount. See 62 FR 37115 (July 10... Act was published on February 4, 1997. 62 FR 5167. At that time, we codified the penalties...

  18. Meshless Local Petrov-Galerkin Euler-Bernoulli Beam Problems: A Radial Basis Function Approach

    NASA Technical Reports Server (NTRS)

    Raju, I. S.; Phillips, D. R.; Krishnamurthy, T.

    2003-01-01

    A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as in the conventional MLPG method. Compactly and noncompactly supported radial basis functions are considered. The non-compactly supported cubic radial basis function is found to perform very well. Results obtained from the radial basis MLPG method are comparable to those obtained using the conventional MLPG method for mixed boundary value problems and problems with discontinuous loading conditions.

  19. A Discontinuous Galerkin Method for Parabolic Problems with Modified hp-Finite Element Approximation Technique

    NASA Technical Reports Server (NTRS)

    Kaneko, Hideaki; Bey, Kim S.; Hou, Gene J. W.

    2004-01-01

    A recent paper is generalized to a case where the spatial region is taken in R(sup 3). The region is assumed to be a thin body, such as a panel on the wing or fuselage of an aerospace vehicle. The traditional h- as well as hp-finite element methods are applied to the surface defined in the x - y variables, while, through the thickness, the technique of the p-element is employed. Time and spatial discretization scheme based upon an assumption of certain weak singularity of double vertical line u(sub t) double vertical line 2, is used to derive an optimal a priori error estimate for the current method.

  20. Implicit filtered PN for high-energy density thermal radiation transport using discontinuous Galerkin finite elements

    NASA Astrophysics Data System (ADS)

    Laboure, Vincent M.; McClarren, Ryan G.; Hauck, Cory D.

    2016-09-01

    In this work, we provide a fully-implicit implementation of the time-dependent, filtered spherical harmonics (FPN) equations for non-linear, thermal radiative transfer. We investigate local filtering strategies and analyze the effect of the filter on the conditioning of the system, showing in particular that the filter improves the convergence properties of the iterative solver. We also investigate numerically the rigorous error estimates derived in the linear setting, to determine whether they hold also for the non-linear case. Finally, we simulate a standard test problem on an unstructured mesh and make comparisons with implicit Monte Carlo (IMC) calculations.

  1. Eighth Amendment & Death Penalty.

    ERIC Educational Resources Information Center

    Shortall, Joseph M.; Merrill, Denise W.

    1987-01-01

    Presents a lesson on capital punishment for juveniles based on three hypothetical cases. The goal of the lesson is to have students understand the complexities of decisions regarding the death penalty for juveniles. (JDH)

  2. Comparison of two Galerkin quadrature methods

    SciTech Connect

    Morel, J. E.; Warsa, J. S.; Franke, B. C.; Prinja, A. K.

    2013-07-01

    We compare two methods for generating Galerkin quadrature for problems with highly forward-peaked scattering. In Method 1, the standard Sn method is used to generate the moment-to-discrete matrix and the discrete-to-moment is generated by inverting the moment-to-discrete matrix. In Method 2, which we introduce here, the standard Sn method is used to generate the discrete-to-moment matrix and the moment-to-discrete matrix is generated by inverting the discrete-to-moment matrix. Method 1 has the advantage that it preserves both N eigenvalues and N eigenvectors (in a pointwise sense) of the scattering operator with an N-point quadrature. Method 2 has the advantage that it generates consistent angular moment equations from the corresponding S{sub N} equations while preserving N eigenvalues of the scattering operator with an N-point quadrature. Our computational results indicate that these two methods are quite comparable for the test problem considered. (authors)

  3. Comparison of continuous and discontinuous discretizations for the Stokes flow

    NASA Astrophysics Data System (ADS)

    Lehmann, Ragnar; Kaus, Boris J. P.; Lukáčová-Medvid'ová, Maria

    2013-04-01

    Finite element methods (FEM) of various types are widely used to solve incompressible flow problems in general and Stokes flow in particular. We present first results of a study comparing two numerical methods: the continuous Galerkin and the discontinuous Galerkin (DG) method. For this purpose a Matlab code was developed employing 2D Stokes flow in a model setup with known analytical solution. [2] Nonlinearities of, e.g., the viscosity can lead to discontinuities in the velocity-pressure solution. Hence, using continuous approximations may result in avoidable inaccuracies. In contrast to the FEM, the DG method allows for discontinuities of velocity and pressure across interior mesh edges. This increases the number of degrees of freedom by a constant factor depending on the chosen element. A parameter is introduced to penalize the jumps in the velocity. The DG method provides the capability to locally adapt the polynomial degree of the shape functions. Moreover, it only needs communication between directly adjacent mesh cells, which makes it highly flexible and easy to parallelize. The velocity and pressure errors of the methods are measured in the L1-norm [1]. Orders of convergence are determined and compared. [1] Duretz, T., May, D.A., Garya, T.V. and Tackley, P.J., 2011. Discretization errors and free surface stabilization in the finite difference and marker-in-cell method for applied geodynamics: A numerical Study, Geochem. Geophys. Geosyst., 12, Q07004, doi:10.1029/2011GC003567. [2] Zhong, S., 1996. Analytic solution for Stokes' flow with lateral variations in viscosity, Geophys. J. Int., 124, 18-128, doi:10.1111/j.1365-246X.1996.tb06349.x.

  4. Penalty Inflation Adjustments for Civil Money Penalties. Interim Final Rule.

    PubMed

    2016-06-27

    In accordance with the Federal Civil Penalties Inflation Adjustment Act of 1990, as amended by the Debt Collection Improvement Act of 1996, and further amended by the Bipartisan Budget Act of 2015, section 701: Federal Civil Penalties Inflation Adjustment Act Improvements Act of 2015, this interim final rule incorporates the penalty inflation adjustments for the civil money penalties contained in the Social Security Act PMID:27373014

  5. 77 FR 55175 - Civil Penalties

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-09-07

    ... $6,000. 71 FR 28279. At the same time, the agency adjusted the maximum civil penalty for a single... to $16,650,000. 75 FR 5246. Also on February 10, 2010, NHTSA last adjusted the maximum civil penalty... policy when determining the appropriate civil penalty amount. See 62 FR 37115 (July 10, 1997)...

  6. 75 FR 5244 - Civil Penalties

    Federal Register 2010, 2011, 2012, 2013, 2014

    2010-02-02

    ...) entitled ``Civil Penalties'' which proposed the adjustment of certain civil penalties for inflation. 74 FR.... See 62 FR 37115 (July 10, 1997) (NHTSA's civil penalty policy under the Small Business Regulatory... April 11, 2000 (65 FR 19477, 19477-78). FOR FURTHER INFORMATION CONTACT: Jessica Lang, Office of...

  7. Low Order Empirical Galerkin Models for Feedback Flow Control

    NASA Astrophysics Data System (ADS)

    Tadmor, Gilead; Noack, Bernd

    2005-11-01

    Model-based feedback control restrictions on model order and complexity stem from several generic considerations: real time computation, the ability to either measure or reliably estimate the state in real time and avoiding sensitivity to noise, uncertainty and numerical ill-conditioning are high on that list. Empirical POD Galerkin models are attractive in the sense that they are simple and (optimally) efficient, but are notoriously fragile, and commonly fail to capture transients and control effects. In this talk we review recent efforts to enhance empirical Galerkin models and make them suitable for feedback design. Enablers include `subgrid' estimation of turbulence and pressure representations, tunable models using modes from multiple operating points, and actuation models. An invariant manifold defines the model's dynamic envelope. It must be respected and can be exploited in observer and control design. These ideas are benchmarked in the cylinder wake system and validated by a systematic DNS investigation of a 3-dimensional Galerkin model of the controlled wake.

  8. Modern Regression Discontinuity Analysis

    ERIC Educational Resources Information Center

    Bloom, Howard S.

    2012-01-01

    This article provides a detailed discussion of the theory and practice of modern regression discontinuity (RD) analysis for estimating the effects of interventions or treatments. Part 1 briefly chronicles the history of RD analysis and summarizes its past applications. Part 2 explains how in theory an RD analysis can identify an average effect of…

  9. A weak Galerkin generalized multiscale finite element method

    DOE PAGESBeta

    Mu, Lin; Wang, Junping; Ye, Xiu

    2016-03-31

    In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin finite element method. Convergence analysis and numerical experiments are obtained for the special case.

  10. Death Penalty in America.

    ERIC Educational Resources Information Center

    Clifford, Amie L.

    1997-01-01

    Examines the legal and moral issues, controversies, and unique trial procedures involved with the death penalty. Discusses the 1972 landmark Supreme Court decision that resulted in many states abolishing this punishment, only to reintroduce it later with different provisions. Reviews the controversial case of Sam Sheppard. (MJP)

  11. The Death Penalty.

    ERIC Educational Resources Information Center

    Crockett, Mark

    1990-01-01

    Provides a lesson plan on the Eighth Amendment to the U.S. Constitution and the imposition of the death penalty. Focuses on the controversy concerning capital punishment and stimulates critical thinking in an analysis and discussion of eight hypothetical situations. Includes suggestions for readings, videotapes, and writing assignments. (NL)

  12. Penalty-finite element analysis of time-dependent two-dimensional free surface film flows

    NASA Astrophysics Data System (ADS)

    Kheshgi, H. S.; Scriven, L. E.

    The Navier-Stokes system with shear-free balanced normal stress and with kinematic boundary conditions at the free surface, which governs the flow of incompressible Newtonian liquid films, is presently solved by the penalty/Galerkin/FEM technique, employing both a tesselation that deforms with the free surface and an implicit time domain method. Results are given for the case of transient flow out of a coating slot, and a more brief presentation of results is made for the cases of the capillary leveling of a disturbed film, the damping of standing waves, and evolving disturbances in a film flowing down an inclined plane.

  13. Aircraft Engine Noise Scattering - A Discontinuous Spectral Element Approach

    NASA Technical Reports Server (NTRS)

    Stanescu, D.; Hussaini, M. Y.; Farassat, F.

    2002-01-01

    The paper presents a time-domain method for computation of sound radiation from aircraft engine sources to the far-field. The effects of nonuniform flow around the aircraft and scattering of sound by fuselage and wings are accounted for in the formulation. Our approach is based on the discretization of the inviscid flow equations through a collocation form of the Discontinuous Galerkin spectral element method. An isoparametric representation of the underlying geometry is used in order to take full advantage of the spectral accuracy of the method. Largescale computations are made possible by a parallel implementation based on message passing. Results obtained for radiation from an axisymmetric nacelle alone are compared with those obtained when the same nacelle is installed in a generic con.guration, with and without a wing.

  14. Non-Galerkin Coarse Grids for Algebraic Multigrid

    SciTech Connect

    Falgout, Robert D.; Schroder, Jacob B.

    2014-06-26

    Algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. And while AMG has been effectively implemented on large scale parallel machines, challenges remain, especially when moving to exascale. Particularly, stencil sizes (the number of nonzeros in a row) tend to increase further down in the coarse grid hierarchy, and this growth leads to more communication. Therefore, as problem size increases and the number of levels in the hierarchy grows, the overall efficiency of the parallel AMG method decreases, sometimes dramatically. This growth in stencil size is due to the standard Galerkin coarse grid operator, $P^T A P$, where $P$ is the prolongation (i.e., interpolation) operator. For example, the coarse grid stencil size for a simple three-dimensional (3D) seven-point finite differencing approximation to diffusion can increase into the thousands on present day machines, causing an associated increase in communication costs. We therefore consider algebraically truncating coarse grid stencils to obtain a non-Galerkin coarse grid. First, the sparsity pattern of the non-Galerkin coarse grid is determined by employing a heuristic minimal “safe” pattern together with strength-of-connection ideas. Second, the nonzero entries are determined by collapsing the stencils in the Galerkin operator using traditional AMG techniques. The result is a reduction in coarse grid stencil size, overall operator complexity, and parallel AMG solve phase times.

  15. Hybrid perturbation/Bubnov-Galerkin technique for nonlinear thermal analysis

    NASA Technical Reports Server (NTRS)

    Noor, A. K.; Balch, C. D.

    1983-01-01

    A two step hybrid analysis technique to predict the nonlinear steady state temperature distribution in structures and solids is presented. The technique is based on the regular perturbation expansion and the classical Bubnov-Galerkin approximation. The functions are obtained by using the regular perturbation method. These functions are selected as coordinate functions and the classical Bubnov-Galerkin technique is used to compute their amplitudes. The potential of the proposed hybrid technique for the solution of nonlinear thermal problems is discussed. The effectiveness of this technique is demonstrated by the effects of conduction, convection, and radiation modes of heat transfer. It is indicated that the hybrid technique overcomes the two major drawbacks of the classical techniques: (1) the requirement of using a small parameter in the regular perturbation method; and (2) the arbitrariness in the choice of the coordinate functions in the Bubnov-Galerkin technique. The proposed technique extends the range of applicability of the regular perturbation method and enhances the effectiveness of the Bubnov-Galerkin technique.

  16. 29 CFR 2570.86 - Reduction of penalty by other penalty assessments.

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... Civil Penalties Under ERISA Section 502(l) § 2570.86 Reduction of penalty by other penalty assessments... ERISA section 502(i) and section 4975 of the Code. Prior to a reduction of penalty under this...

  17. 29 CFR 2570.86 - Reduction of penalty by other penalty assessments.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... Civil Penalties Under ERISA Section 502(l) § 2570.86 Reduction of penalty by other penalty assessments... ERISA section 502(i) and section 4975 of the Code. Prior to a reduction of penalty under this...

  18. 29 CFR 2570.86 - Reduction of penalty by other penalty assessments.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... Civil Penalties Under ERISA Section 502(l) § 2570.86 Reduction of penalty by other penalty assessments... ERISA section 502(i) and section 4975 of the Code. Prior to a reduction of penalty under this...

  19. 29 CFR 2570.86 - Reduction of penalty by other penalty assessments.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... Civil Penalties Under ERISA Section 502(l) § 2570.86 Reduction of penalty by other penalty assessments... ERISA section 502(i) and section 4975 of the Code. Prior to a reduction of penalty under this...

  20. 29 CFR 2570.86 - Reduction of penalty by other penalty assessments.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... Civil Penalties Under ERISA Section 502(l) § 2570.86 Reduction of penalty by other penalty assessments... ERISA section 502(i) and section 4975 of the Code. Prior to a reduction of penalty under this...

  1. 31 CFR 501.709 - Penalty notice.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... reporting on any delinquent penalty amount in the event of a failure to pay the penalty imposed. ... FOREIGN ASSETS CONTROL, DEPARTMENT OF THE TREASURY REPORTING, PROCEDURES AND PENALTIES REGULATIONS Trading With the Enemy Act (TWEA) Penalties § 501.709 Penalty notice. (a) If, after considering any...

  2. Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Liu, Yen; Vinokur, Marcel

    2004-01-01

    A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of

  3. Discontinuous isogeometric analysis methods for the first-order form of the neutron transport equation with discrete ordinate (SN) angular discretisation

    NASA Astrophysics Data System (ADS)

    Owens, A. R.; Welch, J. A.; Kópházi, J.; Eaton, M. D.

    2016-06-01

    In this paper two discontinuous Galerkin isogeometric analysis methods are developed and applied to the first-order form of the neutron transport equation with a discrete ordinate (SN) angular discretisation. The discontinuous Galerkin projection approach was taken on both an element level and the patch level for a given Non-Uniform Rational B-Spline (NURBS) patch. This paper describes the detailed dispersion analysis that has been used to analyse the numerical stability of both of these schemes. The convergence of the schemes for both smooth and non-smooth solutions was also investigated using the method of manufactured solutions (MMS) for multidimensional problems and a 1D semi-analytical benchmark whose solution contains a strongly discontinuous first derivative. This paper also investigates the challenges posed by strongly curved boundaries at both the NURBS element and patch level with several algorithms developed to deal with such cases. Finally numerical results are presented both for a simple pincell test problem as well as the C5G7 quarter core MOX/UOX small Light Water Reactor (LWR) benchmark problem. These numerical results produced by the isogeometric analysis (IGA) methods are compared and contrasted against linear and quadratic discontinuous Galerkin finite element (DGFEM) SN based methods.

  4. Mingus Discontinuous Multiphysics

    2014-05-13

    Mingus provides hybrid coupled local/non-local mechanics analysis capabilities that extend several traditional methods to applications with inherent discontinuities. Its primary features include adaptations of solid mechanics, fluid dynamics and digital image correlation that naturally accommodate dijointed data or irregular solution fields by assimilating a variety of discretizations (such as control volume finite elements, peridynamics and meshless control point clouds). The goal of this software is to provide an analysis framework form multiphysics engineering problems withmore » an integrated image correlation capability that can be used for experimental validation and model« less

  5. Discontinuous ephemeral streams

    NASA Astrophysics Data System (ADS)

    Bull, William B.

    1997-07-01

    Many ephemeral streams in western North America flowed over smooth valley floors before transformation from shallow discontinuous channels into deep arroyos. These inherently unstable streams of semiarid regions are sensitive to short-term climatic changes, and to human impacts, because hillslopes supply abundant sediment to infrequent large streamflow events. Discontinuous ephemeral streams appear to be constantly changing as they alternate between two primary modes of operation; either aggradation or degradation may become dominant. Attainment of equilibrium conditions is brief. Disequilibrium is promoted by channel entrenchment that causes the fall of local base level, and by deposition of channel fans that causes the rise of local base level. These opposing base-level processes in adjacent reaches are maintained by self-enhancing feedback mechanisms. The threshold between erosion and deposition is crossed when aggradational or degradational reaches shift upstream or downstream. Extension of entrenched reaches into channel fans tends to create continuous arroyos. Upvalley migration of fan apexes tends to create depositional valley floors with few stream channels. Less than 100 years is required for arroyo cutting, but more than 500 years is required for complete aggradation of entrenched stream channels and valley floors. Discontinuous ephemeral streams have a repetitive sequence of streamflow characteristics that is as distinctive as sequences of meander bends or braided gravel bars in perennial rivers. The sequence changes from degradation to aggradation — headcuts concentrate sheetflow, a single trunk channel conveys flow to the apex of a channel fan, braided distributary channels end in an area of diverging sheetflow, and converging sheetflow drains to headcuts. The sequence is repeated at intervals ranging from 15 m for small streams to more than 10 km for large streams. Lithologic controls on the response of discontinuous ephemeral streams include: (1

  6. Mingus Discontinuous Multiphysics

    SciTech Connect

    Pat Notz, Dan Turner

    2014-05-13

    Mingus provides hybrid coupled local/non-local mechanics analysis capabilities that extend several traditional methods to applications with inherent discontinuities. Its primary features include adaptations of solid mechanics, fluid dynamics and digital image correlation that naturally accommodate dijointed data or irregular solution fields by assimilating a variety of discretizations (such as control volume finite elements, peridynamics and meshless control point clouds). The goal of this software is to provide an analysis framework form multiphysics engineering problems with an integrated image correlation capability that can be used for experimental validation and model

  7. Reflection-free atomistic-continuum coupling for solid mechanics employing spacetime discontinuous finite element method

    NASA Astrophysics Data System (ADS)

    Kraczek, B.

    2005-03-01

    We present a means for coupling dynamic atomistic and continuum simulations via a spacetime discontinuous Galerkin (SDG) finite element method. Our scheme allows the SDG method to couple a general MD simulation using Verlet time-stepping through the flux conditions on the element boundaries at the interface. These flux conditions ensure weak balance of momentum and energy to achieve reflection-free transfer of disturbance across the interface. Our work is supported by the National Science Foundation (ITR grant DMR-0121695) on Process Simulation and Design and, in part, by the Materials Computation Center (FRG grant DMR-99-76550)

  8. 31 CFR 542.703 - Penalty imposition.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... FOREIGN ASSETS CONTROL, DEPARTMENT OF THE TREASURY SYRIAN SANCTIONS REGULATIONS Penalties § 542.703... violator named in the Pre-Penalty Notice and that a civil monetary penalty is appropriate, the Office...

  9. 31 CFR 539.701 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... Penalties § 539.701 Penalties. (a) Attention is directed to section 206 of the International Emergency... criminal penalties provided in the Act are subject to adjustment pursuant to 18 U.S.C. 3571. (c)...

  10. 31 CFR 540.701 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... REGULATIONS Penalties § 540.701 Penalties. (a) Attention is directed to section 206 of the International... criminal penalties provided in the Act are subject to adjustment pursuant to 18 U.S.C. 3571. (c)...

  11. 31 CFR 539.701 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... Penalties § 539.701 Penalties. (a) Attention is directed to section 206 of the International Emergency... criminal penalties provided in the Act are subject to adjustment pursuant to 18 U.S.C. 3571. (c)...

  12. 31 CFR 540.701 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... REGULATIONS Penalties § 540.701 Penalties. (a) Attention is directed to section 206 of the International... criminal penalties provided in the Act are subject to adjustment pursuant to 18 U.S.C. 3571. (c)...

  13. Kinematics of Strong Discontinuities

    NASA Technical Reports Server (NTRS)

    Peterson, K.; Nguyen, G.; Sulsky, D.

    2006-01-01

    Synthetic Aperture Radar (SAR) provides a detailed view of the Arctic ice cover. When processed with the RADARSAT Geophysical Processor System (RGPS), it provides estimates of sea ice motion and deformation over large regions of the Arctic for extended periods of time. The deformation is dominated by the appearance of linear kinematic features that have been associated with the presence of leads. The RGPS deformation products are based on the assumption that the displacement and velocity are smooth functions of the spatial coordinates. However, if the dominant deformation of multiyear ice results from the opening, closing and shearing of leads, then the displacement and velocity can be discontinuous. This presentation discusses the kinematics associated with strong discontinuities that describe possible jumps in displacement or velocity. Ice motion from SAR data are analyzed using this framework. It is assumed that RGPS cells deform due to the presence of a lead. The lead orientation is calculated to optimally account for the observed deformation. It is shown that almost all observed deformation can be represented by lead opening and shearing. The procedure used to reprocess motion data to account for leads will be described and applied to regions of the Beaufort Sea. The procedure not only provides a new view of ice deformation, it can be used to obtain information about the presence of leads for initialization and/or validation of numerical simulations.

  14. A new weak Galerkin finite element method for elliptic interface problems

    DOE PAGESBeta

    Mu, Lin; Wang, Junping; Ye, Xiu; Zhao, Shan

    2016-08-26

    We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

  15. A new weak Galerkin finite element method for elliptic interface problems

    NASA Astrophysics Data System (ADS)

    Mu, Lin; Wang, Junping; Ye, Xiu; Zhao, Shan

    2016-11-01

    A new weak Galerkin (WG) finite element method is introduced and analyzed in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. Extensive numerical experiments have been conducted to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.

  16. A stochastic Galerkin method for the Euler equations with Roe variable transformation

    SciTech Connect

    Pettersson, Per; Iaccarino, Gianluca; Nordström, Jan

    2014-01-15

    The Euler equations subject to uncertainty in the initial and boundary conditions are investigated via the stochastic Galerkin approach. We present a new fully intrusive method based on a variable transformation of the continuous equations. Roe variables are employed to get quadratic dependence in the flux function and a well-defined Roe average matrix that can be determined without matrix inversion. In previous formulations based on generalized polynomial chaos expansion of the physical variables, the need to introduce stochastic expansions of inverse quantities, or square roots of stochastic quantities of interest, adds to the number of possible different ways to approximate the original stochastic problem. We present a method where the square roots occur in the choice of variables, resulting in an unambiguous problem formulation. The Roe formulation saves computational cost compared to the formulation based on expansion of conservative variables. Moreover, the Roe formulation is more robust and can handle cases of supersonic flow, for which the conservative variable formulation fails to produce a bounded solution. For certain stochastic basis functions, the proposed method can be made more effective and well-conditioned. This leads to increased robustness for both choices of variables. We use a multi-wavelet basis that can be chosen to include a large number of resolution levels to handle more extreme cases (e.g. strong discontinuities) in a robust way. For smooth cases, the order of the polynomial representation can be increased for increased accuracy.

  17. Efficient stochastic Galerkin methods for random diffusion equations

    SciTech Connect

    Xiu Dongbin Shen Jie

    2009-02-01

    We discuss in this paper efficient solvers for stochastic diffusion equations in random media. We employ generalized polynomial chaos (gPC) expansion to express the solution in a convergent series and obtain a set of deterministic equations for the expansion coefficients by Galerkin projection. Although the resulting system of diffusion equations are coupled, we show that one can construct fast numerical methods to solve them in a decoupled fashion. The methods are based on separation of the diagonal terms and off-diagonal terms in the matrix of the Galerkin system. We examine properties of this matrix and show that the proposed method is unconditionally stable for unsteady problems and convergent for steady problems with a convergent rate independent of discretization parameters. Numerical examples are provided, for both steady and unsteady random diffusions, to support the analysis.

  18. 75 FR 79978 - Civil Penalties

    Federal Register 2010, 2011, 2012, 2013, 2014

    2010-12-21

    ... Statement in the Federal Register published on April 11, 2000 (65 FR 19477, 19477-78). FOR FURTHER... penalties under the Adjustment Act was published on February 4, 1997. 62 FR 5167. At that time, we codified.... Since that time, we have adjusted available penalties on a number of occasions. See 75 FR 49879,...

  19. 75 FR 49879 - Civil Penalties

    Federal Register 2010, 2011, 2012, 2013, 2014

    2010-08-16

    ... complete Privacy Act Statement in the Federal Register published on April 11, 2000 (65 FR 19477-78). Docket... Act was published on February 4, 1997. 62 FR ] 5167. At that time, we codified the penalties under... further adjusted certain penalties. 64 FR 37876. In 2000, the Transportation Recall...

  20. Compressible flow calculations employing the Galerkin/least-squares method

    NASA Technical Reports Server (NTRS)

    Shakib, F.; Hughes, T. J. R.; Johan, Zdenek

    1989-01-01

    A multielement group, domain decomposition algorithm is presented for solving linear nonsymmetric systems arising in the finite-element analysis of compressible flows employing the Galerkin/least-squares method. The iterative strategy employed is based on the generalized minimum residual (GMRES) procedure originally proposed by Saad and Shultz. Two levels of preconditioning are investigated. Applications to problems of high-speed compressible flow illustrate the effectiveness of the scheme.

  1. Galerkin/Runge-Kutta discretizations for semilinear parabolic equations

    NASA Technical Reports Server (NTRS)

    Keeling, Stephen L.

    1987-01-01

    A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for semilinear parabolic initial boundary value problems. Unlike any classical counterpart, this class offers arbitrarily high, optimal order convergence. In support of this claim, error estimates are proved, and computational results are presented. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

  2. Robustness of controllers designed using Galerkin type approximations

    NASA Technical Reports Server (NTRS)

    Morris, K. A.

    1990-01-01

    One of the difficulties in designing controllers for infinite-dimensional systems arises from attempting to calculate a state for the system. It is shown that Galerkin type approximations can be used to design controllers which will perform as designed when implemented on the original infinite-dimensional system. No assumptions, other than those typically employed in numerical analysis, are made on the approximating scheme.

  3. A hybrid perturbation-Galerkin technique for partial differential equations

    NASA Technical Reports Server (NTRS)

    Geer, James F.; Anderson, Carl M.

    1990-01-01

    A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.

  4. A hybrid-perturbation-Galerkin technique which combines multiple expansions

    NASA Technical Reports Server (NTRS)

    Geer, James F.; Andersen, Carl M.

    1989-01-01

    A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

  5. Revisiting and Extending Interface Penalties for Multi-Domain Summation-by-Parts Operators

    NASA Technical Reports Server (NTRS)

    Carpenter, Mark H.; Nordstrom, Jan; Gottlieb, David

    2007-01-01

    General interface coupling conditions are presented for multi-domain collocation methods, which satisfy the summation-by-parts (SBP) spatial discretization convention. The combined interior/interface operators are proven to be L2 stable, pointwise stable, and conservative, while maintaining the underlying accuracy of the interior SBP operator. The new interface conditions resemble (and were motivated by) those used in the discontinuous Galerkin finite element community, and maintain many of the same properties. Extensive validation studies are presented using two classes of high-order SBP operators: 1) central finite difference, and 2) Legendre spectral collocation.

  6. A Runge-Kutta discontinuous finite element method for high speed flows

    NASA Technical Reports Server (NTRS)

    Bey, Kim S.; Oden, J. T.

    1991-01-01

    A Runge-Kutta discontinuous finite element method is developed for hyperbolic systems of conservation laws in two space variables. The discontinuous Galerkin spatial approximation to the conservation laws results in a system of ordinary differential equations which are marched in time using Runge-Kutta methods. Numerical results for the two-dimensional Burger's equation show that the method is (p+1)-order accurate in time and space, where p is the degree of the polynomial approximation of the solution within an element and is capable of capturing shocks over a single element without oscillations. Results for this problem also show that the accuracy of the solution in smooth regions is unaffected by the local projection and that the accuracy in smooth regions increases as p increases. Numerical results for the Euler equations show that the method captures shocks without oscillations and with higher resolution than a first-order scheme.

  7. Discontinuous approximation of viscous two-phase flow in heterogeneous porous media

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

    Runge-Kutta Discontinuous Galerkin (RKDG) and Discontinuous Finite Volume Element (DFVE) methods are applied to a coupled flow-transport problem describing the immiscible displacement of a viscous incompressible fluid in a non-homogeneous porous medium. The model problem consists of nonlinear pressure-velocity equations (assuming Brinkman flow) coupled to a nonlinear hyperbolic equation governing the mass balance (saturation equation). The mass conservation properties inherent to finite volume-based methods motivate a DFVE scheme for the approximation of the Brinkman flow in combination with a RKDG method for the spatio-temporal discretization of the saturation equation. The stability of the uncoupled schemes for the flow and for the saturation equations is analyzed, and several numerical experiments illustrate the robustness of the numerical method.

  8. 42 CFR 488.436 - Civil money penalties: Waiver of hearing, reduction of penalty amount.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 42 Public Health 5 2010-10-01 2010-10-01 false Civil money penalties: Waiver of hearing, reduction... Civil money penalties: Waiver of hearing, reduction of penalty amount. (a) Waiver of a hearing. The... the civil money penalty. (b) Reduction of penalty amount. (1) If the facility waives its right to...

  9. 42 CFR 488.440 - Civil money penalties: Effective date and duration of penalty.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 42 Public Health 5 2010-10-01 2010-10-01 false Civil money penalties: Effective date and duration... Civil money penalties: Effective date and duration of penalty. (a)(1) The per day civil money penalty... by CMS or the State. (2) A civil money penalty for each instance of noncompliance is imposed in...

  10. 42 CFR 488.430 - Civil money penalties: Basis for imposing penalty.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 42 Public Health 5 2014-10-01 2014-10-01 false Civil money penalties: Basis for imposing penalty... PROCEDURES Enforcement of Compliance for Long-Term Care Facilities with Deficiencies § 488.430 Civil money penalties: Basis for imposing penalty. (a) CMS or the State may impose a civil money penalty for either...

  11. 42 CFR 488.430 - Civil money penalties: Basis for imposing penalty.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 42 Public Health 5 2010-10-01 2010-10-01 false Civil money penalties: Basis for imposing penalty... PROCEDURES Enforcement of Compliance for Long-Term Care Facilities with Deficiencies § 488.430 Civil money penalties: Basis for imposing penalty. (a) CMS or the State may impose a civil money penalty for either...

  12. 42 CFR 488.430 - Civil money penalties: Basis for imposing penalty.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 42 Public Health 5 2012-10-01 2012-10-01 false Civil money penalties: Basis for imposing penalty... PROCEDURES Enforcement of Compliance for Long-Term Care Facilities with Deficiencies § 488.430 Civil money penalties: Basis for imposing penalty. (a) CMS or the State may impose a civil money penalty for either...

  13. 42 CFR 488.430 - Civil money penalties: Basis for imposing penalty.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 42 Public Health 5 2013-10-01 2013-10-01 false Civil money penalties: Basis for imposing penalty... PROCEDURES Enforcement of Compliance for Long-Term Care Facilities with Deficiencies § 488.430 Civil money penalties: Basis for imposing penalty. (a) CMS or the State may impose a civil money penalty for either...

  14. 42 CFR 488.430 - Civil money penalties: Basis for imposing penalty.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 42 Public Health 5 2011-10-01 2011-10-01 false Civil money penalties: Basis for imposing penalty... PROCEDURES Enforcement of Compliance for Long-Term Care Facilities with Deficiencies § 488.430 Civil money penalties: Basis for imposing penalty. (a) CMS or the State may impose a civil money penalty for either...

  15. 31 CFR 542.701 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... ASSETS CONTROL, DEPARTMENT OF THE TREASURY SYRIAN SANCTIONS REGULATIONS Penalties § 542.701 Penalties. (a... Secretary of the Treasury pursuant to this part or otherwise under the Act. (1) A civil penalty not to... for a maximum civil penalty not to exceed the greater of $250,000 or an amount that is twice...

  16. 31 CFR 542.701 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... ASSETS CONTROL, DEPARTMENT OF THE TREASURY SYRIAN SANCTIONS REGULATIONS Penalties § 542.701 Penalties. (a... Secretary of the Treasury pursuant to this part or otherwise under the Act. (1) A civil penalty not to... for a maximum civil penalty not to exceed the greater of $250,000 or an amount that is twice...

  17. 29 CFR 4302.3 - Penalty amount.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 29 Labor 9 2010-07-01 2010-07-01 false Penalty amount. 4302.3 Section 4302.3 Labor Regulations... PENALTIES FOR FAILURE TO PROVIDE CERTAIN MULTIEMPLOYER PLAN NOTICES § 4302.3 Penalty amount. The maximum daily amount of the penalty under section 4302 of ERISA shall be $110....

  18. 29 CFR 4302.3 - Penalty amount.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... 29 Labor 9 2011-07-01 2011-07-01 false Penalty amount. 4302.3 Section 4302.3 Labor Regulations... PENALTIES FOR FAILURE TO PROVIDE CERTAIN MULTIEMPLOYER PLAN NOTICES § 4302.3 Penalty amount. The maximum daily amount of the penalty under section 4302 of ERISA shall be $110....

  19. 40 CFR 91.1106 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... subject to a civil penalty of not more than $32,500 per day of violation. (6) The maximum penalty values... penalties, published in 40 CFR part 19, reference the applicable U.S. Code citation on which the prohibited... civil penalty to be assessed under this paragraph, the court is to take into account the gravity of...

  20. 49 CFR 107.329 - Maximum penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... maximum civil penalty is $110,000 if the violation results in death, serious illness or severe injury to... 49 Transportation 2 2010-10-01 2010-10-01 false Maximum penalties. 107.329 Section 107.329... PROGRAM PROCEDURES Enforcement Compliance Orders and Civil Penalties § 107.329 Maximum penalties. (a)...

  1. 49 CFR 235.9 - Civil penalty.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 49 Transportation 4 2011-10-01 2011-10-01 false Civil penalty. 235.9 Section 235.9 Transportation... SIGNAL SYSTEM OR RELIEF FROM THE REQUIREMENTS OF PART 236 § 235.9 Civil penalty. Any person (an entity of... penalty of at least $650 and not more than $25,000 per violation, except that: Penalties may be...

  2. 49 CFR 107.329 - Maximum penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... maximum civil penalty is $110,000 if the violation results in death, serious illness or severe injury to... 49 Transportation 2 2011-10-01 2011-10-01 false Maximum penalties. 107.329 Section 107.329... PROGRAM PROCEDURES Enforcement Compliance Orders and Civil Penalties § 107.329 Maximum penalties. (a)...

  3. 49 CFR 107.329 - Maximum penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... maximum civil penalty is $110,000 if the violation results in death, serious illness or severe injury to... 49 Transportation 2 2012-10-01 2012-10-01 false Maximum penalties. 107.329 Section 107.329... PROGRAM PROCEDURES Enforcement Compliance Orders and Civil Penalties § 107.329 Maximum penalties. (a)...

  4. 49 CFR 235.9 - Civil penalty.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 49 Transportation 4 2013-10-01 2013-10-01 false Civil penalty. 235.9 Section 235.9 Transportation... SIGNAL SYSTEM OR RELIEF FROM THE REQUIREMENTS OF PART 236 § 235.9 Civil penalty. Any person (an entity of... penalty of at least $650 and not more than $25,000 per violation, except that: Penalties may be...

  5. 49 CFR 235.9 - Civil penalty.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 49 Transportation 4 2012-10-01 2012-10-01 false Civil penalty. 235.9 Section 235.9 Transportation... SIGNAL SYSTEM OR RELIEF FROM THE REQUIREMENTS OF PART 236 § 235.9 Civil penalty. Any person (an entity of... penalty of at least $650 and not more than $25,000 per violation, except that: Penalties may be...

  6. 49 CFR 235.9 - Civil penalty.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 49 Transportation 4 2014-10-01 2014-10-01 false Civil penalty. 235.9 Section 235.9 Transportation... SIGNAL SYSTEM OR RELIEF FROM THE REQUIREMENTS OF PART 236 § 235.9 Civil penalty. Any person (an entity of... penalty of at least $650 and not more than $25,000 per violation, except that: Penalties may be...

  7. 30 CFR 921.845 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Civil penalties. 921.845 Section 921.845... PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE MASSACHUSETTS § 921.845 Civil penalties. Part 845 of this chapter, Civil Penalties, shall apply when civil penalties are assessed...

  8. 30 CFR 942.845 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Civil penalties. 942.845 Section 942.845... PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE TENNESSEE § 942.845 Civil penalties. Part 845 of this chapter, Civil Penalties, shall apply to the assessment of civil penalties...

  9. 30 CFR 941.845 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Civil penalties. 941.845 Section 941.845... PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE SOUTH DAKOTA § 941.845 Civil penalties. Part 845 of this chapter, Civil Penalties, shall apply when civil penalties are assessed...

  10. 30 CFR 903.845 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Civil penalties. 903.845 Section 903.845... PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE ARIZONA § 903.845 Civil penalties. Part 845 of this chapter, Civil Penalties, applies to the assessment of civil penalties for...

  11. 33 CFR 401.102 - Civil penalty.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 33 Navigation and Navigable Waters 3 2010-07-01 2010-07-01 false Civil penalty. 401.102 Section... TRANSPORTATION SEAWAY REGULATIONS AND RULES Penalties-Violations of Seaway Regulations § 401.102 Civil penalty. (a) A person, as described in § 401.101(b), who violates a regulation is liable to a civil penalty...

  12. 30 CFR 933.845 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Civil penalties. 933.845 Section 933.845... PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE NORTH CAROLINA § 933.845 Civil penalties. Part 845 of this chaper, Civil Penalties, shall apply when civil penalties are assessed...

  13. 30 CFR 922.845 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Civil penalties. 922.845 Section 922.845... PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE MICHIGAN § 922.845 Civil penalties. Part 845 of this chapter, Civil Penalties, shall apply when civil penalties are assessed for...

  14. 30 CFR 905.845 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Civil penalties. 905.845 Section 905.845... PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE CALIFORNIA § 905.845 Civil penalties. Part 845 of this chapter, Civil Penalties, shall apply to the assessment of civil penalties...

  15. 14 CFR 406.9 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 14 Aeronautics and Space 4 2010-01-01 2010-01-01 false Civil penalties. 406.9 Section 406.9... § 406.9 Civil penalties. (a) Civil penalty liability. Under 49 U.S.C. 70115(c), a person found by the... civil penalty of not more than $100,000 for each violation, as adjusted for inflation. A...

  16. 30 CFR 939.845 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Civil penalties. 939.845 Section 939.845... PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE RHODE ISLAND § 939.845 Civil penalties. Part 845 of this chapter, Civil Penalties, shall apply when civil penalties are assessed...

  17. 30 CFR 912.845 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Civil penalties. 912.845 Section 912.845... PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE IDAHO § 912.845 Civil penalties. Part 845 of this chapter, Civil Penalties, shall apply when civil penalties are assessed for...

  18. 10 CFR 2.205 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 10 Energy 1 2010-01-01 2010-01-01 false Civil penalties. 2.205 Section 2.205 Energy NUCLEAR... for Imposing Civil Penalties § 2.205 Civil penalties. (a) Before instituting any proceeding to impose a civil penalty under section 234 of the Act, the Executive Director for Operations or the...

  19. 30 CFR 910.845 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Civil penalties. 910.845 Section 910.845... PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE GEORGIA § 910.845 Civil penalties. Part 845 of this chapter, Civil Penalties, shall apply when civil penalties are assessed for...

  20. 30 CFR 947.845 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Civil penalties. 947.845 Section 947.845... PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE WASHINGTON § 947.845 Civil penalties. Part 845 of this chapter, Civil Penalties, shall apply when civil penalties are assessed...

  1. 30 CFR 937.845 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Civil penalties. 937.845 Section 937.845... PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE OREGON § 937.845 Civil penalties. Part 845 of this chapter, Civil Penalties, shall apply when civil penalties are assessed for...

  2. 6 CFR 9.32 - Penalty procedures.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 6 Domestic Security 1 2010-01-01 2010-01-01 false Penalty procedures. 9.32 Section 9.32 Domestic Security DEPARTMENT OF HOMELAND SECURITY, OFFICE OF THE SECRETARY RESTRICTIONS UPON LOBBYING Penalties and Enforcement § 9.32 Penalty procedures. Agencies shall impose and collect civil penalties pursuant to...

  3. 7 CFR 1463.10 - Civil penalties and criminal penalties.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... repetitive nature; and the disruption the action has caused with respect to other parties subject to this subpart. Any such civil penalty will not exceed two percent of the value of the kind of tobacco...

  4. On the superconvergence of Galerkin methods for hyperbolic IBVP

    NASA Technical Reports Server (NTRS)

    Gottlieb, David; Gustafsson, Bertil; Olsson, Pelle; Strand, BO

    1993-01-01

    Finite element Galerkin methods for periodic first order hyperbolic equations exhibit superconvergence on uniform grids at the nodes, i.e., there is an error estimate 0(h(sup 2r)) instead of the expected approximation order 0(h(sup r)). It will be shown that no matter how the approximating subspace S(sup h) is chosen, the superconvergence property is lost if there are characteristics leaving the domain. The implications of this result when constructing compact implicit difference schemes is also discussed.

  5. Galerkin finite-element simulation of a geothermal reservoir

    USGS Publications Warehouse

    Mercer, J.W.; Pinder, G.F.

    1973-01-01

    The equations describing fluid flow and energy transport in a porous medium can be used to formulate a mathematical model capable of simulating the transient response of a hot-water geothermal reservoir. The resulting equations can be solved accurately and efficiently using a numerical scheme which combines the finite element approach with the Galerkin method of approximation. Application of this numerical model to the Wairakei geothermal field demonstrates that hot-water geothermal fields can be simulated using numerical techniques currently available and under development. ?? 1973.

  6. Spectral methods for discontinuous problems

    NASA Technical Reports Server (NTRS)

    Abarbanel, S.; Gottlieb, D.; Tadmor, E.

    1985-01-01

    Spectral methods yield high-order accuracy even when applied to problems with discontinuities, though not in the sense of pointwise accuracy. Two different procedures are presented which recover pointwise accurate approximations from the spectral calculations.

  7. Regression Discontinuity Designs in Epidemiology

    PubMed Central

    Moscoe, Ellen; Mutevedzi, Portia; Newell, Marie-Louise; Bärnighausen, Till

    2014-01-01

    When patients receive an intervention based on whether they score below or above some threshold value on a continuously measured random variable, the intervention will be randomly assigned for patients close to the threshold. The regression discontinuity design exploits this fact to estimate causal treatment effects. In spite of its recent proliferation in economics, the regression discontinuity design has not been widely adopted in epidemiology. We describe regression discontinuity, its implementation, and the assumptions required for causal inference. We show that regression discontinuity is generalizable to the survival and nonlinear models that are mainstays of epidemiologic analysis. We then present an application of regression discontinuity to the much-debated epidemiologic question of when to start HIV patients on antiretroviral therapy. Using data from a large South African cohort (2007–2011), we estimate the causal effect of early versus deferred treatment eligibility on mortality. Patients whose first CD4 count was just below the 200 cells/μL CD4 count threshold had a 35% lower hazard of death (hazard ratio = 0.65 [95% confidence interval = 0.45–0.94]) than patients presenting with CD4 counts just above the threshold. We close by discussing the strengths and limitations of regression discontinuity designs for epidemiology. PMID:25061922

  8. Resonant frequency calculations using a hybrid perturbation-Galerkin technique

    NASA Technical Reports Server (NTRS)

    Geer, James F.; Andersen, Carl M.

    1991-01-01

    A two-step hybrid perturbation Galerkin technique is applied to the problem of determining the resonant frequencies of one or several degrees of freedom nonlinear systems involving a parameter. In one step, the Lindstedt-Poincare method is used to determine perturbation solutions which are formally valid about one or more special values of the parameter (e.g., for large or small values of the parameter). In step two, a subset of the perturbation coordinate functions determined in step one is used in Galerkin type approximation. The technique is illustrated for several one degree of freedom systems, including the Duffing and van der Pol oscillators, as well as for the compound pendulum. For all of the examples considered, it is shown that the frequencies obtained by the hybrid technique using only a few terms from the perturbation solutions are significantly more accurate than the perturbation results on which they are based, and they compare very well with frequencies obtained by purely numerical methods.

  9. Investigating a hybrid perturbation-Galerkin technique using computer algebra

    NASA Technical Reports Server (NTRS)

    Andersen, Carl M.; Geer, James F.

    1988-01-01

    A two-step hybrid perturbation-Galerkin method is presented for the solution of a variety of differential equations type problems which involve a scalar parameter. The resulting (approximate) solution has the form of a sum where each term consists of the product of two functions. The first function is a function of the independent field variable(s) x, and the second is a function of the parameter lambda. In step one the functions of x are determined by forming a perturbation expansion in lambda. In step two the functions of lambda are determined through the use of the classical Bubnov-Gelerkin method. The resulting hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Bubnov-Galerkin methods applied separately, while combining some of the good features of each. In particular, the results can be useful well beyond the radius of convergence associated with the perturbation expansion. The hybrid method is applied with the aid of computer algebra to a simple two-point boundary value problem where the radius of convergence is finite and to a quantum eigenvalue problem where the radius of convergence is zero. For both problems the hybrid method apparently converges for an infinite range of the parameter lambda. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

  10. Resonant frequency calculations using a hybrid perturbation-Galerkin technique

    NASA Technical Reports Server (NTRS)

    Geer, James F.; Andersen, Carl M.

    1991-01-01

    A two-step hybrid perturbation Galerkin technique is applied to the problem of determining the resonant frequencies of one or several degree of freedom nonlinear systems involving a parameter. In one step, the Lindstedt-Poincare method is used to determine perturbation solutions which are formally valid about one or more special values of the parameter (e.g., for large or small values of the parameter). In step two, a subset of the perturbation coordinate functions determined in step one is used in Galerkin type approximation. The technique is illustrated for several one degree of freedom systems, including the Duffing and van der Pol oscillators, as well as for the compound pendulum. For all of the examples considered, it is shown that the frequencies obtained by the hybrid technique using only a few terms from the perturbation solutions are significantly more accurate than the perturbation results on which they are based, and they compare very well with frequencies obtained by purely numerical methods.

  11. Jacobian Free-Newton Krylov Discontinuous Galerkin Method and Physics-Based Preconditioning for Nuclear Reactor Simulations

    SciTech Connect

    HyeongKae Park; R. Nourgaliev; Richard C. Martineau; Dana A. Knoll

    2008-09-01

    Multidimensional, higher-order (2nd and higher) numerical methods have come to the forefront in recent years due to significant advances of computer technology and numerical algorithms, and have shown great potential as viable design tools for realistic applications. To achieve this goal, implicit high-order accurate coupling of the multiphysics simulations is a critical component. One of the issues that arise from multiphysics simulation is the necessity to resolve multiple time scales. For example, the dynamical time scales of neutron kinetics, fluid dynamics and heat conduction significantly differ (typically >1010 magnitude), with the dominant (fastest) physical mode also changing during the course of transient [Pope and Mousseau, 2007]. This leads to the severe time step restriction for stability in traditional multiphysics (i.e. operator split, semi-implicit discretization) simulations. The lower order methods suffer from an undesirable numerical dissipation. Thus implicit, higher order accurate scheme is necessary to perform seamlessly-coupled multiphysics simulations that can be used to analyze the “what-if” regulatory accident scenarios, or to design and optimize engineering systems.

  12. Jacobian-free Newton Krylov discontinuous Galerkin method and physics-based preconditioning for nuclear reactor simulations

    SciTech Connect

    HyeongKae Park; Robert R. Nourgaliev; Richard C. Martineau; Dana A. Knoll

    2008-09-01

    We present high-order accurate spatiotemporal discretization of all-speed flow solvers using Jacobian-free Newton Krylov framework. One of the key developments in this work is the physics-based preconditioner for the all-speed flow, which makes use of traditional semi-implicit schemes. The physics-based preconditioner is developed in the primitive variable form, which allows a straightforward separation of physical phenomena. Numerical examples demonstrate that the developed preconditioner effectively reduces the number of the Krylov iterations, and the efficiency is independent of the Mach number and mesh sizes under a fixed CFL condition.

  13. THE PREGNANCY PENALTY.

    PubMed

    Goodwin, Michele

    2016-01-01

    Punishing pregnant women increasingly serves as a litmus test in political discourse, inviting more than a metaphor about state sanctioned violence targeted at women. In 2016, candidates for the United States presidency threatened to defund Planned Parenthood if elected and a leading candidate promised he would "punish" pregnant women who seek abortions. Other presidential candidates urged that even victims of rape and incest should be forced to carry their pregnancies to term, imposing yet another penalty or strike against sexually violated women and girls. Local legislatures and governors show equal contempt for and desire to penalize women in their states. In Utah, Gov. Gary Herbert took up the call to use a "very strong stick" in policing reproduction by signing into law the Criminal Homicide and Abortion Revisions Act, which applies only to pregnant women. The law seeks to punish pregnant women who "knowingly" commit acts that might result in miscarriages. In 2011, Texas Rep. Doug Miller authored and introduced a bill in his state legislature that would make it a felony to ingest any controlled substance during pregnancy. Wisconsin's legislature passed a law that forces pregnant women to receive vaginal probes as a pre-condition to receiving an abortion. To obtain an abortion without undergoing the vaginal probe is a punishable violation of law. Some women's groups compare vaginal ultrasound laws such as that in Wisconsin to state sanctioned rape with a rod. Other legislative efforts include establishing personhood in embryos and fetuses. Many of the laws seeking to punish pregnant women and regulate their pregnancies introduce criminal sanctions into gestational conduct, broadly criminalizing any behavior that could harm fetal health. All of these laws selectively target pregnant women. PMID:27263247

  14. Mixing of discontinuously deforming media

    NASA Astrophysics Data System (ADS)

    Smith, L. D.; Rudman, M.; Lester, D. R.; Metcalfe, G.

    2016-02-01

    Mixing of materials is fundamental to many natural phenomena and engineering applications. The presence of discontinuous deformations—such as shear banding or wall slip—creates new mechanisms for mixing and transport beyond those predicted by classical dynamical systems theory. Here, we show how a novel mixing mechanism combining stretching with cutting and shuffling yields exponential mixing rates, quantified by a positive Lyapunov exponent, an impossibility for systems with cutting and shuffling alone or bounded systems with stretching alone, and demonstrate it in a fluid flow. While dynamical systems theory provides a framework for understanding mixing in smoothly deforming media, a theory of discontinuous mixing is yet to be fully developed. New methods are needed to systematize, explain, and extrapolate measurements on systems with discontinuous deformations. Here, we investigate "webs" of Lagrangian discontinuities and show that they provide a template for the overall transport dynamics. Considering slip deformations as the asymptotic limit of increasingly localised smooth shear, we also demonstrate exactly how some of the new structures introduced by discontinuous deformations are analogous to structures in smoothly deforming systems.

  15. Mixing of discontinuously deforming media.

    PubMed

    Smith, L D; Rudman, M; Lester, D R; Metcalfe, G

    2016-02-01

    Mixing of materials is fundamental to many natural phenomena and engineering applications. The presence of discontinuous deformations-such as shear banding or wall slip-creates new mechanisms for mixing and transport beyond those predicted by classical dynamical systems theory. Here, we show how a novel mixing mechanism combining stretching with cutting and shuffling yields exponential mixing rates, quantified by a positive Lyapunov exponent, an impossibility for systems with cutting and shuffling alone or bounded systems with stretching alone, and demonstrate it in a fluid flow. While dynamical systems theory provides a framework for understanding mixing in smoothly deforming media, a theory of discontinuous mixing is yet to be fully developed. New methods are needed to systematize, explain, and extrapolate measurements on systems with discontinuous deformations. Here, we investigate "webs" of Lagrangian discontinuities and show that they provide a template for the overall transport dynamics. Considering slip deformations as the asymptotic limit of increasingly localised smooth shear, we also demonstrate exactly how some of the new structures introduced by discontinuous deformations are analogous to structures in smoothly deforming systems. PMID:26931594

  16. 40 CFR 19.4 - Penalty adjustment and table.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... MONETARY PENALTIES FOR INFLATION § 19.4 Penalty adjustment and table. The adjusted statutory penalty... Inflation Adjustments U.S. Code Citation Environmental statute Statutory penalties, as enacted Penalties... inflation adjustment to the calendar year 1992 penalty amount expressed in section 104B(d)(1)(A), which...

  17. 50 CFR 300.157 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    .... Nationals Fishing in Russian Fisheries § 300.157 Penalties. In addition to any fine, penalty, or forfeiture imposed by the Russian Federation, nationals and vessels of the United States violating the...

  18. 50 CFR 300.157 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    .... Nationals Fishing in Russian Fisheries § 300.157 Penalties. In addition to any fine, penalty, or forfeiture imposed by the Russian Federation, nationals and vessels of the United States violating the...

  19. 31 CFR 100.13 - Criminal penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... CURRENCY AND COIN Exchange of Coin § 100.13 Criminal penalties. Criminal penalties connected with the defacement or mutilation of U.S. coins are provided in the United States Code, Title 18, section 331....

  20. 31 CFR 100.13 - Criminal penalties.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ..., DEPARTMENT OF THE TREASURY EXCHANGE OF PAPER CURRENCY AND COIN Exchange of Coin § 100.13 Criminal penalties. Criminal penalties connected with the defacement or mutilation of U.S. coins are provided in the...

  1. 50 CFR 300.119 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... criminal penalty provisions and forfeiture provisions prescribed in the Act, 15 CFR part 904, and other... Antarctic Marine Living Resources § 300.119 Penalties. Any person or harvesting vessel found to be...

  2. 76 FR 71431 - Civil Penalty Calculation Methodology

    Federal Register 2010, 2011, 2012, 2013, 2014

    2011-11-17

    ... TRANSPORTATION Federal Motor Carrier Safety Administration Civil Penalty Calculation Methodology AGENCY: Federal... its civil penalty methodology. Part of this evaluation includes a forthcoming explanation of the Uniform Fine Assessment (UFA) algorithm, which FMCSA currently uses for calculation of civil...

  3. 27 CFR 70.509 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-04-01

    ..., and Beer Penalties § 70.509 Penalties. It is an offense punishable by fine and imprisonment for anyone... fraudulently execute any documents required by the provisions of the internal revenue laws, or any...

  4. 27 CFR 70.509 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-04-01

    ..., and Beer Penalties § 70.509 Penalties. It is an offense punishable by fine and imprisonment for anyone... fraudulently execute any documents required by the provisions of the internal revenue laws, or any...

  5. 27 CFR 70.509 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-04-01

    ..., and Beer Penalties § 70.509 Penalties. It is an offense punishable by fine and imprisonment for anyone... fraudulently execute any documents required by the provisions of the internal revenue laws, or any...

  6. 27 CFR 70.509 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    ..., and Beer Penalties § 70.509 Penalties. It is an offense punishable by fine and imprisonment for anyone... fraudulently execute any documents required by the provisions of the internal revenue laws, or any...

  7. 27 CFR 70.509 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-04-01

    ..., and Beer Penalties § 70.509 Penalties. It is an offense punishable by fine and imprisonment for anyone... fraudulently execute any documents required by the provisions of the internal revenue laws, or any...

  8. 42 CFR 488.438 - Civil money penalties: Amount of penalty.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 42 Public Health 5 2014-10-01 2014-10-01 false Civil money penalties: Amount of penalty. 488.438... Enforcement of Compliance for Long-Term Care Facilities with Deficiencies § 488.438 Civil money penalties...-participating SNF/NF, or NF-only facility subject to a civil money penalty imposed by CMS self-reports...

  9. 42 CFR 488.438 - Civil money penalties: Amount of penalty.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 42 Public Health 5 2010-10-01 2010-10-01 false Civil money penalties: Amount of penalty. 488.438... Enforcement of Compliance for Long-Term Care Facilities with Deficiencies § 488.438 Civil money penalties... review authority) finds that the basis for imposing a civil money penalty exists, as specified in §...

  10. 42 CFR 488.438 - Civil money penalties: Amount of penalty.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 42 Public Health 5 2011-10-01 2011-10-01 false Civil money penalties: Amount of penalty. 488.438... Enforcement of Compliance for Long-Term Care Facilities with Deficiencies § 488.438 Civil money penalties... review authority) finds that the basis for imposing a civil money penalty exists, as specified in §...

  11. 42 CFR 488.438 - Civil money penalties: Amount of penalty.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 42 Public Health 5 2012-10-01 2012-10-01 false Civil money penalties: Amount of penalty. 488.438... Enforcement of Compliance for Long-Term Care Facilities with Deficiencies § 488.438 Civil money penalties...-participating SNF/NF, or NF-only facility subject to a civil money penalty imposed by CMS self-reports...

  12. Splines and the Galerkin method for solving the integral equations of scattering theory

    NASA Astrophysics Data System (ADS)

    Brannigan, M.; Eyre, D.

    1983-06-01

    This paper investigates the Galerkin method with cubic B-spline approximants to solve singular integral equations that arise in scattering theory. We stress the relationship between the Galerkin and collocation methods.The error bound for cubic spline approximates has a convergence rate of O(h4), where h is the mesh spacing. We test the utility of the Galerkin method by solving both two- and three-body problems. We demonstrate, by solving the Amado-Lovelace equation for a system of three identical bosons, that our numerical treatment of the scattering problem is both efficient and accurate for small linear systems.

  13. Phase unwrapping using discontinuity optimization

    SciTech Connect

    Flynn, T.J.

    1998-03-01

    In SAR interferometry, the periodicity of the phase must be removed using two-dimensional phase unwrapping. The goal of the procedure is to find a smooth surface in which large spatial phase differences, called discontinuities, are restricted to places where their presence is reasonable. The pioneering work of Goldstein et al. identified points of local unwrap inconsistency called residues, which must be connected by discontinuities. This paper presents an overview of recent work that treats phase unwrapping as a discrete optimization problem with the constraint that residues must be connected. Several algorithms use heuristic methods to reduce the total number of discontinuities. Constantini has introduced the weighted sum of discontinuity magnitudes as a criterion of unwrap error and shown how algorithms from optimization theory are used to minimize it. Pixels of low quality are given low weight to guide discontinuities away from smooth, high-quality regions. This method is generally robust, but if noise is severe it underestimates the steepness of slopes and the heights of peaks. This problem is mitigated by subtracting (modulo 2{pi}) a smooth estimate of the unwrapped phase from the data, then unwrapping the resulting residual phase. The unwrapped residual is added to the smooth estimate to produce the final unwrapped phase. The estimate can be computed by lowpass filtering of an existing unwrapped phase; this makes possible an iterative algorithm in which the result of each iteration provides the estimate for the next. An example illustrates the results of optimal discontinuity placement and the improvement from unwrapping of the residual phase.

  14. 44 CFR 18.400 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 44 Emergency Management and Assistance 1 2010-10-01 2010-10-01 false Penalties. 18.400 Section 18.400 Emergency Management and Assistance FEDERAL EMERGENCY MANAGEMENT AGENCY, DEPARTMENT OF HOMELAND SECURITY GENERAL NEW RESTRICTIONS ON LOBBYING Penalties and Enforcement § 18.400 Penalties. (a) Any...

  15. 29 CFR 4071.3 - Penalty amount.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... 29 Labor 9 2011-07-01 2011-07-01 false Penalty amount. 4071.3 Section 4071.3 Labor Regulations... FAILURE TO PROVIDE CERTAIN NOTICES OR OTHER MATERIAL INFORMATION § 4071.3 Penalty amount. The maximum daily amount of the penalty under section 4071 of ERISA shall be $1,100....

  16. 29 CFR 4071.3 - Penalty amount.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 29 Labor 9 2010-07-01 2010-07-01 false Penalty amount. 4071.3 Section 4071.3 Labor Regulations... FAILURE TO PROVIDE CERTAIN NOTICES OR OTHER MATERIAL INFORMATION § 4071.3 Penalty amount. The maximum daily amount of the penalty under section 4071 of ERISA shall be $1,100....

  17. 45 CFR 3.61 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 45 Public Welfare 1 2012-10-01 2012-10-01 false Penalties. 3.61 Section 3.61 Public Welfare DEPARTMENT OF HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATION CONDUCT OF PERSONS AND TRAFFIC ON THE NATIONAL INSTITUTES OF HEALTH FEDERAL ENCLAVE Penalties § 3.61 Penalties. (a) A person found guilty of violating...

  18. 45 CFR 3.61 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 45 Public Welfare 1 2011-10-01 2011-10-01 false Penalties. 3.61 Section 3.61 Public Welfare DEPARTMENT OF HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATION CONDUCT OF PERSONS AND TRAFFIC ON THE NATIONAL INSTITUTES OF HEALTH FEDERAL ENCLAVE Penalties § 3.61 Penalties. (a) A person found guilty of violating...

  19. 45 CFR 3.61 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 45 Public Welfare 1 2014-10-01 2014-10-01 false Penalties. 3.61 Section 3.61 Public Welfare Department of Health and Human Services GENERAL ADMINISTRATION CONDUCT OF PERSONS AND TRAFFIC ON THE NATIONAL INSTITUTES OF HEALTH FEDERAL ENCLAVE Penalties § 3.61 Penalties. (a) A person found guilty of violating...

  20. 45 CFR 3.61 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 45 Public Welfare 1 2013-10-01 2013-10-01 false Penalties. 3.61 Section 3.61 Public Welfare DEPARTMENT OF HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATION CONDUCT OF PERSONS AND TRAFFIC ON THE NATIONAL INSTITUTES OF HEALTH FEDERAL ENCLAVE Penalties § 3.61 Penalties. (a) A person found guilty of violating...

  1. 46 CFR 16.115 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 46 Shipping 1 2010-10-01 2010-10-01 false Penalties. 16.115 Section 16.115 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY MERCHANT MARINE OFFICERS AND SEAMEN CHEMICAL TESTING General § 16.115 Penalties. Violation of this part is subject to the civil penalties set forth in 46 U.S.C. 2115. Any...

  2. 7 CFR 3018.405 - Penalty procedures.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 15 2013-01-01 2013-01-01 false Penalty procedures. 3018.405 Section 3018.405 Agriculture Regulations of the Department of Agriculture (Continued) OFFICE OF THE CHIEF FINANCIAL OFFICER, DEPARTMENT OF AGRICULTURE NEW RESTRICTIONS ON LOBBYING Penalties and Enforcement § 3018.405 Penalty procedures. Agencies shall impose and...

  3. 7 CFR 3018.405 - Penalty procedures.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 15 2012-01-01 2012-01-01 false Penalty procedures. 3018.405 Section 3018.405 Agriculture Regulations of the Department of Agriculture (Continued) OFFICE OF THE CHIEF FINANCIAL OFFICER, DEPARTMENT OF AGRICULTURE NEW RESTRICTIONS ON LOBBYING Penalties and Enforcement § 3018.405 Penalty procedures. Agencies shall impose and...

  4. 49 CFR 221.7 - Civil penalty.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... persons, or has caused death or injury, a penalty not to exceed $100,000 per violation may be assessed... 49 Transportation 4 2011-10-01 2011-10-01 false Civil penalty. 221.7 Section 221.7 Transportation... TRANSPORTATION REAR END MARKING DEVICE-PASSENGER, COMMUTER AND FREIGHT TRAINS General § 221.7 Civil penalty....

  5. 49 CFR 232.11 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $100,000 per... 49 Transportation 4 2010-10-01 2010-10-01 false Penalties. 232.11 Section 232.11 Transportation...-TRAIN DEVICES General § 232.11 Penalties. (a) Any person (including but not limited to a railroad;...

  6. 49 CFR 230.4 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ..., or has caused death or injury, a penalty not to exceed $100,000 per violation may be assessed. Each... 49 Transportation 4 2011-10-01 2011-10-01 false Penalties. 230.4 Section 230.4 Transportation... TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS General § 230.4 Penalties. (a) Any...

  7. 49 CFR 213.15 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 49 Transportation 4 2011-10-01 2011-10-01 false Penalties. 213.15 Section 213.15 Transportation... TRANSPORTATION TRACK SAFETY STANDARDS General § 213.15 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of at...

  8. 49 CFR 217.5 - Penalty.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 49 Transportation 4 2010-10-01 2010-10-01 false Penalty. 217.5 Section 217.5 Transportation Other... TRANSPORTATION RAILROAD OPERATING RULES General § 217.5 Penalty. Any person (an entity of any type covered under... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  9. 49 CFR 227.9 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 49 Transportation 4 2010-10-01 2010-10-01 false Penalties. 227.9 Section 227.9 Transportation... TRANSPORTATION OCCUPATIONAL NOISE EXPOSURE General § 227.9 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  10. 49 CFR 230.4 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ..., or has caused death or injury, a penalty not to exceed $100,000 per violation may be assessed. Each... 49 Transportation 4 2010-10-01 2010-10-01 false Penalties. 230.4 Section 230.4 Transportation... TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS General § 230.4 Penalties. (a) Any...

  11. 49 CFR 224.11 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 49 Transportation 4 2010-10-01 2010-10-01 false Penalties. 224.11 Section 224.11 Transportation... TRANSPORTATION REFLECTORIZATION OF RAIL FREIGHT ROLLING STOCK General § 224.11 Penalties. (a) Any person... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  12. 49 CFR 209.409 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ..., or has caused death or injury, a penalty not to exceed $100,000 per violation may be assessed. Each... 49 Transportation 4 2010-10-01 2010-10-01 false Penalties. 209.409 Section 209.409 Transportation... TRANSPORTATION RAILROAD SAFETY ENFORCEMENT PROCEDURES Reporting of Remedial Actions § 209.409 Penalties....

  13. 49 CFR 217.5 - Penalty.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 49 Transportation 4 2011-10-01 2011-10-01 false Penalty. 217.5 Section 217.5 Transportation Other... TRANSPORTATION RAILROAD OPERATING RULES General § 217.5 Penalty. Any person (an entity of any type covered under... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  14. 49 CFR 227.9 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 49 Transportation 4 2011-10-01 2011-10-01 false Penalties. 227.9 Section 227.9 Transportation... TRANSPORTATION OCCUPATIONAL NOISE EXPOSURE General § 227.9 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  15. 49 CFR 225.29 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... persons, or has caused death or injury, a penalty not to exceed $100,000 per violation may be assessed... 49 Transportation 4 2011-10-01 2011-10-01 false Penalties. 225.29 Section 225.29 Transportation... TRANSPORTATION RAILROAD ACCIDENTS/INCIDENTS: REPORTS CLASSIFICATION, AND INVESTIGATIONS § 225.29 Penalties....

  16. 49 CFR 237.7 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 49 Transportation 4 2010-10-01 2010-10-01 false Penalties. 237.7 Section 237.7 Transportation... TRANSPORTATION BRIDGE SAFETY STANDARDS General § 237.7 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of at...

  17. 49 CFR 238.11 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ..., or has caused death or injury, a penalty not to exceed $100,000 per violation may be assessed. Each... 49 Transportation 4 2011-10-01 2011-10-01 false Penalties. 238.11 Section 238.11 Transportation... TRANSPORTATION PASSENGER EQUIPMENT SAFETY STANDARDS General § 238.11 Penalties. (a) Any person, as defined...

  18. 49 CFR 233.11 - Civil penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ..., or has caused death or injury, a penalty not to exceed $100,000 per violation may be assessed. Each... 49 Transportation 4 2011-10-01 2011-10-01 false Civil penalties. 233.11 Section 233.11..., DEPARTMENT OF TRANSPORTATION SIGNAL SYSTEMS REPORTING REQUIREMENTS § 233.11 Civil penalties. Any person...

  19. 49 CFR 218.9 - Civil penalty.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 49 Transportation 4 2011-10-01 2011-10-01 false Civil penalty. 218.9 Section 218.9 Transportation... TRANSPORTATION RAILROAD OPERATING PRACTICES General § 218.9 Civil penalty. Any person (an entity of any type... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  20. 49 CFR 224.11 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 49 Transportation 4 2011-10-01 2011-10-01 false Penalties. 224.11 Section 224.11 Transportation... TRANSPORTATION REFLECTORIZATION OF RAIL FREIGHT ROLLING STOCK General § 224.11 Penalties. (a) Any person... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  1. 49 CFR 225.29 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... persons, or has caused death or injury, a penalty not to exceed $100,000 per violation may be assessed... 49 Transportation 4 2010-10-01 2010-10-01 false Penalties. 225.29 Section 225.29 Transportation... TRANSPORTATION RAILROAD ACCIDENTS/INCIDENTS: REPORTS CLASSIFICATION, AND INVESTIGATIONS § 225.29 Penalties....

  2. 49 CFR 238.11 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ..., or has caused death or injury, a penalty not to exceed $100,000 per violation may be assessed. Each... 49 Transportation 4 2010-10-01 2010-10-01 false Penalties. 238.11 Section 238.11 Transportation... TRANSPORTATION PASSENGER EQUIPMENT SAFETY STANDARDS General § 238.11 Penalties. (a) Any person, as defined...

  3. 49 CFR 244.5 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... imminent hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $100... 49 Transportation 4 2011-10-01 2011-10-01 false Penalties. 244.5 Section 244.5 Transportation... ACQUISITIONS OF CONTROL General § 244.5 Penalties. (a) Any person who violates any requirement of this part...

  4. 49 CFR 239.11 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 49 Transportation 4 2010-10-01 2010-10-01 false Penalties. 239.11 Section 239.11 Transportation... TRANSPORTATION PASSENGER TRAIN EMERGENCY PREPAREDNESS General § 239.11 Penalties. Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  5. 49 CFR 228.21 - Civil penalty.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... persons, or has caused death or injury, a penalty not to exceed $100,000 per violation may be assessed... 49 Transportation 4 2011-10-01 2011-10-01 false Civil penalty. 228.21 Section 228.21... penalty. Any person (an entity of any type covered under 1 U.S.C. 1, including but not limited to...

  6. 49 CFR 232.11 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $100,000 per... 49 Transportation 4 2011-10-01 2011-10-01 false Penalties. 232.11 Section 232.11 Transportation...-TRAIN DEVICES General § 232.11 Penalties. (a) Any person (including but not limited to a railroad;...

  7. 49 CFR 234.6 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 49 Transportation 4 2011-10-01 2011-10-01 false Penalties. 234.6 Section 234.6 Transportation... TRANSPORTATION GRADE CROSSING SIGNAL SYSTEM SAFETY AND STATE ACTION PLANS General § 234.6 Penalties. (a) Civil penalty. Any person (an entity of any type covered under 1 U.S.C. 1, including but not limited to...

  8. 49 CFR 237.7 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 49 Transportation 4 2011-10-01 2011-10-01 false Penalties. 237.7 Section 237.7 Transportation... TRANSPORTATION BRIDGE SAFETY STANDARDS General § 237.7 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of at...

  9. 49 CFR 244.5 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... imminent hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $100... 49 Transportation 4 2010-10-01 2010-10-01 false Penalties. 244.5 Section 244.5 Transportation... ACQUISITIONS OF CONTROL General § 244.5 Penalties. (a) Any person who violates any requirement of this part...

  10. 49 CFR 220.7 - Penalty.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ..., or has caused death or injury, a penalty not to exceed $100,000 per violation may be assessed; and... 49 Transportation 4 2011-10-01 2011-10-01 false Penalty. 220.7 Section 220.7 Transportation Other... TRANSPORTATION RAILROAD COMMUNICATIONS General § 220.7 Penalty. Any person (including but not limited to...

  11. 49 CFR 239.11 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 49 Transportation 4 2011-10-01 2011-10-01 false Penalties. 239.11 Section 239.11 Transportation... TRANSPORTATION PASSENGER TRAIN EMERGENCY PREPAREDNESS General § 239.11 Penalties. Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  12. Adolescents' Attitudes toward the Death Penalty.

    ERIC Educational Resources Information Center

    Lester, David; Maggioncalda-Aretz, Maria; Stark, Scott Hunter

    1997-01-01

    Examines whether high school (n=142) and college students (n=112) favored the death penalty for certain criminal acts. Findings indicate that high school students rated more criminal acts as meriting the death penalty. Gender and personality were not found to be associated with attitudes toward the death penalty. (RJM)

  13. 49 CFR 220.7 - Penalty.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ..., or has caused death or injury, a penalty not to exceed $100,000 per violation may be assessed; and... 49 Transportation 4 2010-10-01 2010-10-01 false Penalty. 220.7 Section 220.7 Transportation Other... TRANSPORTATION RAILROAD COMMUNICATIONS General § 220.7 Penalty. Any person (including but not limited to...

  14. 49 CFR 213.15 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 49 Transportation 4 2010-10-01 2010-10-01 false Penalties. 213.15 Section 213.15 Transportation... TRANSPORTATION TRACK SAFETY STANDARDS General § 213.15 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of at...

  15. 49 CFR 209.409 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ..., or has caused death or injury, a penalty not to exceed $100,000 per violation may be assessed. Each... 49 Transportation 4 2011-10-01 2011-10-01 false Penalties. 209.409 Section 209.409 Transportation... TRANSPORTATION RAILROAD SAFETY ENFORCEMENT PROCEDURES Reporting of Remedial Actions § 209.409 Penalties....

  16. 31 CFR 597.701 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... Penalties § 597.701 Penalties. (a) Attention is directed to 18 U.S.C. 2339B(a)(1), as added by Public Law... States Code, or imprisoned for not more than 10 years, or both. (b) Attention is directed to 18 U.S.C... inflation pursuant to the Federal Civil Penalties Inflation Adjustment Act of 1990. (c) Attention...

  17. 31 CFR 597.701 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... Penalties § 597.701 Penalties. (a) Attention is directed to 18 U.S.C. 2339B(a)(1), as added by Public Law... States Code, or imprisoned for not more than 10 years, or both. (b) Attention is directed to 18 U.S.C... inflation pursuant to the Federal Civil Penalties Inflation Adjustment Act of 1990. (c) Attention...

  18. 49 CFR 239.11 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 49 Transportation 4 2014-10-01 2014-10-01 false Penalties. 239.11 Section 239.11 Transportation... TRANSPORTATION PASSENGER TRAIN EMERGENCY PREPAREDNESS General § 239.11 Penalties. Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  19. 49 CFR 221.7 - Civil penalty.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... persons, or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed... 49 Transportation 4 2013-10-01 2013-10-01 false Civil penalty. 221.7 Section 221.7 Transportation... TRANSPORTATION REAR END MARKING DEVICE-PASSENGER, COMMUTER AND FREIGHT TRAINS General § 221.7 Civil penalty....

  20. 49 CFR 238.11 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed. Each... 49 Transportation 4 2013-10-01 2013-10-01 false Penalties. 238.11 Section 238.11 Transportation... TRANSPORTATION PASSENGER EQUIPMENT SAFETY STANDARDS General § 238.11 Penalties. (a) Any person, as defined...

  1. 49 CFR 244.5 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... imminent hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $105... 49 Transportation 4 2013-10-01 2013-10-01 false Penalties. 244.5 Section 244.5 Transportation... ACQUISITIONS OF CONTROL General § 244.5 Penalties. (a) Any person who violates any requirement of this part...

  2. 49 CFR 239.11 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 49 Transportation 4 2012-10-01 2012-10-01 false Penalties. 239.11 Section 239.11 Transportation... TRANSPORTATION PASSENGER TRAIN EMERGENCY PREPAREDNESS General § 239.11 Penalties. Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  3. 49 CFR 213.15 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 49 Transportation 4 2014-10-01 2014-10-01 false Penalties. 213.15 Section 213.15 Transportation... TRANSPORTATION TRACK SAFETY STANDARDS General § 213.15 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of at...

  4. 49 CFR 107.329 - Maximum penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... violation, except the maximum civil penalty is $175,000 if the violation results in death, serious illness... civil penalty is $175,000 if the violation results in death, serious illness or severe injury to any... 49 Transportation 2 2013-10-01 2013-10-01 false Maximum penalties. 107.329 Section...

  5. 49 CFR 237.7 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 49 Transportation 4 2013-10-01 2013-10-01 false Penalties. 237.7 Section 237.7 Transportation... TRANSPORTATION BRIDGE SAFETY STANDARDS General § 237.7 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of at...

  6. 49 CFR 233.11 - Civil penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed. Each... 49 Transportation 4 2012-10-01 2012-10-01 false Civil penalties. 233.11 Section 233.11..., DEPARTMENT OF TRANSPORTATION SIGNAL SYSTEMS REPORTING REQUIREMENTS § 233.11 Civil penalties. Any person...

  7. 49 CFR 225.29 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... persons, or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed... 49 Transportation 4 2013-10-01 2013-10-01 false Penalties. 225.29 Section 225.29 Transportation... TRANSPORTATION RAILROAD ACCIDENTS/INCIDENTS: REPORTS CLASSIFICATION, AND INVESTIGATIONS § 225.29 Penalties....

  8. 49 CFR 213.15 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 49 Transportation 4 2013-10-01 2013-10-01 false Penalties. 213.15 Section 213.15 Transportation... TRANSPORTATION TRACK SAFETY STANDARDS General § 213.15 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of at...

  9. 49 CFR 218.9 - Civil penalty.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 49 Transportation 4 2014-10-01 2014-10-01 false Civil penalty. 218.9 Section 218.9 Transportation... TRANSPORTATION RAILROAD OPERATING PRACTICES General § 218.9 Civil penalty. Any person (an entity of any type... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  10. 49 CFR 230.4 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed. Each... 49 Transportation 4 2013-10-01 2013-10-01 false Penalties. 230.4 Section 230.4 Transportation... TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS General § 230.4 Penalties. (a) Any...

  11. 49 CFR 224.11 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 49 Transportation 4 2014-10-01 2014-10-01 false Penalties. 224.11 Section 224.11 Transportation... TRANSPORTATION REFLECTORIZATION OF RAIL FREIGHT ROLLING STOCK General § 224.11 Penalties. (a) Any person... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  12. 49 CFR 217.5 - Penalty.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 49 Transportation 4 2013-10-01 2013-10-01 false Penalty. 217.5 Section 217.5 Transportation Other... TRANSPORTATION RAILROAD OPERATING RULES General § 217.5 Penalty. Any person (an entity of any type covered under... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  13. 49 CFR 233.11 - Civil penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed. Each... 49 Transportation 4 2014-10-01 2014-10-01 false Civil penalties. 233.11 Section 233.11..., DEPARTMENT OF TRANSPORTATION SIGNAL SYSTEMS REPORTING REQUIREMENTS § 233.11 Civil penalties. Any person...

  14. 49 CFR 227.9 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 49 Transportation 4 2014-10-01 2014-10-01 false Penalties. 227.9 Section 227.9 Transportation... TRANSPORTATION OCCUPATIONAL NOISE EXPOSURE General § 227.9 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  15. 49 CFR 220.7 - Penalty.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed; and... 49 Transportation 4 2013-10-01 2013-10-01 false Penalty. 220.7 Section 220.7 Transportation Other... TRANSPORTATION RAILROAD COMMUNICATIONS General § 220.7 Penalty. Any person (including but not limited to...

  16. 49 CFR 209.409 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed. Each... 49 Transportation 4 2012-10-01 2012-10-01 false Penalties. 209.409 Section 209.409 Transportation... TRANSPORTATION RAILROAD SAFETY ENFORCEMENT PROCEDURES Reporting of Remedial Actions § 209.409 Penalties....

  17. 49 CFR 230.4 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed. Each... 49 Transportation 4 2012-10-01 2012-10-01 false Penalties. 230.4 Section 230.4 Transportation... TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS General § 230.4 Penalties. (a) Any...

  18. 49 CFR 224.11 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 49 Transportation 4 2013-10-01 2013-10-01 false Penalties. 224.11 Section 224.11 Transportation... TRANSPORTATION REFLECTORIZATION OF RAIL FREIGHT ROLLING STOCK General § 224.11 Penalties. (a) Any person... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  19. 49 CFR 218.9 - Civil penalty.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 49 Transportation 4 2013-10-01 2013-10-01 false Civil penalty. 218.9 Section 218.9 Transportation... TRANSPORTATION RAILROAD OPERATING PRACTICES General § 218.9 Civil penalty. Any person (an entity of any type... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  20. 49 CFR 238.11 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed. Each... 49 Transportation 4 2012-10-01 2012-10-01 false Penalties. 238.11 Section 238.11 Transportation... TRANSPORTATION PASSENGER EQUIPMENT SAFETY STANDARDS General § 238.11 Penalties. (a) Any person, as defined...

  1. 49 CFR 218.9 - Civil penalty.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 49 Transportation 4 2012-10-01 2012-10-01 false Civil penalty. 218.9 Section 218.9 Transportation... TRANSPORTATION RAILROAD OPERATING PRACTICES General § 218.9 Civil penalty. Any person (an entity of any type... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  2. 49 CFR 213.15 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 49 Transportation 4 2012-10-01 2012-10-01 false Penalties. 213.15 Section 213.15 Transportation... TRANSPORTATION TRACK SAFETY STANDARDS General § 213.15 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of at...

  3. 49 CFR 209.409 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed. Each... 49 Transportation 4 2013-10-01 2013-10-01 false Penalties. 209.409 Section 209.409 Transportation... TRANSPORTATION RAILROAD SAFETY ENFORCEMENT PROCEDURES Reporting of Remedial Actions § 209.409 Penalties....

  4. 49 CFR 232.11 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $105,000 per... 49 Transportation 4 2012-10-01 2012-10-01 false Penalties. 232.11 Section 232.11 Transportation...-TRAIN DEVICES General § 232.11 Penalties. (a) Any person (including but not limited to a railroad;...

  5. 49 CFR 227.9 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 49 Transportation 4 2012-10-01 2012-10-01 false Penalties. 227.9 Section 227.9 Transportation... TRANSPORTATION OCCUPATIONAL NOISE EXPOSURE General § 227.9 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  6. 49 CFR 209.409 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed. Each... 49 Transportation 4 2014-10-01 2014-10-01 false Penalties. 209.409 Section 209.409 Transportation... TRANSPORTATION RAILROAD SAFETY ENFORCEMENT PROCEDURES Reporting of Remedial Actions § 209.409 Penalties....

  7. 49 CFR 237.7 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 49 Transportation 4 2014-10-01 2014-10-01 false Penalties. 237.7 Section 237.7 Transportation... TRANSPORTATION BRIDGE SAFETY STANDARDS General § 237.7 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of at...

  8. 49 CFR 225.29 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... persons, or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed... 49 Transportation 4 2012-10-01 2012-10-01 false Penalties. 225.29 Section 225.29 Transportation... TRANSPORTATION RAILROAD ACCIDENTS/INCIDENTS: REPORTS CLASSIFICATION, AND INVESTIGATIONS § 225.29 Penalties....

  9. 49 CFR 233.11 - Civil penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed. Each... 49 Transportation 4 2013-10-01 2013-10-01 false Civil penalties. 233.11 Section 233.11..., DEPARTMENT OF TRANSPORTATION SIGNAL SYSTEMS REPORTING REQUIREMENTS § 233.11 Civil penalties. Any person...

  10. 49 CFR 221.7 - Civil penalty.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... persons, or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed... 49 Transportation 4 2012-10-01 2012-10-01 false Civil penalty. 221.7 Section 221.7 Transportation... TRANSPORTATION REAR END MARKING DEVICE-PASSENGER, COMMUTER AND FREIGHT TRAINS General § 221.7 Civil penalty....

  11. 49 CFR 238.11 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed. Each... 49 Transportation 4 2014-10-01 2014-10-01 false Penalties. 238.11 Section 238.11 Transportation... TRANSPORTATION PASSENGER EQUIPMENT SAFETY STANDARDS General § 238.11 Penalties. (a) Any person, as defined...

  12. 49 CFR 232.11 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $105,000 per... 49 Transportation 4 2014-10-01 2014-10-01 false Penalties. 232.11 Section 232.11 Transportation...-TRAIN DEVICES General § 232.11 Penalties. (a) Any person (including but not limited to a railroad;...

  13. 49 CFR 230.4 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed. Each... 49 Transportation 4 2014-10-01 2014-10-01 false Penalties. 230.4 Section 230.4 Transportation... TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS General § 230.4 Penalties. (a) Any...

  14. 49 CFR 244.5 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... imminent hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $105... 49 Transportation 4 2014-10-01 2014-10-01 false Penalties. 244.5 Section 244.5 Transportation... ACQUISITIONS OF CONTROL General § 244.5 Penalties. (a) Any person who violates any requirement of this part...

  15. 49 CFR 107.329 - Maximum penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... violation, except the maximum civil penalty is $175,000 if the violation results in death, serious illness... civil penalty is $175,000 if the violation results in death, serious illness or severe injury to any... 49 Transportation 2 2014-10-01 2014-10-01 false Maximum penalties. 107.329 Section...

  16. 49 CFR 239.11 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 49 Transportation 4 2013-10-01 2013-10-01 false Penalties. 239.11 Section 239.11 Transportation... TRANSPORTATION PASSENGER TRAIN EMERGENCY PREPAREDNESS General § 239.11 Penalties. Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  17. 49 CFR 220.7 - Penalty.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed; and... 49 Transportation 4 2014-10-01 2014-10-01 false Penalty. 220.7 Section 220.7 Transportation Other... TRANSPORTATION RAILROAD COMMUNICATIONS General § 220.7 Penalty. Any person (including but not limited to...

  18. 49 CFR 217.5 - Penalty.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 49 Transportation 4 2012-10-01 2012-10-01 false Penalty. 217.5 Section 217.5 Transportation Other... TRANSPORTATION RAILROAD OPERATING RULES General § 217.5 Penalty. Any person (an entity of any type covered under... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  19. 49 CFR 221.7 - Civil penalty.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... persons, or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed... 49 Transportation 4 2014-10-01 2014-10-01 false Civil penalty. 221.7 Section 221.7 Transportation... TRANSPORTATION REAR END MARKING DEVICE-PASSENGER, COMMUTER AND FREIGHT TRAINS General § 221.7 Civil penalty....

  20. 49 CFR 237.7 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 49 Transportation 4 2012-10-01 2012-10-01 false Penalties. 237.7 Section 237.7 Transportation... TRANSPORTATION BRIDGE SAFETY STANDARDS General § 237.7 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of at...

  1. 49 CFR 227.9 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 49 Transportation 4 2013-10-01 2013-10-01 false Penalties. 227.9 Section 227.9 Transportation... TRANSPORTATION OCCUPATIONAL NOISE EXPOSURE General § 227.9 Penalties. (a) Any person who violates any requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  2. 49 CFR 220.7 - Penalty.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ..., or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed; and... 49 Transportation 4 2012-10-01 2012-10-01 false Penalty. 220.7 Section 220.7 Transportation Other... TRANSPORTATION RAILROAD COMMUNICATIONS General § 220.7 Penalty. Any person (including but not limited to...

  3. 49 CFR 225.29 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... persons, or has caused death or injury, a penalty not to exceed $105,000 per violation may be assessed... 49 Transportation 4 2014-10-01 2014-10-01 false Penalties. 225.29 Section 225.29 Transportation... TRANSPORTATION RAILROAD ACCIDENTS/INCIDENTS: REPORTS CLASSIFICATION, AND INVESTIGATIONS § 225.29 Penalties....

  4. 49 CFR 217.5 - Penalty.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 49 Transportation 4 2014-10-01 2014-10-01 false Penalty. 217.5 Section 217.5 Transportation Other... TRANSPORTATION RAILROAD OPERATING RULES General § 217.5 Penalty. Any person (an entity of any type covered under... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  5. 49 CFR 232.11 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $105,000 per... 49 Transportation 4 2013-10-01 2013-10-01 false Penalties. 232.11 Section 232.11 Transportation...-TRAIN DEVICES General § 232.11 Penalties. (a) Any person (including but not limited to a railroad;...

  6. 49 CFR 244.5 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... imminent hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $105... 49 Transportation 4 2012-10-01 2012-10-01 false Penalties. 244.5 Section 244.5 Transportation... ACQUISITIONS OF CONTROL General § 244.5 Penalties. (a) Any person who violates any requirement of this part...

  7. 49 CFR 224.11 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 49 Transportation 4 2012-10-01 2012-10-01 false Penalties. 224.11 Section 224.11 Transportation... TRANSPORTATION REFLECTORIZATION OF RAIL FREIGHT ROLLING STOCK General § 224.11 Penalties. (a) Any person... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  8. 45 CFR 93.400 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 45 Public Welfare 1 2010-10-01 2010-10-01 false Penalties. 93.400 Section 93.400 Public Welfare DEPARTMENT OF HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATION NEW RESTRICTIONS ON LOBBYING Penalties and... of any such penalty, by reason of a violation by any person, the agency shall consider the...

  9. 10 CFR 824.4 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... a civil penalty under this part: (1) 10 CFR part 1016—Safeguarding of Restricted Data; (2) 10 CFR... 10 Energy 4 2010-01-01 2010-01-01 false Civil penalties. 824.4 Section 824.4 Energy DEPARTMENT OF ENERGY PROCEDURAL RULES FOR THE ASSESSMENT OF CIVIL PENALTIES FOR CLASSIFIED INFORMATION...

  10. 12 CFR 215.11 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 12 Banks and Banking 2 2010-01-01 2010-01-01 false Civil penalties. 215.11 Section 215.11 Banks... OFFICERS, DIRECTORS, AND PRINCIPAL SHAREHOLDERS OF MEMBER BANKS (REGULATION O) § 215.11 Civil penalties... subject to civil penalties as specified in section 29 of the Federal Reserve Act (12 U.S.C. 504)....

  11. 50 CFR 300.40 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... South Pacific Tuna Fisheries § 300.40 Civil penalties. The procedures of 15 CFR part 904 apply to the assessment of civil penalties, except as modified by the requirements of section 8 of the Act. ... 50 Wildlife and Fisheries 7 2010-10-01 2010-10-01 false Civil penalties. 300.40 Section...

  12. 78 FR 672 - Civil Monetary Penalties

    Federal Register 2010, 2011, 2012, 2013, 2014

    2013-01-04

    ...; ] DEPARTMENT OF AGRICULTURE Rural Housing Service 7 CFR Part 3560 RIN 0575AC93 Civil Monetary Penalties AGENCY...) proposes to implement two civil monetary penalty provisions. First, RHS proposes to amend its regulations to create a new section, for imposing civil monetary penalties under the authority of 42 U.S.C....

  13. 49 CFR 233.11 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 49 Transportation 4 2010-10-01 2010-10-01 false Civil penalties. 233.11 Section 233.11..., DEPARTMENT OF TRANSPORTATION SIGNAL SYSTEMS REPORTING REQUIREMENTS § 233.11 Civil penalties. Any person (an... subject to a civil penalty of at least $650 and not more than $25,000 per violation, except...

  14. 24 CFR 4.28 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    ... civil money penalty on the employee in accordance with the provisions of 24 CFR part 30. ... 24 Housing and Urban Development 1 2010-04-01 2010-04-01 false Civil penalties. 4.28 Section 4.28... REFORM ACT Prohibition of Advance Disclosure of Funding Decisions § 4.28 Civil penalties. Whenever...

  15. 7 CFR 1435.201 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 10 2010-01-01 2010-01-01 false Civil penalties. 1435.201 Section 1435.201... Recordkeeping Requirements § 1435.201 Civil penalties. (a) Any processor, refiner, or importer of sugar, syrup... false data required under § 1435.200(a) through (e), is subject to a civil penalty of no more than...

  16. 39 CFR 233.12 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 39 Postal Service 1 2010-07-01 2010-07-01 false Civil penalties. 233.12 Section 233.12 Postal... Civil penalties. False representation and lottery orders— (a) Issuance. Pursuant to 39 U.S.C. 3005, the... be liable to the United States for a civil penalty in an amount not to exceed $11,000 for each...

  17. 31 CFR 103.57 - Civil penalty.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 31 Money and Finance: Treasury 1 2010-07-01 2010-07-01 false Civil penalty. 103.57 Section 103.57... REPORTING OF CURRENCY AND FOREIGN TRANSACTIONS General Provisions § 103.57 Civil penalty. (a) For any... willfully participates in the violation, a civil penalty not to exceed $1,000. (b) For any willful...

  18. 49 CFR 221.7 - Civil penalty.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 49 Transportation 4 2010-10-01 2010-10-01 false Civil penalty. 221.7 Section 221.7 Transportation... TRANSPORTATION REAR END MARKING DEVICE-PASSENGER, COMMUTER AND FREIGHT TRAINS General § 221.7 Civil penalty. Any... requirement is subject to a civil penalty of at least $650 and not more than $25,000 per violation,...

  19. 48 CFR 3.807 - Civil penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 48 Federal Acquisition Regulations System 1 2010-10-01 2010-10-01 false Civil penalties. 3.807... Federal Transactions 3.807 Civil penalties. Agencies shall impose and collect civil penalties pursuant to the provisions of the Program Fraud and Civil Remedies Act, 31 U.S.C. 3803 (except subsection...

  20. 10 CFR 110.64 - Civil penalty.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 10 Energy 2 2010-01-01 2010-01-01 false Civil penalty. 110.64 Section 110.64 Energy NUCLEAR... Enforcement § 110.64 Civil penalty. (a) In response to a violation, the Commission may institute a proceeding to impose a civil penalty under section 234 of the Atomic Energy Act by issuing a notice to...

  1. 49 CFR 218.9 - Civil penalty.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 49 Transportation 4 2010-10-01 2010-10-01 false Civil penalty. 218.9 Section 218.9 Transportation... TRANSPORTATION RAILROAD OPERATING PRACTICES General § 218.9 Civil penalty. Any person (an entity of any type... requirement of this part or causes the violation of any such requirement is subject to a civil penalty of...

  2. 10 CFR 1017.29 - Civil penalty.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... subject to a civil penalty under this part: (1) 10 CFR Part 1017—Identification and Protection of... 10 Energy 4 2010-01-01 2010-01-01 false Civil penalty. 1017.29 Section 1017.29 Energy DEPARTMENT... INFORMATION Violations § 1017.29 Civil penalty. Link to an amendment published at 74 FR 66033, Dec. 14,...

  3. 22 CFR 127.10 - Civil penalty.

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    ... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Civil penalty. 127.10 Section 127.10 Foreign... Civil penalty. (a) The Assistant Secretary of State for Political-Military Affairs is authorized to impose a civil penalty in an amount not to exceed that authorized by 22 U.S.C. 2778, 2779a and 2780...

  4. 49 CFR 272.11 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 49 Transportation 4 2014-10-01 2014-10-01 false Penalties. 272.11 Section 272.11 Transportation Other Regulations Relating to Transportation (Continued) FEDERAL RAILROAD ADMINISTRATION, DEPARTMENT OF TRANSPORTATION CRITICAL INCIDENT STRESS PLANS General § 272.11 Penalties. (a) Civil penalties. A person...

  5. 6 CFR 9.31 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 6 Domestic Security 1 2010-01-01 2010-01-01 false Penalties. 9.31 Section 9.31 Domestic Security DEPARTMENT OF HOMELAND SECURITY, OFFICE OF THE SECRETARY RESTRICTIONS UPON LOBBYING Penalties and Enforcement § 9.31 Penalties. (a) Any person who makes an expenditure prohibited herein shall be subject to...

  6. 34 CFR 36.2 - Penalty adjustment.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... 34 Education 1 2014-07-01 2014-07-01 false Penalty adjustment. 36.2 Section 36.2 Education Office of the Secretary, Department of Education ADJUSTMENT OF CIVIL MONETARY PENALTIES FOR INFLATION § 36.2..., Section 36.2—Civil Monetary Penalty Inflation Adjustments Statute Description New maximum (and minimum,...

  7. 34 CFR 36.2 - Penalty adjustment.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... 34 Education 1 2011-07-01 2011-07-01 false Penalty adjustment. 36.2 Section 36.2 Education Office of the Secretary, Department of Education ADJUSTMENT OF CIVIL MONETARY PENALTIES FOR INFLATION § 36.2..., Section 36.2—Civil Monetary Penalty Inflation Adjustments Statute Description New maximum (and minimum,...

  8. 34 CFR 36.2 - Penalty adjustment.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 34 Education 1 2010-07-01 2010-07-01 false Penalty adjustment. 36.2 Section 36.2 Education Office of the Secretary, Department of Education ADJUSTMENT OF CIVIL MONETARY PENALTIES FOR INFLATION § 36.2..., Section 36.2—Civil Monetary Penalty Inflation Adjustments Statute Description New maximum (and minimum,...

  9. 34 CFR 36.2 - Penalty adjustment.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... 34 Education 1 2013-07-01 2013-07-01 false Penalty adjustment. 36.2 Section 36.2 Education Office of the Secretary, Department of Education ADJUSTMENT OF CIVIL MONETARY PENALTIES FOR INFLATION § 36.2..., Section 36.2—Civil Monetary Penalty Inflation Adjustments Statute Description New maximum (and minimum,...

  10. Element free Galerkin formulation of composite beam with longitudinal slip

    SciTech Connect

    Ahmad, Dzulkarnain; Mokhtaram, Mokhtazul Haizad; Badli, Mohd Iqbal; Yassin, Airil Y. Mohd

    2015-05-15

    Behaviour between two materials in composite beam is assumed partially interact when longitudinal slip at its interfacial surfaces is considered. Commonly analysed by the mesh-based formulation, this study used meshless formulation known as Element Free Galerkin (EFG) method in the beam partial interaction analysis, numerically. As meshless formulation implies that the problem domain is discretised only by nodes, the EFG method is based on Moving Least Square (MLS) approach for shape functions formulation with its weak form is developed using variational method. The essential boundary conditions are enforced by Langrange multipliers. The proposed EFG formulation gives comparable results, after been verified by analytical solution, thus signify its application in partial interaction problems. Based on numerical test results, the Cubic Spline and Quartic Spline weight functions yield better accuracy for the EFG formulation, compares to other proposed weight functions.

  11. On the Implementation of 3D Galerkin Boundary Integral Equations

    SciTech Connect

    Nintcheu Fata, Sylvain; Gray, Leonard J

    2010-01-01

    In this article, a reverse contribution technique is proposed to accelerate the construction of the dense influence matrices associated with a Galerkin approximation of singular and hypersingular boundary integral equations of mixed-type in potential theory. In addition, a general-purpose sparse preconditioner for boundary element methods has also been developed to successfully deal with ill-conditioned linear systems arising from the discretization of mixed boundary-value problems on non-smooth surfaces. The proposed preconditioner, which originates from the precorrected-FFT method, is sparse, easy to generate and apply in a Krylov subspace iterative solution of discretized boundary integral equations. Moreover, an approximate inverse of the preconditioner is implicitly built by employing an incomplete LU factorization. Numerical experiments involving mixed boundary-value problems for the Laplace equation are included to illustrate the performance and validity of the proposed techniques.

  12. A Galerkin least squares approach to viscoelastic flow.

    SciTech Connect

    Rao, Rekha R.; Schunk, Peter Randall

    2015-10-01

    A Galerkin/least-squares stabilization technique is applied to a discrete Elastic Viscous Stress Splitting formulation of for viscoelastic flow. From this, a possible viscoelastic stabilization method is proposed. This method is tested with the flow of an Oldroyd-B fluid past a rigid cylinder, where it is found to produce inaccurate drag coefficients. Furthermore, it fails for relatively low Weissenberg number indicating it is not suited for use as a general algorithm. In addition, a decoupled approach is used as a way separating the constitutive equation from the rest of the system. A Pressure Poisson equation is used when the velocity and pressure are sought to be decoupled, but this fails to produce a solution when inflow/outflow boundaries are considered. However, a coupled pressure-velocity equation with a decoupled constitutive equation is successful for the flow past a rigid cylinder and seems to be suitable as a general-use algorithm.

  13. Sinc-Galerkin estimation of diffusivity in parabolic problems

    NASA Technical Reports Server (NTRS)

    Smith, Ralph C.; Bowers, Kenneth L.

    1991-01-01

    A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

  14. Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Reich, Simeon; Rosen, I. G.

    1988-01-01

    An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.

  15. High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang

    2000-01-01

    This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the

  16. Technological Discontinuities and Organizational Environments.

    ERIC Educational Resources Information Center

    Tushman, Michael L.; Anderson, Philip

    1986-01-01

    Technological effects on environmental conditions are analyzed using longitudinal data from the minicomputer, cement, and airline industries. Technology evolves through periods of incremental change punctuated by breakthroughs that enhance or destroy the competence of firms. Competence-destroying discontinuities increase environmental turbulence;…

  17. The Morphosyntax of Discontinuous Exponence

    ERIC Educational Resources Information Center

    Campbell, Amy Melissa

    2012-01-01

    This thesis offers a systematic treatment of discontinuous exponence, a pattern of inflection in which a single feature or a set of features bundled in syntax is expressed by multiple, distinct morphemes. This pattern is interesting and theoretically relevant because it represents a deviation from the expected one-to-one relationship between…

  18. Religious characteristics and the death penalty.

    PubMed

    Miller, Monica K; Hayward, R David

    2008-04-01

    Using one mock trial scenario, this study investigated whether religious and demographic factors were related to death penalty attitudes and sentencing verdicts. Those who favored the death penalty differed from those who had doubts about the penalty in gender, affiliation, fundamentalism, evangelism, literal Biblical interpretism, beliefs about God's attitudes toward murders, and perceptions of how their religious groups felt about the death penalty. These relationships generally held after mock jurors were death qualified. Gender, fundamentalism, literal interpretism, beliefs about God's death penalty position, and perceptions of how one's religious group felt about the death penalty predicted death penalty sentencing verdicts. Future research could determine whether using peremptory challenges to exclude potential jurors based on religion can help lawyers choose a more favorable jury.

  19. A Taylor-Galerkin finite element algorithm for transient nonlinear thermal-structural analysis

    NASA Technical Reports Server (NTRS)

    Thornton, Earl A.; Dechaumphai, Pramote

    1985-01-01

    A Taylor-Galerkin finite element solution algorithm for transient nonlinear thermal-structural analysis of large, complex structural problems subjected to rapidly applied thermal-structural loads is described. The two-step Taylor-Galerkin algorithm is an application of an algorithm recently developed for problems in compressible fluid dynamics. The element integrals that appear in the algorithm can be evaluated in closed form for two and three dimensional elements.

  20. Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations

    SciTech Connect

    Zhou Tao; Tang Tao

    2010-11-01

    In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266-281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question.

  1. Comparison of penalty functions on a penalty approach to mixed-integer optimization

    NASA Astrophysics Data System (ADS)

    Francisco, Rogério B.; Costa, M. Fernanda P.; Rocha, Ana Maria A. C.; Fernandes, Edite M. G. P.

    2016-06-01

    In this paper, we present a comparative study involving several penalty functions that can be used in a penalty approach for globally solving bound mixed-integer nonlinear programming (bMIMLP) problems. The penalty approach relies on a continuous reformulation of the bMINLP problem by adding a particular penalty term to the objective function. A penalty function based on the `erf' function is proposed. The continuous nonlinear optimization problems are sequentially solved by the population-based firefly algorithm. Preliminary numerical experiments are carried out in order to analyze the quality of the produced solutions, when compared with other penalty functions available in the literature.

  2. 38 CFR 21.7635 - Discontinuance dates.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ....S.C. 3680(e)) (b) Course discontinued—course interrupted—course terminated—course not satisfactorily...) (e) Discontinued by VA. If VA discontinues payment to a reservist following the procedures stated...

  3. Bursts in discontinuous Aeolian saltation

    PubMed Central

    Carneiro, M. V.; Rasmussen, K. R.; Herrmann, H. J.

    2015-01-01

    Close to the onset of Aeolian particle transport through saltation we find in wind tunnel experiments a regime of discontinuous flux characterized by bursts of activity. Scaling laws are observed in the time delay between each burst and in the measurements of the wind fluctuations at the fluid threshold Shields number θc. The time delay between each burst decreases on average with the increase of the Shields number until sand flux becomes continuous. A numerical model for saltation including the wind-entrainment from the turbulent fluctuations can reproduce these observations and gives insight about their origin. We present here also for the first time measurements showing that with feeding it becomes possible to sustain discontinuous flux even below the fluid threshold. PMID:26073305

  4. Discontinuities in recurrent neural networks.

    PubMed

    Gavaldá, R; Siegelmann, H T

    1999-04-01

    This article studies the computational power of various discontinuous real computational models that are based on the classical analog recurrent neural network (ARNN). This ARNN consists of finite number of neurons; each neuron computes a polynomial net function and a sigmoid-like continuous activation function. We introduce arithmetic networks as ARNN augmented with a few simple discontinuous (e.g., threshold or zero test) neurons. We argue that even with weights restricted to polynomial time computable reals, arithmetic networks are able to compute arbitrarily complex recursive functions. We identify many types of neural networks that are at least as powerful as arithmetic nets, some of which are not in fact discontinuous, but they boost other arithmetic operations in the net function (e.g., neurons that can use divisions and polynomial net functions inside sigmoid-like continuous activation functions). These arithmetic networks are equivalent to the Blum-Shub-Smale model, when the latter is restricted to a bounded number of registers. With respect to implementation on digital computers, we show that arithmetic networks with rational weights can be simulated with exponential precision, but even with polynomial-time computable real weights, arithmetic networks are not subject to any fixed precision bounds. This is in contrast with the ARNN that are known to demand precision that is linear in the computation time. When nontrivial periodic functions (e.g., fractional part, sine, tangent) are added to arithmetic networks, the resulting networks are computationally equivalent to a massively parallel machine. Thus, these highly discontinuous networks can solve the presumably intractable class of PSPACE-complete problems in polynomial time.

  5. Reinforced ceramics employing discontinuous phases

    SciTech Connect

    Becher, P.F.

    1990-01-01

    The fracture toughness of ceramics can be improved by the incorporation of a variety of discontinuous reinforcing phases and microstructures. Observations of crack paths in these systems indicate that these reinforcing phases bridge the crack tip wake region. Recent developments in micromechanics toughening models applicable to such systems are discussed and compared with experimental observations. Because material parameters and microstructural characteristics are considered, the crack bridging models provide a means to optimize the toughening effects. 18 refs., 2 figs.

  6. 40 CFR 159.167 - Discontinued studies.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... 40 Protection of Environment 25 2013-07-01 2013-07-01 false Discontinued studies. 159.167 Section 159.167 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) PESTICIDE PROGRAMS... Discontinued studies. The fact that a study has been discontinued before the planned termination must...

  7. 40 CFR 159.167 - Discontinued studies.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 40 Protection of Environment 23 2010-07-01 2010-07-01 false Discontinued studies. 159.167 Section 159.167 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) PESTICIDE PROGRAMS... Discontinued studies. The fact that a study has been discontinued before the planned termination must...

  8. 40 CFR 159.167 - Discontinued studies.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... 40 Protection of Environment 24 2014-07-01 2014-07-01 false Discontinued studies. 159.167 Section 159.167 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) PESTICIDE PROGRAMS... Discontinued studies. The fact that a study has been discontinued before the planned termination must...

  9. 40 CFR 159.167 - Discontinued studies.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... 40 Protection of Environment 24 2011-07-01 2011-07-01 false Discontinued studies. 159.167 Section 159.167 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) PESTICIDE PROGRAMS... Discontinued studies. The fact that a study has been discontinued before the planned termination must...

  10. 40 CFR 159.167 - Discontinued studies.

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... 40 Protection of Environment 25 2012-07-01 2012-07-01 false Discontinued studies. 159.167 Section 159.167 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) PESTICIDE PROGRAMS... Discontinued studies. The fact that a study has been discontinued before the planned termination must...

  11. Discontinuous mixed covolume methods for parabolic problems.

    PubMed

    Zhu, Ailing; Jiang, Ziwen

    2014-01-01

    We present the semidiscrete and the backward Euler fully discrete discontinuous mixed covolume schemes for parabolic problems on triangular meshes. We give the error analysis of the discontinuous mixed covolume schemes and obtain optimal order error estimates in discontinuous H(div) and first-order error estimate in L(2).

  12. Discontinuous diffusion synthetic acceleration for S{sub n} transport on 2D arbitrary polygonal meshes

    SciTech Connect

    Turcksin, Bruno Ragusa, Jean C.

    2014-10-01

    In this paper, a Diffusion Synthetic Acceleration (DSA) technique applied to the S{sub n} radiation transport equation is developed using Piece-Wise Linear Discontinuous (PWLD) finite elements on arbitrary polygonal grids. The discretization of the DSA equations employs an Interior Penalty technique, as is classically done for the stabilization of the diffusion equation using discontinuous finite element approximations. The penalty method yields a system of linear equations that is Symmetric Positive Definite (SPD). Thus, solution techniques such as Preconditioned Conjugate Gradient (PCG) can be effectively employed. Algebraic MultiGrid (AMG) and Symmetric Gauss–Seidel (SGS) are employed as conjugate gradient preconditioners for the DSA system. AMG is shown to be significantly more efficient than SGS. Fourier analyses are carried out and we show that this discontinuous finite element DSA scheme is always stable and effective at reducing the spectral radius for iterative transport solves, even for grids with high-aspect ratio cells. Numerical results are presented for different grid types: quadrilateral, hexagonal, and polygonal grids as well as grids with local mesh adaptivity.

  13. Discontinuous diffusion synthetic acceleration for Sn transport on 2D arbitrary polygonal meshes

    NASA Astrophysics Data System (ADS)

    Turcksin, Bruno; Ragusa, Jean C.

    2014-10-01

    In this paper, a Diffusion Synthetic Acceleration (DSA) technique applied to the Sn radiation transport equation is developed using Piece-Wise Linear Discontinuous (PWLD) finite elements on arbitrary polygonal grids. The discretization of the DSA equations employs an Interior Penalty technique, as is classically done for the stabilization of the diffusion equation using discontinuous finite element approximations. The penalty method yields a system of linear equations that is Symmetric Positive Definite (SPD). Thus, solution techniques such as Preconditioned Conjugate Gradient (PCG) can be effectively employed. Algebraic MultiGrid (AMG) and Symmetric Gauss-Seidel (SGS) are employed as conjugate gradient preconditioners for the DSA system. AMG is shown to be significantly more efficient than SGS. Fourier analyses are carried out and we show that this discontinuous finite element DSA scheme is always stable and effective at reducing the spectral radius for iterative transport solves, even for grids with high-aspect ratio cells. Numerical results are presented for different grid types: quadrilateral, hexagonal, and polygonal grids as well as grids with local mesh adaptivity.

  14. 21 CFR 17.2 - Maximum penalty amounts.

    Code of Federal Regulations, 2011 CFR

    2011-04-01

    ... 21 Food and Drugs 1 2011-04-01 2011-04-01 false Maximum penalty amounts. 17.2 Section 17.2 Food... PENALTIES HEARINGS § 17.2 Maximum penalty amounts. The following table shows maximum civil monetary... Penalty Amounts U.S.C. Section Former Maximum Penalty Amount (in dollars) Assessment Method Date of...

  15. A hybrid Pade-Galerkin technique for differential equations

    NASA Technical Reports Server (NTRS)

    Geer, James F.; Andersen, Carl M.

    1993-01-01

    A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated.

  16. 49 CFR 216.7 - Penalties.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $100,000 per... 49 Transportation 4 2010-10-01 2010-10-01 false Penalties. 216.7 Section 216.7 Transportation... § 216.7 Penalties. Any person (an entity of any type covered under 1 U.S.C. 1, including but not...

  17. 49 CFR 216.7 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $100,000 per... 49 Transportation 4 2011-10-01 2011-10-01 false Penalties. 216.7 Section 216.7 Transportation... § 216.7 Penalties. Any person (an entity of any type covered under 1 U.S.C. 1, including but not...

  18. 49 CFR 216.7 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $105,000 per... 49 Transportation 4 2014-10-01 2014-10-01 false Penalties. 216.7 Section 216.7 Transportation... § 216.7 Penalties. Any person (an entity of any type covered under 1 U.S.C. 1, including but not...

  19. 49 CFR 216.7 - Penalties.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $105,000 per... 49 Transportation 4 2013-10-01 2013-10-01 false Penalties. 216.7 Section 216.7 Transportation... § 216.7 Penalties. Any person (an entity of any type covered under 1 U.S.C. 1, including but not...

  20. 49 CFR 216.7 - Penalties.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... hazard of death or injury to persons, or has caused death or injury, a penalty not to exceed $105,000 per... 49 Transportation 4 2012-10-01 2012-10-01 false Penalties. 216.7 Section 216.7 Transportation... § 216.7 Penalties. Any person (an entity of any type covered under 1 U.S.C. 1, including but not...

  1. Iterative CBCT reconstruction using Hessian penalty

    NASA Astrophysics Data System (ADS)

    Sun, Tao; Sun, Nanbo; Wang, Jing; Tan, Shan

    2015-03-01

    Statistical iterative reconstruction algorithms have shown potential to improve cone-beam CT (CBCT) image quality. Most iterative reconstruction algorithms utilize prior knowledge as a penalty term in the objective function. The penalty term greatly affects the performance of a reconstruction algorithm. The total variation (TV) penalty has demonstrated great ability in suppressing noise and improving image quality. However, calculated from the first-order derivatives, the TV penalty leads to the well-known staircase effect, which sometimes makes the reconstructed images oversharpen and unnatural. In this study, we proposed to use a second-order derivative penalty that involves the Frobenius norm of the Hessian matrix of an image for CBCT reconstruction. The second-order penalty retains some of the most favorable properties of the TV penalty like convexity, homogeneity, and rotation and translation invariance, and has a better ability in preserving the structures of gradual transition in the reconstructed images. An effective algorithm was developed to minimize the objective function with the majorization-minimization (MM) approach. The experiments on a digital phantom and two physical phantoms demonstrated the priority of the proposed penalty, particularly in suppressing the staircase effect of the TV penalty.

  2. 49 CFR Appendix B to Part 386 - Penalty Schedule; Violations and Monetary Penalties

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... subject to a civil penalty not to exceed $2,750. (5) Violation of 49 CFR 392.5. A driver placed out of... 49 Transportation 5 2014-10-01 2014-10-01 false Penalty Schedule; Violations and Monetary Penalties B Appendix B to Part 386 Transportation Other Regulations Relating to Transportation...

  3. 49 CFR Appendix B to Part 386 - Penalty Schedule; Violations and Monetary Penalties

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... subject to a civil penalty not to exceed $2,750. (5) Violation of 49 CFR 392.5. A driver placed out of... civil penalties set out in paragraphs (e)(1) through (4) of this appendix results in death, serious... receiving a final “unsatisfactory” safety rating, to a civil penalty of not more than $11,000 (49 CFR...

  4. 49 CFR Appendix B to Part 386 - Penalty Schedule; Violations and Monetary Penalties

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... subject to a civil penalty not to exceed $2,750. (5) Violation of 49 CFR 392.5. A driver placed out of... 49 Transportation 5 2013-10-01 2013-10-01 false Penalty Schedule; Violations and Monetary Penalties B Appendix B to Part 386 Transportation Other Regulations Relating to Transportation...

  5. 49 CFR Appendix B to Part 386 - Penalty Schedule; Violations and Monetary Penalties

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... subject to a civil penalty not to exceed $2,750. (5) Violation of 49 CFR 392.5. A driver placed out of... 49 Transportation 5 2012-10-01 2012-10-01 false Penalty Schedule; Violations and Monetary Penalties B Appendix B to Part 386 Transportation Other Regulations Relating to Transportation...

  6. 29 CFR 2700.30 - Assessment of penalty.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... Contests of Proposed Penalties § 2700.30 Assessment of penalty. (a) In assessing a penalty the Judge shall... the Act, 30 U.S.C. 820(i), and incorporate such determination in a written decision. The...

  7. Discontinuous dynamics with grazing points

    NASA Astrophysics Data System (ADS)

    Akhmet, M. U.; Kıvılcım, A.

    2016-09-01

    Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of solutions are thoroughly analyzed. A variational system around a grazing solution which depends on near solutions is constructed. Orbital stability of grazing cycles is examined by linearization. Small parameter method is extended for analysis of grazing orbits, and bifurcation of cycles is observed in an example. Linearization around an equilibrium grazing point is discussed. The results can be extended on functional differential equations, partial differential equations and others. Appropriate illustrations are depicted to support the theoretical results.

  8. A diffusion synthetic acceleration scheme for rectangular geometries based on bilinear discontinuous finite elements

    SciTech Connect

    Turcksin, B.; Ragusa, J. C.

    2013-07-01

    A DSA technique to accelerate the iterative convergence of S{sub n} transport solves is derived for bilinear discontinuous (BLD) finite elements on rectangular grids. The diffusion synthetic acceleration equations are discretized using BLD elements by adapting the Modified Interior Penalty technique, introduced in [4] for triangular grids. The MIP-DSA equations are SPD and thus are solved using a preconditioned CG technique. Fourier analyses and implementation of the technique in a BLD S{sub n} transport code show that the technique is stable is effective. (authors)

  9. Galerkin projection methods for solving multiple related linear systems

    SciTech Connect

    Chan, T.F.; Ng, M.; Wan, W.L.

    1996-12-31

    We consider using Galerkin projection methods for solving multiple related linear systems A{sup (i)}x{sup (i)} = b{sup (i)} for 1 {le} i {le} s, where A{sup (i)} and b{sup (i)} are different in general. We start with the special case where A{sup (i)} = A and A is symmetric positive definite. The method generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed system, by the CG method and then projects the residuals of other systems orthogonally onto the generated Krylov subspace to get the approximate solutions. The whole process is repeated with another unsolved system as a seed until all the systems are solved. We observe in practice a super-convergence behaviour of the CG process of the seed system when compared with the usual CG process. We also observe that only a small number of restarts is required to solve all the systems if the right-hand sides are close to each other. These two features together make the method particularly effective. In this talk, we give theoretical proof to justify these observations. Furthermore, we combine the advantages of this method and the block CG method and propose a block extension of this single seed method. The above procedure can actually be modified for solving multiple linear systems A{sup (i)}x{sup (i)} = b{sup (i)}, where A{sup (i)} are now different. We can also extend the previous analytical results to this more general case. Applications of this method to multiple related linear systems arising from image restoration and recursive least squares computations are considered as examples.

  10. POD-Galerkin reduced-order modeling with adaptive finite element snapshots

    NASA Astrophysics Data System (ADS)

    Ullmann, Sebastian; Rotkvic, Marko; Lang, Jens

    2016-11-01

    We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical issues arising from the fact that the snapshots are members of different finite element spaces. We propose a method to create a POD-Galerkin model without interpolating the snapshots onto their common finite element mesh. The error of the reduced-order solution is not necessarily Galerkin orthogonal to the reduced space created from space-adapted snapshot. We analyze how this influences the error assessment for POD-Galerkin models of linear elliptic boundary value problems. As a numerical example we consider a two-dimensional convection-diffusion equation with a parametrized convective direction. To illustrate the applicability of our techniques to non-linear time-dependent problems, we present a test case of a two-dimensional viscous Burgers equation with parametrized initial data.

  11. 31 CFR 536.701 - Penalties.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... 31 Money and Finance:Treasury 3 2011-07-01 2011-07-01 false Penalties. 536.701 Section 536.701 Money and Finance: Treasury Regulations Relating to Money and Finance (Continued) OFFICE OF FOREIGN ASSETS CONTROL, DEPARTMENT OF THE TREASURY NARCOTICS TRAFFICKING SANCTIONS REGULATIONS Penalties §...

  12. 31 CFR 536.701 - Penalties.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... 31 Money and Finance:Treasury 3 2014-07-01 2014-07-01 false Penalties. 536.701 Section 536.701 Money and Finance: Treasury Regulations Relating to Money and Finance (Continued) OFFICE OF FOREIGN ASSETS CONTROL, DEPARTMENT OF THE TREASURY NARCOTICS TRAFFICKING SANCTIONS REGULATIONS Penalties §...

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    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 31 Money and Finance: Treasury 3 2010-07-01 2010-07-01 false Penalties. 536.701 Section 536.701 Money and Finance: Treasury Regulations Relating to Money and Finance (Continued) OFFICE OF FOREIGN ASSETS CONTROL, DEPARTMENT OF THE TREASURY NARCOTICS TRAFFICKING SANCTIONS REGULATIONS Penalties §...

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    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... 31 Money and Finance:Treasury 3 2013-07-01 2013-07-01 false Penalties. 536.701 Section 536.701 Money and Finance: Treasury Regulations Relating to Money and Finance (Continued) OFFICE OF FOREIGN ASSETS CONTROL, DEPARTMENT OF THE TREASURY NARCOTICS TRAFFICKING SANCTIONS REGULATIONS Penalties §...

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    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... 31 Money and Finance:Treasury 3 2012-07-01 2012-07-01 false Penalties. 536.701 Section 536.701 Money and Finance: Treasury Regulations Relating to Money and Finance (Continued) OFFICE OF FOREIGN ASSETS CONTROL, DEPARTMENT OF THE TREASURY NARCOTICS TRAFFICKING SANCTIONS REGULATIONS Penalties §...

  16. 10 CFR 1017.30 - Criminal penalty.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... INFORMATION Violations § 1017.30 Criminal penalty. Any person who violates section 148 of the Atomic Energy Act or any regulation or order of the Secretary issued under section 148 of the Atomic Energy Act, including these regulations, may be subject to a criminal penalty under section 223 of the Atomic Energy...

  17. 10 CFR 1017.30 - Criminal penalty.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... INFORMATION Violations § 1017.30 Criminal penalty. Any person who violates section 148 of the Atomic Energy Act or any regulation or order of the Secretary issued under section 148 of the Atomic Energy Act, including these regulations, may be subject to a criminal penalty under section 223 of the Atomic Energy...

  18. 10 CFR 1017.30 - Criminal penalty.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... INFORMATION Violations § 1017.30 Criminal penalty. Any person who violates section 148 of the Atomic Energy Act or any regulation or order of the Secretary issued under section 148 of the Atomic Energy Act, including these regulations, may be subject to a criminal penalty under section 223 of the Atomic Energy...

  19. 10 CFR 76.133 - Criminal penalties.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 10 Energy 2 2012-01-01 2012-01-01 false Criminal penalties. 76.133 Section 76.133 Energy NUCLEAR REGULATORY COMMISSION (CONTINUED) CERTIFICATION OF GASEOUS DIFFUSION PLANTS Enforcement § 76.133 Criminal penalties. (a) Section 223 of the Atomic Energy Act of 1954, as amended, provides for criminal sanctions...

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    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 10 Energy 2 2010-01-01 2010-01-01 false Criminal penalties. 76.133 Section 76.133 Energy NUCLEAR REGULATORY COMMISSION (CONTINUED) CERTIFICATION OF GASEOUS DIFFUSION PLANTS Enforcement § 76.133 Criminal penalties. (a) Section 223 of the Atomic Energy Act of 1954, as amended, provides for criminal sanctions...