Computational characterization of chromatin domain boundary-associated genomic elements.
Hong, Seungpyo; Kim, Dongsup
2017-08-23
Topologically associated domains (TADs) are 3D genomic structures with high internal interactions that play important roles in genome compaction and gene regulation. Their genomic locations and their association with CCCTC-binding factor (CTCF)-binding sites and transcription start sites (TSSs) were recently reported. However, the relationship between TADs and other genomic elements has not been systematically evaluated. This was addressed in the present study, with a focus on the enrichment of these genomic elements and their ability to predict the TAD boundary region. We found that consensus CTCF-binding sites were strongly associated with TAD boundaries as well as with the transcription factors (TFs) Zinc finger protein (ZNF)143 and Yin Yang (YY)1. TAD boundary-associated genomic elements include DNase I-hypersensitive sites, H3K36 trimethylation, TSSs, RNA polymerase II, and TFs such as Specificity protein 1, ZNF274 and SIX homeobox 5. Computational modeling with these genomic elements suggests that they have distinct roles in TAD boundary formation. We propose a structural model of TAD boundaries based on these findings that provides a basis for studying the mechanism of chromatin structure formation and gene regulation. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.
Boundary element analysis on vector and parallel computers
NASA Technical Reports Server (NTRS)
Kane, J. H.
1994-01-01
Boundary element analysis (BEA) can be characterized as a numerical technique that generally shifts the computational burden in the analysis toward numerical integration and the solution of nonsymmetric and either dense or blocked sparse systems of algebraic equations. Researchers have explored the concept that the fundamental characteristics of BEA can be exploited to generate effective implementations on vector and parallel computers. In this paper, the results of some of these investigations are discussed. The performance of overall algorithms for BEA on vector supercomputers, massively data parallel single instruction multiple data (SIMD), and relatively fine grained distributed memory multiple instruction multiple data (MIMD) computer systems is described. Some general trends and conclusions are discussed, along with indications of future developments that may prove fruitful in this regard.
NASA Technical Reports Server (NTRS)
Atluri, S. N.
1986-01-01
Computational finite-element and boundary-element methods are reviewed, and their application to the mechanics of solids is discussed. Stability conditions for general FEMs are considered in addition to the use of least-order, stable, invariant, or hybrid/mixed isoparametric elements as alternatives to the displacement-based isoparametric elements. The use of symbolic manipulation, adaptive mesh refinement, transient dynamic response, and boundary-element methods for linear elaslticity and finite-strain problems of inelastic materials are also discussed.
Computation of Sound Propagation by Boundary Element Method
NASA Technical Reports Server (NTRS)
Guo, Yueping
2005-01-01
This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which
Computation of molecular electrostatics with boundary element methods.
Liang, J; Subramaniam, S
1997-01-01
In continuum approaches to molecular electrostatics, the boundary element method (BEM) can provide accurate solutions to the Poisson-Boltzmann equation. However, the numerical aspects of this method pose significant problems. We describe our approach, applying an alpha shape-based method to generate a high-quality mesh, which represents the shape and topology of the molecule precisely. We also describe an analytical method for mapping points from the planar mesh to their exact locations on the surface of the molecule. We demonstrate that derivative boundary integral formulation has numerical advantages over the nonderivative formulation: the well-conditioned influence matrix can be maintained without deterioration of the condition number when the number of the mesh elements scales up. Singular integrand kernels are characteristics of the BEM. Their accurate integration is an important issue. We describe variable transformations that allow accurate numerical integration. The latter is the only plausible integral evaluation method when using curve-shaped boundary elements. Images FIGURE 3 FIGURE 5 FIGURE 6 FIGURE 7 FIGURE 8 PMID:9336178
Computational solution of acoustic radiation problems by Kussmaul's boundary element method
NASA Astrophysics Data System (ADS)
Kirkup, S. M.; Henwood, D. J.
1992-10-01
The problem of computing the properties of the acoustic field exterior to a vibrating surface for the complete wavenumber range by the boundary element method is considered. A particular computational method based on the Kussmaul formulation is described. The method is derived through approximating the surface by a set of planar triangles and approximating the surface functions by a constant on each element. The method is successfully applied to test problems and to the Ricardo crankcase simulation rig.
THERM3D -- A boundary element computer program for transient heat conduction problems
Ingber, M.S.
1994-02-01
The computer code THERM3D implements the direct boundary element method (BEM) to solve transient heat conduction problems in arbitrary three-dimensional domains. This particular implementation of the BEM avoids performing time-consuming domain integrations by approximating a ``generalized forcing function`` in the interior of the domain with the use of radial basis functions. An approximate particular solution is then constructed, and the original problem is transformed into a sequence of Laplace problems. The code is capable of handling a large variety of boundary conditions including isothermal, specified flux, convection, radiation, and combined convection and radiation conditions. The computer code is benchmarked by comparisons with analytic and finite element results.
NASA Technical Reports Server (NTRS)
Perucchio, R.; Ingraffea, A. R.
1984-01-01
The establishment of the boundary element method (BEM) as a valid tool for solving problems in structural mechanics and in other fields of applied physics is discussed. The development of an integrated interactive computer graphic system for the application of the BEM to three dimensional problems in elastostatics is described. The integration of interactive computer graphic techniques and the BEM takes place at the preprocessing and postprocessing stages of the analysis process, when, respectively, the data base is generated and the results are interpreted. The interactive computer graphic modeling techniques used for generating and discretizing the boundary surfaces of a solid domain are outlined.
NASA Technical Reports Server (NTRS)
Perucchio, R.; Ingraffea, A. R.
1984-01-01
The establishment of the boundary element method (BEM) as a valid tool for solving problems in structural mechanics and in other fields of applied physics is discussed. The development of an integrated interactive computer graphic system for the application of the BEM to three dimensional problems in elastostatics is described. The integration of interactive computer graphic techniques and the BEM takes place at the preprocessing and postprocessing stages of the analysis process, when, respectively, the data base is generated and the results are interpreted. The interactive computer graphic modeling techniques used for generating and discretizing the boundary surfaces of a solid domain are outlined.
NASA Technical Reports Server (NTRS)
Walston, W. H., Jr.
1986-01-01
The comparative computational efficiencies of the finite element (FEM), boundary element (BEM), and hybrid boundary element-finite element (HVFEM) analysis techniques are evaluated for representative bounded domain interior and unbounded domain exterior problems in elastostatics. Computational efficiency is carefully defined in this study as the computer time required to attain a specified level of solution accuracy. The study found the FEM superior to the BEM for the interior problem, while the reverse was true for the exterior problem. The hybrid analysis technique was found to be comparable or superior to both the FEM and BEM for both the interior and exterior problems.
Yuan, Dajing; Bakker, Eric
2017-08-01
Finite difference analysis of ion-selective membranes is a valuable tool for understanding a range of time dependent phenomena such as response times, long and medium term potential drifts, determination of selectivity, and (re)conditioning kinetics. It is here shown that an established approach based on the diffusion layer model applied to an ion-exchange membrane fails to use mass transport to account for concentration changes at the membrane side of the phase boundary. Instead, such concentrations are imposed by the ion-exchange equilibrium condition, without taking into account the source of these ions. The limitation is illustrated with a super-Nernstian potential jump, where a membrane initially void of analyte ion is exposed to incremental concentrations of analyte in the sample. To overcome this limitation, the two boundary elements, one at either side of the sample-membrane interface, are treated here as a combined entity and its total concentration change is dictated by diffusional fluxes into and out of the interface. For each time step, the concentration distribution between the two boundary elements is then computed by ion-exchange theory. The resulting finite difference simulation is much more robust than the earlier model and gives a good correlation to experiments.
Gravenkamp, Hauke; Birk, Carolin; Song, Chongmin
2014-07-01
This paper addresses the computation of dispersion curves and mode shapes of elastic guided waves in axisymmetric waveguides. The approach is based on a Scaled Boundary Finite Element formulation, that has previously been presented for plate structures and general three-dimensional waveguides with complex cross-section. The formulation leads to a Hamiltonian eigenvalue problem for the computation of wavenumbers and displacement amplitudes, that can be solved very efficiently. In the axisymmetric representation, only the radial direction in a cylindrical coordinate system has to be discretized, while the circumferential direction as well as the direction of propagation are described analytically. It is demonstrated, how the computational costs can drastically be reduced by employing spectral elements of extremely high order. Additionally, an alternative formulation is presented, that leads to real coefficient matrices. It is discussed, how these two approaches affect the computational efficiency, depending on the elasticity matrix. In the case of solid cylinders, the singularity of the governing equations that occurs in the center of the cross-section is avoided by changing the quadrature scheme. Numerical examples show the applicability of the approach to homogeneous as well as layered structures with isotropic or anisotropic material behavior.
Aragon, Sergio; Hahn, David K.
2006-01-01
A precise boundary element method for the computation of hydrodynamic properties has been applied to the study of a large suite of 41 soluble proteins ranging from 6.5 to 377 kDa in molecular mass. A hydrodynamic model consisting of a rigid protein excluded volume, obtained from crystallographic coordinates, surrounded by a uniform hydration thickness has been found to yield properties in excellent agreement with experiment. The hydration thickness was determined to be δ = 1.1 ± 0.1 Å. Using this value, standard deviations from experimental measurements are: 2% for the specific volume; 2% for the translational diffusion coefficient, and 6% for the rotational diffusion coefficient. These deviations are comparable to experimental errors in these properties. The precision of the boundary element method allows the unified description of all of these properties with a single hydration parameter, thus far not achieved with other methods. An approximate method for computing transport properties with a statistical precision of 1% or better (compared to 0.1–0.2% for the full computation) is also presented. We have also estimated the total amount of hydration water with a typical −9% deviation from experiment in the case of monomeric proteins. Both the water of hydration and the more precise translational diffusion data hint that some multimeric proteins may not have the same solution structure as that in the crystal because the deviations are systematic and larger than in the monomeric case. On the other hand, the data for monomeric proteins conclusively show that there is no difference in the protein structure going from the crystal into solution. PMID:16714342
Cheng, J Y; Chahine, G L
2001-12-01
The slender body theory, lifting surface theories, and more recently panel methods and Navier-Stokes solvers have been used to study the hydrodynamics of fish swimming. This paper presents progress on swimming hydrodynamics using a boundary integral equation method (or boundary element method) based on potential flow model. The unsteady three-dimensional BEM code 3DynaFS that we developed and used is able to model realistic body geometries, arbitrary movements, and resulting wake evolution. Pressure distribution over the body surface, vorticity in the wake, and the velocity field around the body can be computed. The structure and dynamic behavior of the vortex wakes generated by the swimming body are responsible for the underlying fluid dynamic mechanisms to realize the high-efficiency propulsion and high-agility maneuvering. Three-dimensional vortex wake structures are not well known, although two-dimensional structures termed 'reverse Karman Vortex Street' have been observed and studied. In this paper, simulations about a swimming saithe (Pollachius virens) using our BEM code have demonstrated that undulatory swimming reduces three-dimensional effects due to substantially weakened tail tip vortex, resulting in a reverse Karman Vortex Street as the major flow pattern in the three-dimensional wake of an undulating swimming fish.
Probabilistic boundary element method
NASA Technical Reports Server (NTRS)
Cruse, T. A.; Raveendra, S. T.
1989-01-01
The purpose of the Probabilistic Structural Analysis Method (PSAM) project is to develop structural analysis capabilities for the design analysis of advanced space propulsion system hardware. The boundary element method (BEM) is used as the basis of the Probabilistic Advanced Analysis Methods (PADAM) which is discussed. The probabilistic BEM code (PBEM) is used to obtain the structural response and sensitivity results to a set of random variables. As such, PBEM performs analogous to other structural analysis codes such as finite elements in the PSAM system. For linear problems, unlike the finite element method (FEM), the BEM governing equations are written at the boundary of the body only, thus, the method eliminates the need to model the volume of the body. However, for general body force problems, a direct condensation of the governing equations to the boundary of the body is not possible and therefore volume modeling is generally required.
Wright, Louise; Robinson, Stephen P; Humphrey, Victor F
2009-03-01
This paper presents a computational technique using the boundary element method for prediction of radiated acoustic waves from axisymmetric surfaces with nonaxisymmetric boundary conditions. The aim is to predict the far-field behavior of underwater acoustic transducers based on their measured behavior in the near-field. The technique is valid for all wavenumbers and uses a volume integral method to calculate the singular integrals required by the boundary element formulation. The technique has been implemented on a distributed computing system to take advantage of its parallel nature, which has led to significant reductions in the time required to generate results. Measurement data generated by a pair of free-flooding underwater acoustic transducers encapsulated in a polyurethane polymer have been used to validate the technique against experiment. The dimensions of the outer surface of the transducers (including the polymer coating) were an outer diameter of 98 mm with an 18 mm wall thickness and a length of 92 mm. The transducers were mounted coaxially, giving an overall length of 185 mm. The cylinders had resonance frequencies at 13.9 and 27.5 kHz, and the data were gathered at these frequencies.
Program Helps Generate Boundary-Element Mathematical Models
NASA Technical Reports Server (NTRS)
Goldberg, R. K.
1995-01-01
Composite Model Generation-Boundary Element Method (COM-GEN-BEM) computer program significantly reduces time and effort needed to construct boundary-element mathematical models of continuous-fiber composite materials at micro-mechanical (constituent) scale. Generates boundary-element models compatible with BEST-CMS boundary-element code for anlaysis of micromechanics of composite material. Written in PATRAN Command Language (PCL).
Program Helps Generate Boundary-Element Mathematical Models
NASA Technical Reports Server (NTRS)
Goldberg, R. K.
1995-01-01
Composite Model Generation-Boundary Element Method (COM-GEN-BEM) computer program significantly reduces time and effort needed to construct boundary-element mathematical models of continuous-fiber composite materials at micro-mechanical (constituent) scale. Generates boundary-element models compatible with BEST-CMS boundary-element code for anlaysis of micromechanics of composite material. Written in PATRAN Command Language (PCL).
Introducing the Boundary Element Method with MATLAB
ERIC Educational Resources Information Center
Ang, Keng-Cheng
2008-01-01
The boundary element method provides an excellent platform for learning and teaching a computational method for solving problems in physical and engineering science. However, it is often left out in many undergraduate courses as its implementation is deemed to be difficult. This is partly due to the perception that coding the method requires…
Introducing the Boundary Element Method with MATLAB
ERIC Educational Resources Information Center
Ang, Keng-Cheng
2008-01-01
The boundary element method provides an excellent platform for learning and teaching a computational method for solving problems in physical and engineering science. However, it is often left out in many undergraduate courses as its implementation is deemed to be difficult. This is partly due to the perception that coding the method requires…
Boundary elements for structural analysis
NASA Technical Reports Server (NTRS)
1989-01-01
The intent here is to discuss the status of the boundary element method (BEM) for structural analysis, both in terms of the present and anticipated capabilities of the method and in terms of the incorporation of the method in the design/analysis process, particularly for gas turbine engine components.
The boundary element method in enginering practice
NASA Astrophysics Data System (ADS)
Brebbia, C. A.
1984-03-01
In order to eliminate the need for complex geometric definitions when working with three dimensional engineering problems, boundary element methods are presented which are applicable to a number of different common three dimensional engineering problems. Some of the general advantages of boundary element methods over domain methods in computer analysis and design are described, including simpler data preparation; greater accuracy in solving infinite or semi-infinite problems; more accurate results for stress and flux variables; and internal results for only the points where they are needed. Some representative applications of boundary element methods are: for thermo-elastic analysis; cathodic protection solutions; ideal elastoplasicity problems; tunnelling problems; time dependent heart transfer analysis; membrane vibrations; and free vibrations of a shear wall.
Gumerov, Nail A; O'Donovan, Adam E; Duraiswami, Ramani; Zotkin, Dmitry N
2010-01-01
The head-related transfer function (HRTF) is computed using the fast multipole accelerated boundary element method. For efficiency, the HRTF is computed using the reciprocity principle by placing a source at the ear and computing its field. Analysis is presented to modify the boundary value problem accordingly. To compute the HRTF corresponding to different ranges via a single computation, a compact and accurate representation of the HRTF, termed the spherical spectrum, is developed. Computations are reduced to a two stage process, the computation of the spherical spectrum and a subsequent evaluation of the HRTF. This representation allows easy interpolation and range extrapolation of HRTFs. HRTF computations are performed for the range of audible frequencies up to 20 kHz for several models including a sphere, human head models [the Neumann KU-100 ("Fritz") and the Knowles KEMAR ("Kemar") manikins], and head-and-torso model (the Kemar manikin). Comparisons between the different cases are provided. Comparisons with the computational data of other authors and available experimental data are conducted and show satisfactory agreement for the frequencies for which reliable experimental data are available. Results show that, given a good mesh, it is feasible to compute the HRTF over the full audible range on a regular personal computer.
Composite micromechanical modeling using the boundary element method
NASA Technical Reports Server (NTRS)
Goldberg, Robert K.; Hopkins, Dale A.
1993-01-01
The use of the boundary element method for analyzing composite micromechanical behavior is demonstrated. Stress-strain, heat conduction, and thermal expansion analyses are conducted using the boundary element computer code BEST-CMS, and the results obtained are compared to experimental observations, analytical calculations, and finite element analyses. For each of the analysis types, the boundary element results agree reasonably well with the results from the other methodologies, with explainable discrepancies. Overall, the boundary element method shows promise in providing an alternative method to analyze composite micromechanical behavior.
Boundary elements and surface plasmons
Goloskie, R.; Thio, T.; Ram-Mohan, L.R.
1996-09-01
We present an elementary introduction to the boundary element method (BEM). We use the BEM to calculate the electromagnetic field enhancements in the vicinity of metallic wires of arbitrary cross-section. The local electric field shows resonant peaks, as a function of the frequency of incident radiation, at the natural frequencies of the electronic plasma in the wires. We consider the effect of the shape of the cross-section of the wire on the resonant frequency, the proximity effect due to neighboring wires, and the influence of a substrate. The calculations are performed using enhanced continuity conditions at the boundaries. We discuss the advantages of such an approach. The field enhancements are predicted for a number of geometries. {copyright} {ital 1996 American Institute of Physics.}
Boundary element solution for periodic acoustic problems
NASA Astrophysics Data System (ADS)
Karimi, M.; Croaker, P.; Kessissoglou, N.
2016-01-01
This work shows when using the boundary element method to solve 3D acoustic scattering problems from periodic structures, the coefficient matrix can be represented as a block Toeplitz matrix. By exploiting the Toeplitz structure, the computational time and storage requirements to construct the coefficient matrix are significantly reduced. To solve the linear system of equations, the original matrix is embedded into a larger and more structured matrix called the block circulant matrix. Discrete Fourier transform is then employed in an iterative algorithm to solve the block Toeplitz system. To demonstrate the effectiveness of the formulation for periodic acoustic problems, two exterior acoustic case studies are considered. The first case study examines a continuous structure to predict the noise generated by a sharp-edged flat plate under quadrupole excitation. Directivity plots obtained using the periodic boundary element method technique are compared with numerical results obtained using a conventional boundary element model. The second case study examines a discrete periodic structure to predict the acoustic performance of a sonic crystal noise barrier. Results for the barrier insertion loss are compared with both finite element results and available data in the literature.
Design sensitivity analysis of boundary element substructures
NASA Technical Reports Server (NTRS)
Kane, James H.; Saigal, Sunil; Gallagher, Richard H.
1989-01-01
The ability to reduce or condense a three-dimensional model exactly, and then iterate on this reduced size model representing the parts of the design that are allowed to change in an optimization loop is discussed. The discussion presents the results obtained from an ongoing research effort to exploit the concept of substructuring within the structural shape optimization context using a Boundary Element Analysis (BEA) formulation. The first part contains a formulation for the exact condensation of portions of the overall boundary element model designated as substructures. The use of reduced boundary element models in shape optimization requires that structural sensitivity analysis can be performed. A reduced sensitivity analysis formulation is then presented that allows for the calculation of structural response sensitivities of both the substructured (reduced) and unsubstructured parts of the model. It is shown that this approach produces significant computational economy in the design sensitivity analysis and reanalysis process by facilitating the block triangular factorization and forward reduction and backward substitution of smaller matrices. The implementatior of this formulation is discussed and timings and accuracies of representative test cases presented.
Periodic Boundary Conditions in the ALEGRA Finite Element Code
AIDUN,JOHN B.; ROBINSON,ALLEN C.; WEATHERBY,JOE R.
1999-11-01
This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given.
Advanced three-dimensional dynamic analysis by boundary element methods
NASA Technical Reports Server (NTRS)
Banerjee, P. K.; Ahma, S.
1985-01-01
Advanced formulations of boundary element method for periodic, transient transform domain and transient time domain solution of three-dimensional solids have been implemented using a family of isoparametric boundary elements. The necessary numerical integration techniques as well as the various solution algorithms are described. The developed analysis has been incorporated in a fully general purpose computer program BEST3D which can handle up to 10 subregions. A number of numerical examples are presented to demonstrate the accuracy of the dynamic analyses.
Advanced three-dimensional dynamic analysis by boundary element methods
NASA Technical Reports Server (NTRS)
Banerjee, P. K.; Ahma, S.
1985-01-01
Advanced formulations of boundary element method for periodic, transient transform domain and transient time domain solution of three-dimensional solids have been implemented using a family of isoparametric boundary elements. The necessary numerical integration techniques as well as the various solution algorithms are described. The developed analysis has been incorporated in a fully general purpose computer program BEST3D which can handle up to 10 subregions. A number of numerical examples are presented to demonstrate the accuracy of the dynamic analyses.
Boundary element analysis of post-tensioned slabs
NASA Astrophysics Data System (ADS)
Rashed, Youssef F.
2015-06-01
In this paper, the boundary element method is applied to carry out the structural analysis of post-tensioned flat slabs. The shear-deformable plate-bending model is employed. The effect of the pre-stressing cables is taken into account via the equivalent load method. The formulation is automated using a computer program, which uses quadratic boundary elements. Verification samples are presented, and finally a practical application is analyzed where results are compared against those obtained from the finite element method. The proposed method is efficient in terms of computer storage and processing time as well as the ease in data input and modifications.
Solution of exterior acoustic problems by the boundary element method
NASA Astrophysics Data System (ADS)
Kirkup, Stephen Martin
The boundary element method is described and investigated, especially in respect of its application to exterior two-dimensional Laplace problems. Both empirical and algebraic analyses (including the effects of approximation of the boundary and boundary functions and the precision of the evaluation of the discrete forms) are developed. Methods for the automatic evaluation of the discrete forms of the Laplace and Helmholtz integral operators are reviewed and extended. Boundary element methods for the solution of exterior Helmholtz problems with general (but most importantly Neumann) boundary conditions are reviewed and some are explicitly stated using a new notation. Boundary element methods based on the boundary integral equations introduced by Brakhage and Werner/Leis/Panich/Kussmaul (indirect) and Burton and Miller (direct) are given prime consideration and implemented for three-dimensional problems. The influence of the choice of weighting parameter on the performance of the methods is explored and further guidance is given. The application of boundary element methods and methods based on the Rayleigh integral to acoustic radiation problems are considered. Methods for speeding up their solution via the boundary element method are developed. Library subroutines for the solution of acoustic radiation problems are described and demonstrated. Computational techniques for the problem of predicting the noise produced by a running engine are reviewed and appraised. The application of the boundary element method to low-noise engine design and in the design of noise shields is considered. The boundary element method is applied to the Ricardo crankcase simulation rig, which is an engine-like structure. A comparison of predicted and measured sound power spectra is given.
Solution of Exterior Acoustic Problems by the Boundary Element Method.
NASA Astrophysics Data System (ADS)
Kirkup, Stephen Martin
Available from UMI in association with The British Library. The boundary element method is described and investigated, especially in respect of its application to exterior two -dimensional Laplace problems. Both empirical and algebraic analyses (including the effects of approximation of the boundary and boundary functions and the precision of the evaluation of the discrete forms) are developed. Methods for the automatic evaluation of the discrete forms of the Laplace and Helmholtz integral operators are reviewed and extended. Boundary element methods for the solution of exterior Helmholtz problems with general (but most importantly Neumann) boundary conditions are reviewed and some are explicitly stated using a new notation. Boundary element methods based on the boundary integral equations introduced by Brakhage & Werner/ Leis/ Panich/ Kussmaul (indirect) and Burton & Miller (direct) are given prime consideration and implemented for three -dimensional problems. The influence of the choice of weighting parameter on the performance of the methods is explored and further guidance is given. The application of boundary element methods and methods based on the Rayleigh integral to acoustic radiation problems are considered. Methods for speeding up their solution via the boundary element method are developed. Library subroutines for the solution of acoustic radiation problems are described and demonstrated. Computational techniques for the problem of predicting the noise produced by a running engine are reviewed and appraised. The application of the boundary element method to low-noise engine design and in the design of noise shields is considered. The boundary element method is applied to the Ricardo crankcase simulation rig, which is an engine -like structure. A comparison of predicted and measured sound power spectra is given.
(Environmental and geophysical modeling, fracture mechanics, and boundary element methods)
Gray, L.J.
1990-11-09
Technical discussions at the various sites visited centered on application of boundary integral methods for environmental modeling, seismic analysis, and computational fracture mechanics in composite and smart'' materials. The traveler also attended the International Association for Boundary Element Methods Conference at Rome, Italy. While many aspects of boundary element theory and applications were discussed in the papers, the dominant topic was the analysis and application of hypersingular equations. This has been the focus of recent work by the author, and thus the conference was highly relevant to research at ORNL.
Boundary-element shape sensitivity analysis for thermal problems with nonlinear boundary conditions
NASA Technical Reports Server (NTRS)
Kane, James H.; Wang, Hua
1991-01-01
Implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solid objects subjected to nonlinear boundary conditions is shown to generate an accurate and economical approach for the computation of shape sensitivities for this class of problems. This approach involves the employment of analytical derivatives of boundary-element kernel functions with respect to shape design variables. A formulation is presented that can consistently account for both temperature-dependent convection and radiation boundary conditions. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems are presented that have closed-form solutions.
COMPLEX VARIABLE BOUNDARY ELEMENT METHOD: APPLICATIONS.
Hromadka, T.V.; Yen, C.C.; Guymon, G.L.
1985-01-01
The complex variable boundary element method (CVBEM) is used to approximate several potential problems where analytical solutions are known. A modeling result produced from the CVBEM is a measure of relative error in matching the known boundary condition values of the problem. A CVBEM error-reduction algorithm is used to reduce the relative error of the approximation by adding nodal points in boundary regions where error is large. From the test problems, overall error is reduced significantly by utilizing the adaptive integration algorithm.
An inverse problem by boundary element method
Tran-Cong, T.; Nguyen-Thien, T.; Graham, A.L.
1996-02-01
Boundary Element Methods (BEM) have been established as useful and powerful tools in a wide range of engineering applications, e.g. Brebbia et al. In this paper, we report a particular three dimensional implementation of a direct boundary integral equation (BIE) formulation and its application to numerical simulations of practical polymer processing operations. In particular, we will focus on the application of the present boundary element technology to simulate an inverse problem in plastics processing.by extrusion. The task is to design profile extrusion dies for plastics. The problem is highly non-linear due to material viscoelastic behaviours as well as unknown free surface conditions. As an example, the technique is shown to be effective in obtaining the die profiles corresponding to a square viscoelastic extrudate under different processing conditions. To further illustrate the capability of the method, examples of other non-trivial extrudate profiles and processing conditions are also given.
Efficient elastoplastic analysis with the boundary element method
NASA Astrophysics Data System (ADS)
Ribeiro, T. S. A.; Beer, G.; Duenser, C.
2008-02-01
Conventional numerical implementation of the boundary element method (BEM) for elasto-plastic analysis requires a domain discretization into cells. This requires more effort for the discretization of the problem and additional computational effort. A new technique is proposed here for the analysis of 2D and 3D elasto-plastic problems with the boundary element method. In this approach the domain does not need to be discretised into cells prior to the analysis. Plasticity is assumed to start from the boundary and the cells are generated from the boundary data automatically during the analysis. Using the cell generation process, elasto-plastic analysis with the BEM becomes much more user friendly and efficient than the standard approach with a pre-definition of cells. The accuracy and efficiency of the solution obtained by the new approach is verified by several numerical examples.
On modelling three-dimensional piezoelectric smart structures with boundary spectral element method
NASA Astrophysics Data System (ADS)
Zou, Fangxin; Aliabadi, M. H.
2017-05-01
The computational efficiency of the boundary element method in elastodynamic analysis can be significantly improved by employing high-order spectral elements for boundary discretisation. In this work, for the first time, the so-called boundary spectral element method is utilised to formulate the piezoelectric smart structures that are widely used in structural health monitoring (SHM) applications. The resultant boundary spectral element formulation has been validated by the finite element method (FEM) and physical experiments. The new formulation has demonstrated a lower demand on computational resources and a higher numerical stability than commercial FEM packages. Comparing to the conventional boundary element formulation, a significant reduction in computational expenses has been achieved. In summary, the boundary spectral element formulation presented in this paper provides a highly efficient and stable mathematical tool for the development of SHM applications.
A dual reciprocal boundary element formulation for viscous flows
NASA Technical Reports Server (NTRS)
Lafe, Olu
1993-01-01
The advantages inherent in the boundary element method (BEM) for potential flows are exploited to solve viscous flow problems. The trick is the introduction of a so-called dual reciprocal technique in which the convective terms are represented by a global function whose unknown coefficients are determined by collocation. The approach, which is necessarily iterative, converts the governing partial differential equations into integral equations via the distribution of fictitious sources or dipoles of unknown strength on the boundary. These integral equations consist of two parts. The first is a boundary integral term, whose kernel is the unknown strength of the fictitious sources and the fundamental solution of a convection-free flow problem. The second part is a domain integral term whose kernel is the convective portion of the governing PDEs. The domain integration can be transformed to the boundary by using the dual reciprocal (DR) concept. The resulting formulation is a pure boundary integral computational process.
Supervised learning method for predicting chromatin boundary associated insulator elements.
Bednarz, Paweł; Wilczyński, Bartek
2014-12-01
In eukaryotic cells, the DNA material is densely packed inside the nucleus in the form of a DNA-protein complex structure called chromatin. Since the actual conformation of the chromatin fiber defines the possible regulatory interactions between genes and their regulatory elements, it is very important to understand the mechanisms governing folding of chromatin. In this paper, we show that supervised methods for predicting chromatin boundary elements are much more effective than the currently popular unsupervised methods. Using boundary locations from published Hi-C experiments and modEncode tracks as features, we can tell the insulator elements from randomly selected background sequences with great accuracy. In addition to accurate predictions of the training boundary elements, our classifiers make new predictions. Many of them correspond to the locations of known insulator elements. The key features used for predicting boundary elements do not depend on the prediction method. Because of its miniscule size, chromatin state cannot be measured directly, we need to rely on indirect measurements, such as ChIP-Seq and fill in the gaps with computational models. Our results show that currently, at least in the model organisms, where we have many measurements including ChIP-Seq and Hi-C, we can make accurate predictions of insulator positions.
Boundary element modeling of the external human auditory system
NASA Astrophysics Data System (ADS)
Walsh, Timothy; Demkowicz, Leszek; Charles, Richard
2004-03-01
In this paper the response of the external auditory system to acoustical waves of varying frequencies and angles of incidence is computed using a boundary element method. The resonance patterns of both the ear canal and the concha are computed and compared with experimental data. Specialized numerical algorithms are developed that allow for the efficient computation of the eardrum pressures. In contrast to previous results in the literature that consider only the ``blocked meatus'' configuration, in this work the simulations are conducted on a boundary element mesh that includes both the external head/ear geometry, as well as the ear canal and eardrum. The simulation technology developed in this work is intended to demonstrate the utility of numerical analysis in studying physical phenomena related to the external auditory system. Later work could extend this towards simulating in situ hearing aids, and possibly using the simulations as a tool for optimizing hearing aid technologies for particular individuals.
A Navier-Stokes boundary element solver
NASA Technical Reports Server (NTRS)
Reddy, D. R.; Lafe, O.; Cheng, A. H-D.
1995-01-01
Using global interpolation functions (GIF's) boundary element solutions are obtained for two-dimensional laminar flows. Two schemes are proposed for handling the convective terms. The first treats convection as a forcing function, and converts the flow equations to pseudo-Poisson equations. In the second scheme, some convective effect is incorporated into the fundamental solution used in constructing the pertinent integral equations. The lid-driven cavity flow is selected as the benchmark problem.
A posteriori pointwise error estimates for the boundary element method
Paulino, G.H.; Gray, L.J.; Zarikian, V.
1995-01-01
This report presents a new approach for a posteriori pointwise error estimation in the boundary element method. The estimator relies upon the evaluation of hypersingular integral equations, and is therefore intrinsic to the boundary integral equation approach. This property allows some theoretical justification by mathematically correlating the exact and estimated errors. A methodology is developed for approximating the error on the boundary as well as in the interior of the domain. In the interior, error estimates for both the function and its derivatives (e.g. potential and interior gradients for potential problems, displacements and stresses for elasticity problems) are presented. Extensive computational experiments have been performed for the two dimensional Laplace equation on interior domains, employing Dirichlet and mixed boundary conditions. The results indicate that the error estimates successfully track the form of the exact error curve. Moreover, a reasonable estimate of the magnitude of the actual error is also obtained.
Mean Flow Boundary Conditions for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Hixon, R.; Nallasamy, M.; Sawyer, S.; Dyson, R.
2003-01-01
In this work, a new type of boundary condition for time-accurate Computational Aeroacoustics solvers is described. This boundary condition is designed to complement the existing nonreflective boundary conditions while ensuring that the correct mean flow conditions are maintained throughout the flow calculation. Results are shown for a loaded 2D cascade, started with various initial conditions.
An hp-adaptive finite element/boundary element coupling method for electromagnetic problems
NASA Astrophysics Data System (ADS)
Stephan, E. P.; Maischak, M.; Leydecker, F.
2007-04-01
We present an hp-version of the finite element / boundary element coupling method to solve the eddy current problem for the time-harmonic Maxwell’s equations. We use H(curl, Ω -conforming vector-valued polynomials to approximate the electric field in the conductor Ω and surface curls of continuous piecewise polynomials on the boundary Γ of Ω to approximate the twisted tangential trace of the magnetic field on Γ. We present both a priori and a posteriori error estimates together with a three-fold hp-adaptive algorithm to compute the fem/bem coupling solution with appropriate distributions of polynomial degrees on suitably refined meshes.
Baradari, F.
1982-01-01
In this work the applicability of a ''Boundary Element method'' for the numerical solution of the Liouville and Helmholtz eigenvalue problem for different two dimensional geometries including a typical reactor configuration was investigated. The method is based on the discretization of the unknown along the boundary and Green's function representation of the governing equation. To compare the capability of this method with the finite element method, a finite element code which uses quadratic quadrilateral isoparametric elements was developed. A boundary element code was also written. These codes were used to determine the fundamental eigenvalue for several two dimensional geometries--square, ''L'' shaped, circular, and a quarter of a typical reactor core. The results of both codes were compared with each other and with analytical solutions where available. To optimize the computer time for the code based on the boundary element method, a powerful search technique called Fibonacci search was used to determine the fundamental eigenvalues. During the course of this study, it was found that eliminating the imaginary part of the fundamental solution of the Helmholtz equation produced an instability in the result. The results show that, due to the use of the iteration procedure in the boundary element method to evaluate the determinant of the deduced matrix, more computer time is required for the boundary element solution than the finite element solution. However, the results obtained on the basis of the boundary element technique are more accurate than those from the finite element method.
A boundary element method for steady incompressible thermoviscous flow
NASA Technical Reports Server (NTRS)
Dargush, G. F.; Banerjee, P. K.
1991-01-01
A boundary element formulation is presented for moderate Reynolds number, steady, incompressible, thermoviscous flows. The governing integral equations are written exclusively in terms of velocities and temperatures, thus eliminating the need for the computation of any gradients. Furthermore, with the introduction of reference velocities and temperatures, volume modeling can often be confined to only a small portion of the problem domain, typically near obstacles or walls. The numerical implementation includes higher order elements, adaptive integration and multiregion capability. Both the integral formulation and implementation are discussed in detail. Several examples illustrate the high level of accuracy that is obtainable with the current method.
ERIC Educational Resources Information Center
Edwards, Judith B.; And Others
This textbook is intended to provide students with an awareness of the possible alternatives in the computer field and with the background information necessary for them to evaluate those alternatives intelligently. Problem solving and simulated work experiences are emphasized as students are familiarized with the functions and limitations of…
A combined finite element-boundary element formulation for solution of axially symmetric bodies
NASA Technical Reports Server (NTRS)
Collins, Jeffrey D.; Volakis, John L.
1991-01-01
A new method is presented for the computation of electromagnetic scattering from axially symmetric bodies. To allow the simulation of inhomogeneous cross sections, the method combines the finite element and boundary element techniques. Interior to a fictitious surface enclosing the scattering body, the finite element method is used which results in a sparce submatrix, whereas along the enclosure the Stratton-Chu integral equation is enforced. By choosing the fictitious enclosure to be a right circular cylinder, most of the resulting boundary integrals are convolutional and may therefore be evaluated via the FFT with which the system is iteratively solved. In view of the sparce matrix associated with the interior fields, this reduces the storage requirement of the entire system to O(N) making the method attractive for large scale computations. The details of the corresponding formulation and its numerical implementation are described.
Plate stability by boundary element method
Elzein, A.; Brebbia, C.A.; Orszag, S.A.
1991-12-31
As indicated by the title, this publication is devoted to the application of the Boundary Element Method (BEM) to the analysis of elastic plastes subjected to inplane forces. Three classes of plate problems associated with the buckling phenomenon are considered, viz: The state of plane stress, buckling of plates caused by edge loads, and moderately large deflections of slightly warped plates. The first (introductory) chapter gives an historical background and the behavior, theory, and analyses of plates. Chapter 2 briefly comments on the phenomenon of buckling and clearly presents the universal expressions and equations of the linear and nonlinear theories established by Kirchhoff for thin plates. A prominent place is assigned to the airy plane-stress function introduced into the nonlinear flexural theory of plates by A Foeppl and Th von Karman.
Comparison of boundary element and finite element methods in spur gear root stress analysis
NASA Technical Reports Server (NTRS)
Sun, H.; Mavriplis, D.; Huston, R. L.; Oswald, F. B.
1989-01-01
The boundary element method (BEM) is used to compute fillet stress concentration in spur gear teeth. The results are shown to compare favorably with analogous results obtained using the finite element method (FEM). A partially supported thin rim gear is studied. The loading is applied at the pitch point. A three-dimensional analysis is conducted using both the BEM and FEM (NASTRAN). The results are also compared with those of a two-dimensional finite element model. An advantage of the BEM over the FEM is that fewer elements are needed with the BEM. Indeed, in the current study the BEM used 92 elements and 270 nodes whereas the FEM used 320 elements and 2037 nodes. Moreover, since the BEM is especially useful in problems with high stress gradients it is potentially a very useful tool for fillet stress analyses.
The boundary element method in stress-state problems for an ansiotropic plate with holes
Neskorodev, N.M.
1995-12-25
We propose a method of solving the problem of the stress state of an anisotropic plate with holes of arbitrary shape. The method is based on approximating the boundary of a region by curved boundary elements. These elements are taken to be a family of semi-ellipses. To satisfy the boundary conditions we use the pointwise least-square method. Numerical experiments showed good agreement of the computations with results known earlier.
Comparative efficiency of finite, boundary and hybrid element methods in elastostatics
NASA Technical Reports Server (NTRS)
Schwartz, C. W.; Lee, C. W.
1986-01-01
The comparative computational efficiencies of the finite element (FEM), boundary element (BEM), and hybrid boundary element-finite element (HBFEM) analysis techniques are evaluated for representative bounded domain interior and unbounded domain exterior problems in elastostatics. Computational efficiency is carefully defined in this study as the computer time required to attain a specified level of solution accuracy. The study found the FEM superior to the BEM for the interior problem, while the reverse was true for the exterior problem. The hybrid analysis technique was found to be comparable or superior to both the FEM and BEM for both the interior and exterior problems.
The Numerical Computation of Three-Dimensional Turbulent Boundary Layers.
1982-04-01
begin by saying what an honour and a pleasure it is for me t," this review lecture. To some extent my pleasure is enhanced by a sense of deja vu as...A.J. Baker Finite element solution theory tor three-dimensional boundary flows. Computer Methods in Applied Mechanics and Engineering, Vol.4, pp.367-386
Boundary Conditions for Jet Flow Computations
NASA Technical Reports Server (NTRS)
Hayder, M. E.; Turkel, E.
1994-01-01
Ongoing activities are focused on capturing the sound source in a supersonic jet through careful large eddy simulation (LES). One issue that is addressed is the effect of the boundary conditions, both inflow and outflow, on the predicted flow fluctuations, which represent the sound source. In this study, we examine the accuracy of several boundary conditions to determine their suitability for computations of time-dependent flows. Various boundary conditions are used to compute the flow field of a laminar axisymmetric jet excited at the inflow by a disturbance given by the corresponding eigenfunction of the linearized stability equations. We solve the full time dependent Navier-Stokes equations by a high order numerical scheme. For very small excitations, the computed growth of the modes closely corresponds to that predicted by the linear theory. We then vary the excitation level to see the effect of the boundary conditions in the nonlinear flow regime.
Chromatin domain boundary element search tool for Drosophila
Srinivasan, Arumugam; Mishra, Rakesh K.
2012-01-01
Chromatin domain boundary elements prevent inappropriate interaction between distant or closely spaced regulatory elements and restrict enhancers and silencers to correct target promoters. In spite of having such a general role and expected frequent occurrence genome wide, there is no DNA sequence analysis based tool to identify boundary elements. Here, we report chromatin domain Boundary Element Search Tool (cdBEST), to identify boundary elements. cdBEST uses known recognition sequences of boundary interacting proteins and looks for ‘motif clusters’. Using cdBEST, we identified boundary sequences across 12 Drosophila species. Of the 4576 boundary sequences identified in Drosophila melanogaster genome, >170 sequences are repetitive in nature and have sequence homology to transposable elements. Analysis of such sequences across 12 Drosophila genomes showed that the occurrence of repetitive sequences in the context of boundaries is a common feature of drosophilids. We use a variety of genome organization criteria and also experimental test on a subset of the cdBEST boundaries in an enhancer-blocking assay and show that 80% of them indeed function as boundaries in vivo. These observations highlight the role of cdBEST in better understanding of chromatin domain boundaries in Drosophila and setting the stage for comparative analysis of boundaries across closely related species. PMID:22287636
Finite element computational fluid mechanics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
Finite element computational fluid mechanics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
Volume dependence of computed grain boundary energy
Bristowe, P.D.; Brokman, A.
1980-08-01
Over the past five years there have been numerous studies of grain boundary structure using the method of computer molecular statics which assume pairwise central potentials for the interatomic interaction. Emphasis is usually placed on relative grain boundary energies but these may be inaccurate due to various, but related, approximations and constraints implicity imposed on the calculation-namely central forces, finite model size, fixed border conditions and volume dependent contributions to the energy of the system. It is the purpose of this work to clarify how these particular properties of the model can affect the computed grain boundary energy and demonstrate instances in which the quoted energy has strictly been inaccurate. The implication of these results, especially on how they affect the method of relaxation and the resulting grain boundary structure is discussed.
Boundary element modeling of nondissipative and dissipative waves
Chen, Genmeng; Zhou, Huawei
1994-01-01
A boundary element (BE) algorithm is developed to compute acoustic or SH-waves in models consisting of limited or unlimited volumes and irregular interfaces. The authors solve the BE system in the frequency domain so that anelasticity can be easily represented by different viscoelastic models, such as the Kelvin-Voigt type. Three illustrative computations are shown. The waveform given by the BE method for a circular inclusion model agrees well with that given by the finite-difference (FD) method. Dissipation of waves at high frequency caused by the presence of multi-cracks in an elastic medium resembles the masking effect of anelasticity. The waveforms for nondissipative and dissipative models containing hexagonal inclusions illustrate some interesting characteristics of the composite media.
High-order Finite Element Analysis of Boundary Layer Flows
NASA Astrophysics Data System (ADS)
Zhang, Alvin; Sahni, Onkar
2014-11-01
Numerical analysis of boundary layer flows requires careful approximations, specifically the use of a mesh with layered and graded elements near the (viscous) walls. This is referred to as a boundary layer mesh, which for complex geometries is composed of triangular elements on the walls that are inflated or extruded into the volume along the wall-normal direction up to a desired height while the rest of the domain is filled with unstructured tetrahedral elements. Linear elements with C0 inter-element continuity are employed and in some situations higher order C0 elements are also used. However, these elements only enforce continuity whereas high-order smoothness is not attained as will be the case with C1 inter-element continuity and higher. As a result, C0 elements result in a poor approximation of the high-order boundary layer behavior. To achieve greater inter-element continuity in boundary layer region, we employ B-spline basis functions along the wall-normal direction (i.e., only in the layered portion of the mesh). In the rest of the fully unstructured mesh, linear or higher order C0 elements are used as appropriate. In this study we demonstrate the benefits of finite-element analysis based on such higher order and continuity basis functions for boundary layer flows.
A boundary element alternating method for two-dimensional mixed-mode fracture problems
NASA Technical Reports Server (NTRS)
Raju, I. S.; Krishnamurthy, T.
1992-01-01
A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort.
Fluorescence photon migration by the boundary element method
Fedele, Francesco; Eppstein, Margaret J. . E-mail: maggie.eppstein@uvm.edu; Laible, Jeffrey P.; Godavarty, Anuradha; Sevick-Muraca, Eva M.
2005-11-20
The use of the boundary element method (BEM) is explored as an alternative to the finite element method (FEM) solution methodology for the elliptic equations used to model the generation and transport of fluorescent light in highly scattering media, without the need for an internal volume mesh. The method is appropriate for domains where it is reasonable to assume the fluorescent properties are regionally homogeneous, such as when using highly specific molecularly targeted fluorescent contrast agents in biological tissues. In comparison to analytical results on a homogeneous sphere, BEM predictions of complex emission fluence are shown to be more accurate and stable than those of the FEM. Emission fluence predictions made with the BEM using a 708-node mesh, with roughly double the inter-node spacing of boundary nodes as in a 6956-node FEM mesh, match experimental frequency-domain fluorescence emission measurements acquired on a 1087 cm{sup 3} breast-mimicking phantom at least as well as those of the FEM, but require only 1/8 to 1/2 the computation time.
Boundary element method with bioheat equation for skin burn injury.
Ng, E Y K; Tan, H M; Ooi, E H
2009-11-01
Burns are second to vehicle crashes as the leading cause of non-intentional injury deaths in the United States. The survival of a burn patient actually depends on the seriousness of the burn. It is important to understand the physiology of burns for a successful treatment of a burn patient. This has prompted researchers to conduct investigations both numerically and experimentally to understand the thermal behaviour of the human skin when subjected to heat injury. In this study, a model of the human skin is developed where the steady state temperature during burns is simulated using the boundary element method (BEM). The BEM is used since it requires boundary only discretion and thus, reduces the requirement of high computer memory. The skin is modeled as three layered in axisymmetric coordinates. The three layers are the epidermis (uppermost), dermis (middle) and subcutaneous fat. Burning is applied via a heating disk which is assumed to be at constant temperature. The results predicted by the BEM model showed very good agreement with the results obtained using the finite element method (FEM). The good agreement despite using only linear elements as compared to quadratic elements in the FEM model shows the versatility of the BEM. A sensitivity analysis was conducted to investigate how changes in the values of certain skin variables such as the thermal conductivity and environmental conditions like the ambient convection coefficient affect the temperature distribution inside the skin. The Taguchi method was also applied to identify the combination of parameters which produces the largest increase in skin temperature during burns.
The complex variable boundary element method: Applications in determining approximative boundaries
Hromadka, T.V.
1984-01-01
The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary. ?? 1984.
Advances in Numerical Boundary Conditions for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.
1997-01-01
Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some much needed research in numerical boundary conditions for CAA.
Equivariant preconditioners for boundary element methods
Tausch, J.
1994-12-31
In this paper the author proposes and discusses two preconditioners for boundary integral equations on domains which are nearly symmetric. The preconditioners under consideration are equivariant, that is, they commute with a group of permutation matrices. Numerical experiments demonstrate their efficiency for the GMRES method.
NASA Technical Reports Server (NTRS)
Collins, Jeffery D.; Jin, Jian-Ming; Volakis, John L.
1990-01-01
A method for the computation of electromagnetic scattering from arbitrary two-dimensional bodies is presented. The method combines the finite element and boundary element methods leading to a system for solution via the conjugate gradient Fast Fourier Transform (FFT) algorithm. Two forms of boundaries aimed at reducing the storage requirement of the boundary integral are investigated. It is shown that the boundary integral becomes convolutional when a circular enclosure is chosen, resulting in reduced storage requirement when the system is solved via the conjugate gradient FFT method. The same holds for the ogival enclosure, except that some of the boundary integrals are not convolutional and must be carefully treated to maintain O(N) memory requirement. Results for several circular and ogival structures are presented and shown to be in excellent agreement with those obtained by traditional methods.
Element-topology-independent preconditioners for parallel finite element computations
NASA Technical Reports Server (NTRS)
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
Element-topology-independent preconditioners for parallel finite element computations
NASA Technical Reports Server (NTRS)
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
Automatic computational labeling of glomerular textural boundaries
NASA Astrophysics Data System (ADS)
Ginley, Brandon; Tomaszewski, John E.; Sarder, Pinaki
2017-03-01
The glomerulus, a specialized bundle of capillaries, is the blood filtering unit of the kidney. Each human kidney contains about 1 million glomeruli. Structural damages in the glomerular micro-compartments give rise to several renal conditions; most severe of which is proteinuria, where excessive blood proteins flow freely to the urine. The sole way to confirm glomerular structural damage in renal pathology is by examining histopathological or immunofluorescence stained needle biopsies under a light microscope. However, this method is extremely tedious and time consuming, and requires manual scoring on the number and volume of structures. Computational quantification of equivalent features promises to greatly ease this manual burden. The largest obstacle to computational quantification of renal tissue is the ability to recognize complex glomerular textural boundaries automatically. Here we present a computational pipeline to accurately identify glomerular boundaries with high precision and accuracy. The computational pipeline employs an integrated approach composed of Gabor filtering, Gaussian blurring, statistical F-testing, and distance transform, and performs significantly better than standard Gabor based textural segmentation method. Our integrated approach provides mean accuracy/precision of 0.89/0.97 on n = 200Hematoxylin and Eosin (HE) glomerulus images, and mean 0.88/0.94 accuracy/precision on n = 200 Periodic Acid Schiff (PAS) glomerulus images. Respective accuracy/precision of the Gabor filter bank based method is 0.83/0.84 for HE and 0.78/0.8 for PAS. Our method will simplify computational partitioning of glomerular micro-compartments hidden within dense textural boundaries. Automatic quantification of glomeruli will streamline structural analysis in clinic, and can help realize real time diagnoses and interventions.
Electrodynamic boundary conditions for planar arrays of thin magnetic elements
Lisenkov, Ivan; Tyberkevych, Vasyl; Slavin, Andrei; Nikitov, Sergei
2015-08-24
Approximate electrodynamic boundary conditions are derived for an array of dipolarly coupled magnetic elements. It is assumed that the elements' thickness is small compared to the wavelength of an electromagnetic wave in a free space. The boundary conditions relate electric and magnetic fields existing at the top and bottom sides of the array through the averaged uniform dynamic magnetization of the array. This dynamic magnetization is determined by the collective dynamic eigen-excitations (spin wave modes) of the array and is found using the external magnetic susceptibility tensor. The problem of oblique scattering of a plane electromagnetic wave on the array is considered to illustrate the use of the derived boundary conditions.
Increasing Accuracy in Computed Inviscid Boundary Conditions
NASA Technical Reports Server (NTRS)
Dyson, Roger
2004-01-01
A technique has been devised to increase the accuracy of computational simulations of flows of inviscid fluids by increasing the accuracy with which surface boundary conditions are represented. This technique is expected to be especially beneficial for computational aeroacoustics, wherein it enables proper accounting, not only for acoustic waves, but also for vorticity and entropy waves, at surfaces. Heretofore, inviscid nonlinear surface boundary conditions have been limited to third-order accuracy in time for stationary surfaces and to first-order accuracy in time for moving surfaces. For steady-state calculations, it may be possible to achieve higher accuracy in space, but high accuracy in time is needed for efficient simulation of multiscale unsteady flow phenomena. The present technique is the first surface treatment that provides the needed high accuracy through proper accounting of higher-order time derivatives. The present technique is founded on a method known in art as the Hermitian modified solution approximation (MESA) scheme. This is because high time accuracy at a surface depends upon, among other things, correction of the spatial cross-derivatives of flow variables, and many of these cross-derivatives are included explicitly on the computational grid in the MESA scheme. (Alternatively, a related method other than the MESA scheme could be used, as long as the method involves consistent application of the effects of the cross-derivatives.) While the mathematical derivation of the present technique is too lengthy and complex to fit within the space available for this article, the technique itself can be characterized in relatively simple terms: The technique involves correction of surface-normal spatial pressure derivatives at a boundary surface to satisfy the governing equations and the boundary conditions and thereby achieve arbitrarily high orders of time accuracy in special cases. The boundary conditions can now include a potentially infinite number
Boundary element analysis of corrosion problems for pumps and pipes
Miyasaka, M.; Amaya, K.; Kishimoto, K.; Aoki, S.
1995-12-31
Three-dimensional (3D) and axi-symmetric boundary element methods (BEM) were developed to quantitatively estimate cathodic protection and macro-cell corrosion. For 3D analysis, a multiple-region method (MRM) was developed in addition to a single-region method (SRM). The validity and usefulness of the BEMs were demonstrated by comparing numerical results with experimental data from galvanic corrosion systems of a cylindrical model and a seawater pipe, and from a cathodic protection system of an actual seawater pump. It was shown that a highly accurate analysis could be performed for fluid machines handling seawater with complex 3D fields (e.g. seawater pump) by taking account of flow rate and time dependencies of polarization curve. Compared to the 3D BEM, the axi-symmetric BEM permitted large reductions in numbers of elements and nodes, which greatly simplified analysis of axi-symmetric fields such as pipes. Computational accuracy and CPU time were compared between analyses using two approximation methods for polarization curves: a logarithmic-approximation method and a linear-approximation method.
Numerical Computations of Hypersonic Boundary-Layer over Surface Irregularities
NASA Technical Reports Server (NTRS)
Chang, Chau-Lyan; Choudhari, Meelan M.; Li, Fei
2010-01-01
Surface irregularities such as protuberances inside a hypersonic boundary layer may lead to premature transition on the vehicle surface. Early transition in turn causes large localized surface heating that could damage the thermal protection system. Experimental measurements as well as numerical computations aimed at building a knowledge base for transition Reynolds numbers with respect to different protuberance sizes and locations have been actively pursued in recent years. This paper computationally investigates the unsteady wake development behind large isolated cylindrical roughness elements and the scaled wind-tunnel model of the trip used in a recent flight measurement during the reentry of space shuttle Discovery. An unstructured mesh, compressible flow solver based on the space-time conservation element, solution element (CESE) method is used to perform time-accurate Navier-Stokes calculations for the flow past a roughness element under several wind-tunnel conditions. For a cylindrical roughness element with a height to the boundary-layer thickness ratio from 0.8 to 2.5, the wake flow is characterized by a mushroom-shaped centerline streak and horse-shoe vortices. While time-accurate solutions converged to a steady-state for a ratio of 0.8, strong flow unsteadiness is present for a ratio of 1.3 and 2.5. Instability waves marked by distinct disturbance frequencies were found in the latter two cases. Both the centerline streak and the horse-shoe vortices become unstable downstream. The oscillatory vortices eventually reach an early breakdown stage for the largest roughness element. Spectral analyses in conjunction with the computed root mean square variations suggest that the source of the unsteadiness and instability waves in the wake region may be traced back to possible absolute instability in the front-side separation region.
NASA Technical Reports Server (NTRS)
Mei, Chuh; Pates, Carl S., III
1994-01-01
A coupled boundary element (BEM)-finite element (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels.
Laminar-Turbulent Transition Behind Discrete Roughness Elements in a High-Speed Boundary Layer
NASA Technical Reports Server (NTRS)
Choudhari, Meelan M.; Li, Fei; Wu, Minwei; Chang, Chau-Lyan; Edwards, Jack R., Jr.; Kegerise, Michael; King, Rudolph
2010-01-01
Computations are performed to study the flow past an isolated roughness element in a Mach 3.5, laminar, flat plate boundary layer. To determine the effects of the roughness element on the location of laminar-turbulent transition inside the boundary layer, the instability characteristics of the stationary wake behind the roughness element are investigated over a range of roughness heights. The wake flow adjacent to the spanwise plane of symmetry is characterized by a narrow region of increased boundary layer thickness. Beyond the near wake region, the centerline streak is surrounded by a pair of high-speed streaks with reduced boundary layer thickness and a secondary, outer pair of lower-speed streaks. Similar to the spanwise periodic pattern of streaks behind an array of regularly spaced roughness elements, the above wake structure persists over large distances and can sustain strong enough convective instabilities to cause an earlier onset of transition when the roughness height is sufficiently large. Time accurate computations are performed to clarify additional issues such as the role of the nearfield of the roughness element during the generation of streak instabilities, as well as to reveal selected details of their nonlinear evolution. Effects of roughness element shape on the streak amplitudes and the interactions between multiple roughness elements aligned along the flow direction are also investigated.
Development of boundary element analysis system for corrosion protection design
Miyasaka, M.; Takayama, H.; Amaya, K.; Aoki, S.
1997-12-01
In order to make a practical application of boundary element method (BEM) for quantitative predictions of cathodic protection and macro-cell corrosion, a BEM analysis system based on the 2D, 3D and axi-symmetric programs was developed. The system consists of a polarization curve database and programs to perform element discretization, input file set-up, boundary element analysis and graphic display of input and output data. Even an engineer with no knowledge of corrosion will be able to operate this system easily and perform effective analyses. The usefulness of the system was demonstrated by an application example for the cathodic protection design of a seawater pump. In this system, the effects of flow-rate and time on the polarization curve can be taken into account for defining the boundary conditions.
Acoustic viscoelastic modeling by frequency-domain boundary element method
NASA Astrophysics Data System (ADS)
Guan, Xizhu; Fu, Li-Yun; Sun, Weijia
2017-04-01
Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods. Targeted at viscoelastic numerical modeling for multilayered media, the constant- Q acoustic wave equation is transformed into the corresponding wave integral representation with its Green's function accounting for viscoelastic coefficients. An efficient alternative for full-waveform solution to the integral equation is proposed in this article by extending conventional frequency-domain boundary element methods to viscoelastic media. The viscoelastic boundary element method enjoys a distinct characteristic of the explicit use of boundary continuity conditions of displacement and traction, leading to a semi-analytical solution with sufficient accuracy for simulating the viscoelastic effect across irregular interfaces. Numerical experiments to study the viscoelastic absorption of different Q values demonstrate the accuracy and applicability of the method.
NASA Technical Reports Server (NTRS)
Vlahopoulos, Nickolas; Lyle, Karen H.; Burley, Casey L.
1998-01-01
An algorithm for generating appropriate velocity boundary conditions for an acoustic boundary element analysis from the kinematics of an operating propeller is presented. It constitutes the initial phase of Integrating sophisticated rotorcraft models into a conventional boundary element analysis. Currently, the pressure field is computed by a linear approximation. An initial validation of the developed process was performed by comparing numerical results to test data for the external acoustic pressure on the surface of a tilt-rotor aircraft for one flight condition.
Treatment of domain integrals in boundary element methods
Nintcheu Fata, Sylvain
2012-01-01
A systematic and rigorous technique to calculate domain integrals without a volume-fitted mesh has been developed and validated in the context of a boundary element approximation. In the proposed approach, a domain integral involving a continuous or weakly-singular integrand is first converted into a surface integral by means of straight-path integrals that intersect the underlying domain. Then, the resulting surface integral is carried out either via analytic integration over boundary elements or by use of standard quadrature rules. This domain-to-boundary integral transformation is derived from an extension of the fundamental theorem of calculus to higher dimension, and the divergence theorem. In establishing the method, it is shown that the higher-dimensional version of the first fundamental theorem of calculus corresponds to the well-known Poincare lemma. The proposed technique can be employed to evaluate integrals defined over simply- or multiply-connected domains with Lipschitz boundaries which are embedded in an Euclidean space of arbitrary but finite dimension. Combined with the singular treatment of surface integrals that is widely available in the literature, this approach can also be utilized to effectively deal with boundary-value problems involving non-homogeneous source terms by way of a collocation or a Galerkin boundary integral equation method using only the prescribed surface discretization. Sample problems associated with the three-dimensional Poisson equation and featuring the Newton potential are successfully solved by a constant element collocation method to validate this study.
Virtual boundary element method for multistage depressed collector of traveling-wave tubes
NASA Astrophysics Data System (ADS)
Lai, Jianqiang; Gong, Yubin; Yin, Hairong; Duan, Zhaoyun; Wei, Yanyu
2011-04-01
In this study, virtual boundary element (VBE) method has been employed in multistage depressed collector (MDC) simulation for high efficiency traveling-wave tubes (TWTs). The basic idea of this method is establishing a mapping relation between the source on the real and virtual boundaries. When calculating the potential of the problem field, the virtual source on virtual boundary is only used, instead of the source on real boundary. We discussed the distance between the virtual and real boundaries and the discrete density of virtual boundary, which are closely related to the calculation accuracy. Based on the VBE method, a new computer aided design code CCAD is developed for the MDC system of high efficiency TWT. The results of simulations performed on an axisymmetric four-stage depressed collector are reported. The advantages of VBE method mainly lie in fast calculation and accurate solution. This is of benefit to designing high efficiency MDC thus developing high efficiency TWT, especially for space TWT.
de Munck, J C
1992-09-01
A method is presented to compute the potential distribution on the surface of a homogeneous isolated conductor of arbitrary shape. The method is based on an approximation of a boundary integral equation as a set linear algebraic equations. The potential is described as a piecewise linear or quadratic function. The matrix elements of the discretized equation are expressed as analytical formulas.
Analysis of two-dimensional ducts with sudden area changes using the boundary element method
NASA Technical Reports Server (NTRS)
Pates, Carl S., III
1992-01-01
In this paper, the boundary element method (BEM) is applied to two-dimensional acoustic ducts with sudden area changes. The mathematical basis of BEM along with the technique of handling singularities is presented in a systematic manner. The computer code is verified by comparison with the exact solutions and a number of illustrative examples are included.
NASA Astrophysics Data System (ADS)
Ptaszny, Jacek
2015-09-01
In this work, a fast multipole boundary element method for 3D elasticity problem was developed by the application of the fast multipole algorithm and isoparametric 8-node boundary elements with quadratic shape functions. The problem is described by the boundary integral equation involving the Kelvin solutions. In order to keep the numerical integration error on appropriate level, an adaptive method with subdivision of boundary elements into subelements, described in the literature, was applied. An extension of the neighbour list of boundary element clusters, corresponding to near-field computations, was proposed in order to reduce the truncation error of expansions in problems with high stress concentration. Efficiency of the method is illustrated by numerical examples including a solid with single spherical cavity, solids with two interacting spherical cavities, and numerical homogenization of solids with cubic arrangement of spherical cavities. All results agree with analytical models available in the literature. The examples show that the method can be applied to the analysis of porous structures.
Experimental validation of boundary element methods for noise prediction
NASA Technical Reports Server (NTRS)
Seybert, A. F.; Oswald, Fred B.
1992-01-01
Experimental validation of methods to predict radiated noise is presented. A combined finite element and boundary element model was used to predict the vibration and noise of a rectangular box excited by a mechanical shaker. The predicted noise was compared to sound power measured by the acoustic intensity method. Inaccuracies in the finite element model shifted the resonance frequencies by about 5 percent. The predicted and measured sound power levels agree within about 2.5 dB. In a second experiment, measured vibration data was used with a boundary element model to predict noise radiation from the top of an operating gearbox. The predicted and measured sound power for the gearbox agree within about 3 dB.
Lubrication approximation in completed double layer boundary element method
NASA Astrophysics Data System (ADS)
Nasseri, S.; Phan-Thien, N.; Fan, X.-J.
This paper reports on the results of the numerical simulation of the motion of solid spherical particles in shear Stokes flows. Using the completed double layer boundary element method (CDLBEM) via distributed computing under Parallel Virtual Machine (PVM), the effective viscosity of suspension has been calculated for a finite number of spheres in a cubic array, or in a random configuration. In the simulation presented here, the short range interactions via lubrication forces are also taken into account, via the range completer in the formulation, whenever the gap between two neighbouring particles is closer than a critical gap. The results for particles in a simple cubic array agree with the results of Nunan and Keller (1984) and Stoksian Dynamics of Brady etal. (1988). To evaluate the lubrication forces between particles in a random configuration, a critical gap of 0.2 of particle's radius is suggested and the results are tested against the experimental data of Thomas (1965) and empirical equation of Krieger-Dougherty (Krieger, 1972). Finally, the quasi-steady trajectories are obtained for time-varying configuration of 125 particles.
Boundary Element Microhydrodynamics: Stagnation of flow in protein cavities
NASA Astrophysics Data System (ADS)
Aragon, Sergio; Hahn, David
2007-03-01
A very precise boundary element solution of the exact Stokes flow surface integral equation has been implemented in our Fortan 90 program BEST. In our previous work (Aragon & Hahn, Biophys. J. 2006, 91: 1591-1603; J. Chem. Theory and Comput. 2006, 2: 1416-1428) we obtained very precise values of the tensorial transport properties (translation, rotation, and intrinsic viscosity) for a large set of proteins with a uniform water hydration thickness of 0.11 nm. In this work, we utilize the surface stress distribution thus obtained to evaluate the flow field as a function of distance away from the hydrodynamic surface for a variety of surface features in a dimpled sphere (test case) and for the proteins myoglobin, lysozyme, and human serum albumin. We demonstrate that solvent in small to large pockets on the hydrodynamic surface moves with the protein with distances up to 2 nm for deep pockets regardless of the direction of motion of the protein. On the other hand, the fluid flow pattern on protruding portions of the hydrodynamic surface decays much more rapidly with distance from the surface. The implications of these results with respect to the amount of water of associated with the surface and the rate of transport to active enzymatic sites in stirred solutions is discussed.
A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions
NASA Astrophysics Data System (ADS)
Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.
2014-01-01
We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.
Computer Security: The Human Element.
ERIC Educational Resources Information Center
Guynes, Carl S.; Vanacek, Michael T.
1981-01-01
The security and effectiveness of a computer system are dependent on the personnel involved. Improved personnel and organizational procedures can significantly reduce the potential for computer fraud. (Author/MLF)
The coupling of boundary elements and finite elements for nondestructive testing applications
Fetzer, J.; Kurz, S.; Lehner, G.
1997-01-01
In this paper, the coupling of finite elements and boundary elements, referred to as BEM-FEM coupling, is used to numerically treat a nondestructive testing (NDT) problem based on eddy currents. BEM-FEM coupling is especially well suited for NDT problems because it greatly reduces the discretization effort. A general formulation for such problems involving FEM and BEM is given. The coupling of both methods is achieved using the boundary conditions on the common boundaries between FEM and BEM domains. Only the conducting parts and the exciting coil are discretized by finite elements. The surrounding air space is taken into account by boundary elements. As an example, problem No. 8 (coil above a crack) of the TEAM workshop (Testing Electromagnetic Analysis Methods) is considered.
Enhanced pre-computed finite element models for surgical simulation.
Zhong, Hualiang; Wachowiak, Mark P; Peters, Terry M
2005-01-01
Soft tissue modeling is an important component in effective surgical simulation systems. A pre-computed finite element method based on elastic models is well suited to modeling soft tissue deformation. This paper addresses two principal issues: the flexibility of the pre-computed FE method and the approximation approach to non-linear elastic models. We describe a dynamic mechanism of the reconfiguration of the contacted nodes and the fixed boundary, without re-computing the inverse of the global stiffness matrix. The flexibility of the pre-computed models is described for both linear and non-linear elastic models.
A new conformal absorbing boundary condition for finite element meshes and parallelization of FEMATS
NASA Technical Reports Server (NTRS)
Chatterjee, A.; Volakis, J. L.; Nguyen, J.; Nurnberger, M.; Ross, D.
1993-01-01
Some of the progress toward the development and parallelization of an improved version of the finite element code FEMATS is described. This is a finite element code for computing the scattering by arbitrarily shaped three dimensional surfaces composite scatterers. The following tasks were worked on during the report period: (1) new absorbing boundary conditions (ABC's) for truncating the finite element mesh; (2) mixed mesh termination schemes; (3) hierarchical elements and multigridding; (4) parallelization; and (5) various modeling enhancements (antenna feeds, anisotropy, and higher order GIBC).
NASA Astrophysics Data System (ADS)
Ballandras, S.; Lardat, R.; Wilm, M.; Pastureaud, Th.; Reinhardt, A.; Champavert, N.; Steichen, W.; Daniau, W.; Laude, V.; Armati, R.; Martin, G.
2009-01-01
The development of new surface acoustic wave devices exhibiting complicated electrode patterns or layered excitation transducers has been favored by an intense innovative activity in this area. For instance, devices exhibiting interdigital transducers covered by piezoelectric or dielectric layers have been fabricated and tested, but the design of such structures requires simulation tools capable to accurately take into account the actual shape of the wave guide elements. A modeling approach able to address complicated surface acoustic wave periodic structures (defined in the saggital plane) exhibiting any geometry then has been developed and implemented. It is based on the combination of a finite element analysis and a boundary element method. A first validation of the computation is reported by comparison with standard surface wave devices. Surface transverse wave resonators covered by amorphous silica have been built and consequently used for theory/experiment assessment. Also the case of recessed electrodes has been considered. The proposed model offers large opportunities for modeling any two-dimensional periodic elastic wave guide.
Three-dimensional Stress Analysis Using the Boundary Element Method
NASA Technical Reports Server (NTRS)
Wilson, R. B.; Banerjee, P. K.
1984-01-01
The boundary element method is to be extended (as part of the NASA Inelastic Analysis Methods program) to the three-dimensional stress analysis of gas turbine engine hot section components. The analytical basis of the method (as developed in elasticity) is outlined, its numerical implementation is summarized, and the approaches to be followed in extending the method to include inelastic material response indicated.
An efficient stabilized boundary element formulation for 2D time-domain acoustics and elastodynamics
NASA Astrophysics Data System (ADS)
Soares, D.; Mansur, W. J.
2007-07-01
The present paper describes a procedure that improves efficiency, stability and reduces artificial energy dissipation of the standard time-domain direct boundary element method (BEM) for acoustics and elastodynamics. Basically, the developed procedure modifies the boundary element convolution-related vector, being very easy to implement into existing codes. A stabilization parameter is introduced into the recent-in-time convolution operations and the operations related to the distant-in-time convolution contributions are approximated by matrix interpolations. As it is shown in the numerical examples presented at the end of the text, the proposed formulation substantially reduces the BEM computational cost, as well as its numerical instabilities.
Treatment of body forces in boundary element design sensitivity analysis
NASA Technical Reports Server (NTRS)
Saigal, Sunil; Kane, James H.; Aithal, R.; Cheng, Jizu
1989-01-01
The inclusion of body forces has received a good deal of attention in boundary element research. The consideration of such forces is essential in the desgin of high performance components such as fan and turbine disks in a gas turbine engine. Due to their critical performance requirements, optimal shapes are often desired for these components. The boundary element method (BEM) offers the possibility of being an efficient method for such iterative analysis as shape optimization. The implicit-differentiation of the boundary integral equations is performed to obtain the sensitivity equations. The body forces are accounted for by either the particular integrals for uniform body forces or by a surface integration for non-uniform body forces. The corresponding sensitivity equations for both these cases are presented. The validity of present formulations is established through a close agreement with exact analytical results.
NASA Astrophysics Data System (ADS)
Li, FengLian; Wang, YueSheng; Zhang, ChuanZeng
2016-06-01
A boundary element method (BEM) is presented to compute the transmission spectra of two-dimensional (2-D) phononic crystals of a square lattice which are finite along the x-direction and infinite along the y-direction. The cross sections of the scatterers may be circular or square. For a periodic cell, the boundary integral equations of the matrix and the scatterers are formulated. Substituting the periodic boundary conditions and the interface continuity conditions, a linear equation set is formed, from which the elastic wave transmission can be obtained. From the transmission spectra, the band gaps can be identified, which are compared with the band structures of the corresponding infinite systems. It is shown that generally the transmission spectra completely correspond to the band structures. In addition, the accuracy and the efficiency of the boundary element method are analyzed and discussed.
Coupled NASTRAN/boundary element formulation for acoustic scattering
NASA Technical Reports Server (NTRS)
Everstine, Gordon C.; Henderson, Francis M.; Schuetz, Luise S.
1987-01-01
A coupled finite element/boundary element capability is described for calculating the sound pressure field scattered by an arbitrary submerged 3-D elastic structure. Structural and fluid impedances are calculated with no approximation other than discretization. The surface fluid pressures and normal velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior field. Far field pressures are then evaluated from the surface solution using the Helmholtz exterior integral equation. The overall approach is illustrated and validated using a known analytic solution for scattering from submerged spherical shells.
Development of non-linear finite element computer code
NASA Technical Reports Server (NTRS)
Becker, E. B.; Miller, T.
1985-01-01
Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows finite element analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional finite element code, TEXLESP-S, which is documented herein.
A finite element-boundary integral method for cavities in a circular cylinder
NASA Technical Reports Server (NTRS)
Kempel, Leo C.; Volakis, John L.
1992-01-01
Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. However, due to a lack of rigorous mathematical models for conformal antenna arrays, antenna designers resort to measurement and planar antenna concepts for designing non-planar conformal antennas. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We extend this formulation to conformal arrays on large metallic cylinders. In this report, we develop the mathematical formulation. In particular, we discuss the shape functions, the resulting finite elements and the boundary integral equations, and the solution of the conformal finite element-boundary integral system. Some validation results are presented and we further show how this formulation can be applied with minimal computational and memory resources.
A Hybrid Boundary Element-Finite Volume Method for Unsteady Transonic Airfoil Flows
NASA Technical Reports Server (NTRS)
Hu, Hong; Kandil, Osama A.
1996-01-01
A hybrid boundary element finite volume method for unsteady transonic flow computation has been developed. In this method, the unsteady Euler equations in a moving frame of reference are solved in a small embedded domain (inner domain) around the airfoil using an implicit finite volume scheme. The unsteady full-potential equation, written in the same frame of reference and in the form of the Poisson equation. is solved in the outer domain using the integral equation boundary element method to provide the boundary conditions for the inner Euler domain. The solution procedure is a time-accurate stepping procedure, where the outer boundary conditions for the inner domain are updated using the integral equation -- boundary element solution over the outer domain. The method is applied to unsteady transonic flows around the NACA0012 airfoil undergoing pitching oscillation and ramp motion. The results are compared with those of an implicit Euler equation solver, which is used throughout a large computational domain, and experimental data.
NASA Astrophysics Data System (ADS)
Hooper, Russell; Toose, Matthijs; Macosko, Christopher W.; Derby, Jeffrey J.
2001-12-01
A modified boundary element method (BEM) and the DEVSS-G finite element method (FEM) are applied to model the deformation of a polymeric drop suspended in another fluid subjected to start-up uniaxial extensional flow. The effects of viscoelasticity, via the Oldroyd-B differential model, are considered for the drop phase using both FEM and BEM and for both the drop and matrix phases using FEM. Where possible, results are compared with the linear deformation theory. Consistent predictions are obtained among the BEM, FEM, and linear theory for purely Newtonian systems and between FEM and linear theory for fully viscoelastic systems. FEM and BEM predictions for viscoelastic drops in a Newtonian matrix agree very well at short times but differ at longer times, with worst agreement occurring as critical flow strength is approached. This suggests that the dominant computational advantages held by the BEM over the FEM for this and similar problems may diminish or even disappear when the issue of accuracy is appropriately considered. Fully viscoelastic problems, which are only feasible using the FEM formulation, shed new insight on the role of viscoelasticity of the matrix fluid in drop deformation. Copyright
Geodynamic simulations using the fast multipole boundary element method
NASA Astrophysics Data System (ADS)
Drombosky, Tyler W.
Interaction between viscous fluids models two important phenomena in geophysics: (i) the evolution of partially molten rocks, and (ii) the dynamics of Ultralow-Velocity Zones. Previous attempts to numerically model these behaviors have been plagued either by poor resolution at the fluid interfaces or high computational costs. We employ the Fast Multipole Boundary Element Method, which tracks the evolution of the fluid interfaces explicitly and is scalable to large problems, to model these systems. The microstructure of partially molten rocks strongly influences the macroscopic physical properties. The fractional area of intergranular contact, contiguity, is a key parameter that controls the elastic strength of the grain network in the partially molten aggregate. We study the influence of matrix deformation on the contiguity of an aggregate by carrying out pure shear and simple shear deformations of an aggregate. We observe that the differential shortening, the normalized difference between the major and minor axes of grains is inversely related to the ratio between the principal components of the contiguity tensor. From the numerical results, we calculate the seismic anisotropy resulting from melt redistribution during pure and simple shear deformation. During deformation, the melt is expelled from tubules along three grain corners to films along grain edges. The initially isotropic fractional area of intergranular contact, contiguity, becomes anisotropic due to deformation. Consequently, the component of contiguity evaluated on the plane parallel to the axis of maximum compressive stress decreases. We demonstrate that the observed global shear wave anisotropy and shear wave speed reduction of the Lithosphere-Asthenosphere Boundary are best explained by 0.1 vol% partial melt distributed in horizontal films created by deformation. We use our microsimulation in conjunction with a large scale mantle deep Earth simulation to gain insight into the formation of
NASA Technical Reports Server (NTRS)
Gong, J.; Volakis, J. L.; Chatterjee, A.; Jin, J. M.
1992-01-01
A hybrid finite element boundary integral formulation is developed using tetrahedral and/or triangular elements for discretizing the cavity and/or aperture of microstrip antenna arrays. The tetrahedral elements with edge based linear expansion functions are chosen for modeling the volume region and triangular elements are used for discretizing the aperture. The edge based expansion functions are divergenceless thus removing the requirement to introduce a penalty term and the tetrahedral elements permit greater geometrical adaptability than the rectangular bricks. The underlying theory and resulting expressions are discussed in detail together with some numerical scattering examples for comparison and demonstration.
Impact of new computing systems on finite element computations
NASA Technical Reports Server (NTRS)
Noor, A. K.; Storassili, O. O.; Fulton, R. E.
1983-01-01
Recent advances in computer technology that are likely to impact finite element computations are reviewed. The characteristics of supersystems, highly parallel systems, and small systems (mini and microcomputers) are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario is presented for future hardware/software environment and finite element systems. A number of research areas which have high potential for improving the effectiveness of finite element analysis in the new environment are identified.
Boundary element based multiresolution shape optimisation in electrostatics
NASA Astrophysics Data System (ADS)
Bandara, Kosala; Cirak, Fehmi; Of, Günther; Steinbach, Olaf; Zapletal, Jan
2015-09-01
We consider the shape optimisation of high-voltage devices subject to electrostatic field equations by combining fast boundary elements with multiresolution subdivision surfaces. The geometry of the domain is described with subdivision surfaces and different resolutions of the same geometry are used for optimisation and analysis. The primal and adjoint problems are discretised with the boundary element method using a sufficiently fine control mesh. For shape optimisation the geometry is updated starting from the coarsest control mesh with increasingly finer control meshes. The multiresolution approach effectively prevents the appearance of non-physical geometry oscillations in the optimised shapes. Moreover, there is no need for mesh regeneration or smoothing during the optimisation due to the absence of a volume mesh. We present several numerical experiments and one industrial application to demonstrate the robustness and versatility of the developed approach.
Material nonlinearity plate bending analysis with boundary element method
NASA Astrophysics Data System (ADS)
Supriyono, Effendy, Marwan; Wijianto
2017-06-01
In this paper, material nonlinearity plate bending analysis with boundary element method is presented. The nonlinear term in the formula is analysed by considering that the material is assumed to undergo small strains. The von Mises criterion is used to evaluate the plastic zone and elastic perfectly plastic material behaviour is assumed. The domain integral due to material nonlinearity is evaluated using a cell discretization technique and a total incremental method is implemented to solve the nonlinear system of equation. The size of the increment, the number of boundary elements and the number of domain cells are varied to study the convergence of the analysis. The size of load increment shows big influence on the results. The smaller the size the better results can be obtained, however 200 steps to reach the final load is a reasonable size to get a good results. The number of boundary and domain cells has an influence on the accuracy of the results. The increased number of boundary as well as domain cells gives better results, however a relative coarser mesh can be implemented to have a good results. The current results have a good agreement with the previous results by other researchers.
Advanced boundary element methods in aeroacoustics and elastodynamics
NASA Astrophysics Data System (ADS)
Lee, Li
In the first part of this dissertation, advanced boundary element methods (BEM) are developed for acoustic radiation in the presence of subsonic flows. A direct boundary integral formulation is first introduced for acoustic radiation in a uniform flow. This new formulation uses the Green's function derived from the adjoint operator of the governing differential equation. Therefore, it requires no coordinate transformation. This direct BEM formulation is then extended to acoustic radiation in a nonuniform-flow field. All the terms due to the nonuniform-flow effect are taken to the right-hand side and treated as source terms. The source terms result in a domain integral in the standard boundary integral formulation. The dual reciprocity method is then used to convert the domain integral into a number of boundary integrals. The second part of this dissertation is devoted to the development of advanced BEM algorithms to overcome the multi-frequency and nonuniqueness difficulties in steady-state elastodynamics. For the multi-frequency difficulty, two different interpolation schemes, borrowed from recent developments in acoustics, are first extended to elastodynamics to accelerate the process of matrix re-formation. Then, a hybrid scheme that retains only the merits of the two different interpolation schemes is suggested. To overcome the nonuniqueness difficulty, an enhanced CHIEF (Combined Helmholtz Integral Equation Formulation) method using a linear combination of the displacement and the traction boundary integral equations on the surface of a small interior volume is proposed. Numerical examples are given to demonstrate all the advanced BEM formulations.
Computation of Asteroid Proper Elements: Recent Advances
NASA Astrophysics Data System (ADS)
Knežević, Z.
2017-06-01
The recent advances in computation of asteroid proper elements are briefly reviewed. Although not representing real breakthroughs in computation and stability assessment of proper elements, these advances can still be considered as important improvements offering solutions to some practical problems encountered in the past. The problem of getting unrealistic values of perihelion frequency for very low eccentricity orbits is solved by computing frequencies using the frequency-modified Fourier transform. The synthetic resonant proper elements adjusted to a given secular resonance helped to prove the existence of Astraea asteroid family. The preliminary assessment of stability with time of proper elements computed by means of the analytical theory provides a good indication of their poorer performance with respect to their synthetic counterparts, and advocates in favor of ceasing their regular maintenance; the final decision should, however, be taken on the basis of more comprehensive and reliable direct estimate of their individual and sample average deviations from constancy.
Lamb mode conversion at edges. A hybrid boundary element-finite-element solution.
Galán, José M; Abascal, Ramón
2005-04-01
Two general and flexible numerical techniques based on the finite-element and boundary element methods developed by the authors in a previous paper are applied to study Lamb wave propagation in multilayered plates and Lamb mode conversion at free edges for frequencies beyond the first cutoff frequency. Both techniques are supported by a meshing criterion which guarantees the accuracy of the results when a condition is fulfilled. A finite-element formulation is directly applicable to study Lamb wave propagation and reflection by simple obstacles such as a flat edge. In order to tackle Lamb wave diffraction problems by defects with more complex geometries, a hybrid boundary element-finite-element formulation is used. This technique provides a major improvement with respect to the only previous boundary element application on Lamb waves: the connecting boundary might be placed as close to the reflector as desired, reducing greatly the requirement on mesh size. Two main application problems on practical metallic plates are studied and compared with reported numerical, theoretical, and experimental results: (1) Lamb wave propagation in degraded titanium diffusion bonds, and (2) Lamb mode conversion at inclined or perpendicular free edges of steel plates for frequencies beyond the first cutoff frequency.
Wake Instabilities Behind Discrete Roughness Elements in High Speed Boundary Layers
NASA Technical Reports Server (NTRS)
Choudhari, Meelan; Li, Fei; Chang, Chau-Lyan; Norris, Andrew; Edwards, Jack
2013-01-01
Computations are performed to study the flow past an isolated, spanwise symmetric roughness element in zero pressure gradient boundary layers at Mach 3.5 and 5.9, with an emphasis on roughness heights of less than 55 percent of the local boundary layer thickness. The Mach 5.9 cases include flow conditions that are relevant to both ground facility experiments and high altitude flight ("cold wall" case). Regardless of the Mach number, the mean flow distortion due to the roughness element is characterized by long-lived streamwise streaks in the roughness wake, which can support instability modes that did not exist in the absence of the roughness element. The higher Mach number cases reveal a variety of instability mode shapes with velocity fluctuations concentrated in different localized regions of high base flow shear. The high shear regions vary from the top of a mushroom shaped structure characterizing the centerline streak to regions that are concentrated on the sides of the mushroom. Unlike the Mach 3.5 case with nearly same values of scaled roughness height k/delta and roughness height Reynolds number Re(sub kk), the odd wake modes in both Mach 5.9 cases are significantly more unstable than the even modes of instability. Additional computations for a Mach 3.5 boundary layer indicate that the presence of a roughness element can also enhance the amplification of first mode instabilities incident from upstream. Interactions between multiple roughness elements aligned along the flow direction are also explored.
Dong, Y.; Tagavi, K.A.; Wu, T.W.; Chow, L.C.
1996-09-01
Voids (a kind of flaw) are not desired in the products of many industrial and manufacturing processes. In this article, the authors seek effective ways to remove the void by modeling the void migration and predicting the intermediate and the final shape of the cavity. The boundary element method (BEM) is applied to the quasi-steady state void migration process governed by Laplace`s equation. The conduction solution depends on the void shape, and the void shape depends on the conduction solution. Hence this is a conjugate problem. The analytical formulation and the numerical approach are outlined. The Overhauser spline elements are used in the BEM to ensure continuous first-order derivatives on the void boundary. Given the material properties, geometry of the physical model, and boundary conditions, this computer model can predict detailed information such as flux, velocity and direction of void motion, and temperature at any stage of the void migration. Different strategies for void removal are investigated.
A non-local computational boundary condition for duct acoustics
NASA Technical Reports Server (NTRS)
Zorumski, William E.; Watson, Willie R.; Hodge, Steve L.
1994-01-01
A non-local boundary condition is formulated for acoustic waves in ducts without flow. The ducts are two dimensional with constant area, but with variable impedance wall lining. Extension of the formulation to three dimensional and variable area ducts is straightforward in principle, but requires significantly more computation. The boundary condition simulates a nonreflecting wave field in an infinite duct. It is implemented by a constant matrix operator which is applied at the boundary of the computational domain. An efficient computational solution scheme is developed which allows calculations for high frequencies and long duct lengths. This computational solution utilizes the boundary condition to limit the computational space while preserving the radiation boundary condition. The boundary condition is tested for several sources. It is demonstrated that the boundary condition can be applied close to the sound sources, rendering the computational domain small. Computational solutions with the new non-local boundary condition are shown to be consistent with the known solutions for nonreflecting wavefields in an infinite uniform duct.
Application of the boundary element method to transient heat conduction
NASA Technical Reports Server (NTRS)
Dargush, G. F.; Banerjee, P. K.
1991-01-01
An advanced boundary element method (BEM) is presented for the transient heat conduction analysis of engineering components. The numerical implementation necessarily includes higher-order conforming elements, self-adaptive integration and a multiregion capability. Planar, three-dimensional and axisymmetric analyses are all addressed with a consistent time-domain convolution approach, which completely eliminates the need for volume discretization for most practical analyses. The resulting general purpose algorithm establishes BEM as an attractive alternative to the more familiar finite difference and finite element methods for this class of problems. Several detailed numerical examples are included to emphasize the accuracy, stability and generality of the present BEM. Furthermore, a new efficient treatment is introduced for bodies with embedded holes. This development provides a powerful analytical tool for transient solutions of components, such as casting moulds and turbine blades, which are cumbersome to model when employing the conventional domain-based methods.
Application of the boundary element method to transient heat conduction
NASA Technical Reports Server (NTRS)
Dargush, G. F.; Banerjee, P. K.
1991-01-01
An advanced boundary element method (BEM) is presented for the transient heat conduction analysis of engineering components. The numerical implementation necessarily includes higher-order conforming elements, self-adaptive integration and a multiregion capability. Planar, three-dimensional and axisymmetric analyses are all addressed with a consistent time-domain convolution approach, which completely eliminates the need for volume discretization for most practical analyses. The resulting general purpose algorithm establishes BEM as an attractive alternative to the more familiar finite difference and finite element methods for this class of problems. Several detailed numerical examples are included to emphasize the accuracy, stability and generality of the present BEM. Furthermore, a new efficient treatment is introduced for bodies with embedded holes. This development provides a powerful analytical tool for transient solutions of components, such as casting moulds and turbine blades, which are cumbersome to model when employing the conventional domain-based methods.
Stenroos, M; Mäntynen, V; Nenonen, J
2007-12-01
The boundary element method (BEM) is commonly used in the modeling of bioelectromagnetic phenomena. The Matlab language is increasingly popular among students and researchers, but there is no free, easy-to-use Matlab library for boundary element computations. We present a hands-on, freely available Matlab BEM source code for solving bioelectromagnetic volume conduction problems and any (quasi-)static potential problems that obey the Laplace equation. The basic principle of the BEM is presented and discretization of the surface integral equation for electric potential is worked through in detail. Contents and design of the library are described, and results of example computations in spherical volume conductors are validated against analytical solutions. Three application examples are also presented. Further information, source code for application examples, and information on obtaining the library are available in the WWW-page of the library: (http://biomed.tkk.fi/BEM).
An outflow boundary condition for aeroacoustic computations
NASA Technical Reports Server (NTRS)
Hayder, M. Ehtesham; Hagstrom, Thomas
1995-01-01
A formulation of boundary condition for flows with small disturbances is presented. The authors test their methodology in an axisymmetric jet flow calculation, using both the Navier-Stokes and Euler equations. Solutions in the far field are assumed to be oscillatory. If the oscillatory disturbances are small, the growth of the solution variables can be predicted by linear theory. Eigenfunctions of the linear theory are used explicitly in the formulation of the boundary conditions. This guarantees correct solutions at the boundary in the limit where the predictions of linear theory are valid.
A finite element-boundary integral method for conformal antenna arrays on a circular cylinder
NASA Technical Reports Server (NTRS)
Kempel, Leo C.; Volakis, John L.; Woo, Alex C.; Yu, C. Long
1992-01-01
Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This is due to the lack of rigorous mathematical models for conformal antenna arrays, and as a result the design of conformal arrays is primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. Herewith we shall extend this formulation for conformal arrays on large metallic cylinders. In this we develop the mathematical formulation. In particular we discuss the finite element equations, the shape elements, and the boundary integral evaluation, and it is shown how this formulation can be applied with minimal computation and memory requirements. The implementation shall be discussed in a later report.
A finite element-boundary integral method for conformal antenna arrays on a circular cylinder
NASA Technical Reports Server (NTRS)
Kempel, Leo C.; Volakis, John L.
1992-01-01
Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This was due to the lack of rigorous mathematical models for conformal antenna arrays. As a result, the design of conformal arrays was primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We are extending this formulation to conformal arrays on large metallic cylinders. In doing so, we will develop a mathematical formulation. In particular, we discuss the finite element equations, the shape elements, and the boundary integral evaluation. It is shown how this formulation can be applied with minimal computation and memory requirements.
Multi-domain boundary element method with dissipation
NASA Astrophysics Data System (ADS)
Chen, Xiaobo; Duan, Wenyang
2012-03-01
The wave diffraction and radiation around a floating body is considered within the framework of the linear potential theory in a fairly perfect fluid. The fluid domain extended infinitely in the horizontal directions but is limited by the sea bed, the body hull, and the part of the free surface excluding the body waterplane, and is subdivided into two subdomains according to the body geometry. The two subdomains are connected by a control surface in fluid. In each subdomain, the velocity potential is described by using the usual boundary integral representation involving Green functions. The boundary integral equations are then established by satisfying the boundary conditions and the continuous condition of the potential and the normal derivation across the control surface. This multi-domain boundary element method (MDBEM) is particularly interesting for bodies with a hull form including moonpools to which the usual BEM presents singularities and slow convergence of numerical results. The application of the MDBEM to study the resonant motion of a water column in moonpools shows that the MDBEM provides an efficient and reliable prediction method.
NASA Technical Reports Server (NTRS)
Goldberg, Robert K.; Hopkins, Dale A.
1993-01-01
The boundary element method is utilized to analyze the effects of fiber/matrix interfaces on the micromechanical behavior of laminated composites as well as the elastic behavior of woven composites. Effective composite properties are computed for laminated SiC/RBSN and SiC/Ti-15-3 composites, as well as a woven SiC/SiC composite. The properties calculated using the computerized tool BEST-CMS match the experimental results well.
Finite-element numerical modeling of atmospheric turbulent boundary layer
NASA Technical Reports Server (NTRS)
Lee, H. N.; Kao, S. K.
1979-01-01
A dynamic turbulent boundary-layer model in the neutral atmosphere is constructed, using a dynamic turbulent equation of the eddy viscosity coefficient for momentum derived from the relationship among the turbulent dissipation rate, the turbulent kinetic energy and the eddy viscosity coefficient, with aid of the turbulent second-order closure scheme. A finite-element technique was used for the numerical integration. In preliminary results, the behavior of the neutral planetary boundary layer agrees well with the available data and with the existing elaborate turbulent models, using a finite-difference scheme. The proposed dynamic formulation of the eddy viscosity coefficient for momentum is particularly attractive and can provide a viable alternative approach to study atmospheric turbulence, diffusion and air pollution.
An adaptive grid scheme using the boundary element method
Munipalli, R.; Anderson, D.A.
1996-09-01
A technique to solve the Poisson grid generation equations by Green`s function related methods has been proposed, with the source terms being purely position dependent. The use of distributed singularities in the flow domain coupled with the boundary element method (BEM) formulation is presented in this paper as a natural extension of the Green`s function method. This scheme greatly simplifies the adaption process. The BEM reduces the dimensionality of the given problem by one. Internal grid-point placement can be achieved for a given boundary distribution by adding continuous and discrete source terms in the BEM formulation. A distribution of vortex doublets is suggested as a means of controlling grid-point placement and grid-line orientation. Examples for sample adaption problems are presented and discussed. 15 refs., 20 figs.
Time-Domain Impedance Boundary Conditions for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Auriault, Laurent
1996-01-01
It is an accepted practice in aeroacoustics to characterize the properties of an acoustically treated surface by a quantity known as impedance. Impedance is a complex quantity. As such, it is designed primarily for frequency-domain analysis. Time-domain boundary conditions that are the equivalent of the frequency-domain impedance boundary condition are proposed. Both single frequency and model broadband time-domain impedance boundary conditions are provided. It is shown that the proposed boundary conditions, together with the linearized Euler equations, form well-posed initial boundary value problems. Unlike ill-posed problems, they are free from spurious instabilities that would render time-marching computational solutions impossible.
Steady-State and Transient Boundary Element Methods for Coupled Heat Conduction
NASA Technical Reports Server (NTRS)
Kontinos, Dean A.
1997-01-01
Boundary element algorithms for the solution of steady-state and transient heat conduction are presented. The algorithms are designed for efficient coupling with computational fluid dynamic discretizations and feature piecewise linear elements with offset nodal points. The steady-state algorithm employs the fundamental solution approach; the integration kernels are computed analytically based on linear shape functions, linear elements, and variably offset nodal points. The analytic expressions for both singular and nonsingular integrands are presented. The transient algorithm employs the transient fundamental solution; the temporal integration is performed analytically and the nonsingular spatial integration is performed numerically using Gaussian quadrature. A series solution to the integration is derived for the instance of a singular integrand. The boundary-only character of the algorithm is maintained by integrating the influence coefficients from initial time. Numerical results are compared to analytical solutions to verify the current boundary element algorithms. The steady-state and transient algorithms are numerically shown to be second-order accurate in space and time, respectively.
Physiologically based boundary conditions in finite element modelling.
Speirs, Andrew D; Heller, Markus O; Duda, Georg N; Taylor, William R
2007-01-01
Finite element analysis has been used extensively in the study of bone loading and implant performance, such as in the femur. The boundary conditions applied vary widely, generally producing excessive femoral deformation, and although it has been shown that the muscle forces influence femoral deflections and loading, little consideration has been given to the displacement constraints. It is hypothesised that careful application of physiologically based constraints can produce physiological deformation, and therefore straining, of the femur. Joint contact forces and a complete set of muscle forces were calculated based on the geometry of the Standardised Femur using previously validated musculoskeletal models. Five boundary condition cases were applied to a finite element model of the Standardised Femur: (A) diaphyseally constrained with hip contact and abductor forces; (B) case A plus vasti forces; (C) case A with complete set of muscle forces; (D) distally constrained with all muscle forces; (E) physiological constraints with all muscle forces. It was seen that only the physiological boundary conditions, case E, produced physiological deflections (< 2.0mm) of the femoral head in both the coronal and sagittal planes, which resulted in minimal reaction forces at the constrained nodes. Strains in the mid-diaphysis varied by up to 600 micro-strain under walking loads and 1000 micro-strain under stair climbing loads. The mode of loading, as indicated by the strain profiles on the cortex also varied substantially under these boundary conditions, which has important consequences for studies that examine localised bone loading such as fracture or bone remodelling simulations.
High speed propeller acoustics and aerodynamics - A boundary element approach
NASA Technical Reports Server (NTRS)
Farassat, F.; Myers, M. K.; Dunn, M. H.
1989-01-01
The Boundary Element Method (BEM) is applied in this paper to the problems of acoustics and aerodynamics of high speed propellers. The underlying theory is described based on the linearized Ffowcs Williams-Hawkings equation. The surface pressure on the blade is assumed unknown in the aerodynamic problem. It is obtained by solving a singular integral equation. The acoustic problem is then solved by moving the field point inside the fluid medium and evaluating some surface and line integrals. Thus the BEM provides a powerful technique in calculation of high speed propeller aerodynamics and acoustics.
Boundary element analysis of a straight-through hybrid silencer
NASA Astrophysics Data System (ADS)
Ji, Z. L.
2006-04-01
Combining the acoustic attenuation behaviors of reactive and dissipative silencers, a straight-through hybrid silencer consisting of a concentric folded resonator and a dissipative chamber is presented and the substructure boundary element approach is employed to predict and analyze the acoustic attenuation characteristics in absence of mean flow. The BEM predictions demonstrated the acoustic attenuation effectiveness of the hybrid silencer over a wide frequency range. The effects of internal geometry, porosity of perforation and flow-resistivity of sound-absorbing material on acoustic attenuation performance of the hybrid silencer are investigated in detail.
High speed propeller acoustics and aerodynamics - A boundary element approach
NASA Technical Reports Server (NTRS)
Farassat, F.; Myers, M. K.; Dunn, M. H.
1989-01-01
The Boundary Element Method (BEM) is applied in this paper to the problems of acoustics and aerodynamics of high speed propellers. The underlying theory is described based on the linearized Ffowcs Williams-Hawkings equation. The surface pressure on the blade is assumed unknown in the aerodynamic problem. It is obtained by solving a singular integral equation. The acoustic problem is then solved by moving the field point inside the fluid medium and evaluating some surface and line integrals. Thus the BEM provides a powerful technique in calculation of high speed propeller aerodynamics and acoustics.
A shell element for computing 3D eddy currents -- Applications to transformers
Guerin, C.; Tanneau, G.; Meunier, G.; Labie, P.; Ngnegueu, T.; Sacotte, M.
1995-05-01
A skin depth-independent shell element to model thin conducting sheets is described in a finite element context. This element takes into account the field variation through depth due to skin effect. The finite element formulation is first described, then boundary conditions at the edge of conducting shells and the possibility of describing non conducting line gaps and holes are discussed. Finally, a computation of an earthing transformer model with an aluminium shield modelled with shell elements is presented.
Webb, Christopher J; Zakian, Virginia A
2015-09-08
The stem terminus element (STE), which was discovered 13 y ago in human telomerase RNA, is required for telomerase activity, yet its mode of action is unknown. We report that the Schizosaccharomyces pombe telomerase RNA, TER1 (telomerase RNA 1), also contains a STE, which is essential for telomere maintenance. Cells expressing a partial loss-of-function TER1 STE allele maintained short stable telomeres by a recombination-independent mechanism. Remarkably, the mutant telomere sequence was different from that of wild-type cells. Generation of the altered sequence is explained by reverse transcription into the template boundary element, demonstrating that the STE helps maintain template boundary element function. The altered telomeres bound less Pot1 (protection of telomeres 1) and Taz1 (telomere-associated in Schizosaccharomyces pombe 1) in vivo. Thus, the S. pombe STE, although distant from the template, ensures proper telomere sequence, which in turn promotes proper assembly of the shelterin complex.
A new fast direct solver for the boundary element method
NASA Astrophysics Data System (ADS)
Huang, S.; Liu, Y. J.
2017-04-01
A new fast direct linear equation solver for the boundary element method (BEM) is presented in this paper. The idea of the new fast direct solver stems from the concept of the hierarchical off-diagonal low-rank matrix. The hierarchical off-diagonal low-rank matrix can be decomposed into the multiplication of several diagonal block matrices. The inverse of the hierarchical off-diagonal low-rank matrix can be calculated efficiently with the Sherman-Morrison-Woodbury formula. In this paper, a more general and efficient approach to approximate the coefficient matrix of the BEM with the hierarchical off-diagonal low-rank matrix is proposed. Compared to the current fast direct solver based on the hierarchical off-diagonal low-rank matrix, the proposed method is suitable for solving general 3-D boundary element models. Several numerical examples of 3-D potential problems with the total number of unknowns up to above 200,000 are presented. The results show that the new fast direct solver can be applied to solve large 3-D BEM models accurately and with better efficiency compared with the conventional BEM.
Boundary conditions for direct computation of aerodynamic sound generation
NASA Technical Reports Server (NTRS)
Colonius, Tim; Lele, Sanjiva K.; Moin, Parviz
1992-01-01
A numerical scheme suitable for the computation of both the near field acoustic sources and the far field sound produced by turbulent free shear flows utilizing the Navier-Stokes equations is presented. To produce stable numerical schemes in the presence of shear, damping terms must be added to the boundary conditions. The numerical technique and boundary conditions are found to give stable results for computations of spatially evolving mixing layers.
Boundary conditions for direct computation of aerodynamic sound generation
NASA Technical Reports Server (NTRS)
Colonius, Tim; Lele, Sanjiva K.; Moin, Parviz
1992-01-01
A numerical scheme suitable for the computation of both the near field acoustic sources and the far field sound produced by turbulent free shear flows utilizing the Navier-Stokes equations is presented. To produce stable numerical schemes in the presence of shear, damping terms must be added to the boundary conditions. The numerical technique and boundary conditions are found to give stable results for computations of spatially evolving mixing layers.
NASA Technical Reports Server (NTRS)
Gloss, R. J.
1971-01-01
A finite difference turbulent boundary layer computer program which allows for mass transfer wall cooling and equilibrium chemistry effects is presented. The program is capable of calculating laminar or turbulent boundary layer solutions for an arbitrary ideal gas or an equilibrium hydrogen oxygen system. Either two dimensional or axisymmetric geometric configurations may be considered. The equations are solved, in nondimension-alized physical coordinates, using the implicit Crank-Nicolson technique. The finite difference forms of the conservation of mass, momentum, total enthalpy and elements equations are linearized and uncoupled, thereby generating easily solvable tridiagonal sets of algebraic equations. A detailed description of the computer program, as well as a program user's manual is provided. Detailed descriptions of all boundary layer subroutines are included, as well as a section defining all program symbols of principal importance. Instructions are then given for preparing card input to the program and for interpreting the printed output. Finally, two sample cases are included to illustrate the use of the program.
Parallel computation with the spectral element method
Ma, Hong
1995-12-01
Spectral element models for the shallow water equations and the Navier-Stokes equations have been successfully implemented on a data parallel supercomputer, the Connection Machine model CM-5. The nonstaggered grid formulations for both models are described, which are shown to be especially efficient in data parallel computing environment.
Central control element expands computer capability
NASA Technical Reports Server (NTRS)
Easton, R. A.
1975-01-01
Redundant processing and multiprocessing modes can be obtained from one computer by using logic configuration. Configuration serves as central control element which can automatically alternate between high-capacity multiprocessing mode and high-reliability redundant mode using dynamic mode switching in real time.
NASA Technical Reports Server (NTRS)
Goldberg, Robert K.; Hopkins, Dale A.
1994-01-01
The boundary element method is utilized in this study to conduct thermal analysis of functionally graded composites, materials in which the internal microstructure or properties are explicitly tailored in order to obtain an optimal response, on the micromechanical (constituent) scale. A unique feature of the boundary element formulations used here is the use of circular shape functions to convert the two-dimensional integrations of the composite fibers to one dimensional integrations. Using the computer code BEST-CMS, the through the thickness temperature profiles are computed for a representative material with varying numbers of fibers and fiber spacing in the thickness direction. The computed temperature profiles are compared to those obtained using an alternate analytical theory which explicitly couples the heterogeneous microstructure to the global analysis. The boundary element results compared favorably to the analytical calculations, with discrepancies that are explainable based on the boundary element formulation. The results serve both to demonstrate the ability of the boundary element method to analyze these types of materials, and to verify the accuracy of the analytical theory.
OPTIMIZATION OF 3-D IMAGE-GUIDED NEAR INFRARED SPECTROSCOPY USING BOUNDARY ELEMENT METHOD
Srinivasan, Subhadra; Carpenter, Colin; Pogue, Brian W.; Paulsen, Keith D.
2010-01-01
Multimodality imaging systems combining optical techniques with MRI/CT provide high-resolution functional characterization of tissue by imaging molecular and vascular biomarkers. To optimize these hybrid systems for clinical use, faster and automatable algorithms are required for 3-D imaging. Towards this end, a boundary element model was used to incorporate tissue boundaries from MRI/CT into image formation process. This method uses surface rendering to describe light propagation in 3-D using diffusion equation. Parallel computing provided speedup of up to 54% in time of computation. Simulations showed that location of NIRS probe was crucial for quantitatively accurate estimation of tumor response. A change of up to 61% was seen between cycles 1 and 3 in monitoring tissue response to neoadjuvant chemotherapy. PMID:20523751
Arc Flash Boundary Calculations Using Computer Software Tools
Gibbs, M.D.
2005-01-07
Arc Flash Protection boundary calculations have become easier to perform with the availability of personal computer software. These programs incorporate arc flash protection boundary formulas for different voltage and current levels, calculate the bolted fault current at each bus, and use built in time-current coordination curves to determine the clearing time of protective devices in the system. Results of the arc flash protection boundary calculations can be presented in several different forms--as an annotation to the one-line diagram, as a table of arc flash protection boundary distances, and as printed placards to be attached to the appropriate equipment. Basic arc flash protection boundary principles are presented in this paper along with several helpful suggestions for performing arc flash protection boundary calculations.
Bendickson, J M; Glytsis, E N; Gaylord, T K; Peterson, A F
2001-07-01
Critical modeling issues relating to rigorous boundary element method (BEM) analysis of diffractive optical elements (DOEs) are identified. Electric-field integral equation (EFIE) and combined-field integral equation (CFIE) formulations of the BEM are introduced and implemented. The nonphysical interior resonance phenomenon and thin-shape breakdown are illustrated in the context of a guided-mode resonant subwavelength grating. It is shown that modeling such structures by using an open geometric configuration eliminates these problems that are associated with the EFIE BEM. Necessary precautions in defining the incident fields are also presented for the analysis of multiple-layer DOEs.
Theory of patch inverse boundary element method (IBEM)
NASA Astrophysics Data System (ADS)
Valdivia, Nicholas; Williams, Earl G.; Herdic, Peter; Klos, Jacob; Palumbo, Daniel; Silcox, Richard; Slanka, Bernard
2005-09-01
Near-field acoustical holography (NAH) based on boundary element methods require the measurement of the near-field pressure field over a conformal and close surface in order to recover the acoustic field on a nearby surface. In this work a new technique called patch IBEM is introduced. This new technique eliminates the need to measure over an entire closed surface, but instead the measurements are taken over a small area to reconstruct the acoustic field. Patch IBEM is used for the reconstruction of the acoustic field over a fuselage panel in a Boeing 757 aircraft, using measurement taken at Boeing's interior noise test facility (INTF). The measurements taken include a 120 mikes planar array positioned conformal to the fuselage panel surface and a 50 mikes spherical array. Results will be showed when the fuselage panel is excited by a shaker. [Work supported by ONR and NASA.
Boundary element method for surface nonlinear optics of nanoparticles.
Mäkitalo, Jouni; Suuriniemi, Saku; Kauranen, Martti
2011-11-07
We present the frequency-domain boundary element formulation for solving surface second-harmonic generation from nanoparticles of virtually arbitrary shape and material. We use the Rao-Wilton-Glisson basis functions and Galerkin's testing, which leads to very accurate solutions for both near and far fields. This is verified by a comparison to a solution obtained via multipole expansion for the case of a spherical particle. The frequency-domain formulation allows the use of experimentally measured linear and nonlinear material parameters or the use of parameters obtained using ab-initio principles. As an example, the method is applied to a non-centrosymmetric L-shaped gold nanoparticle to illustrate the formation of surface nonlinear polarization and the second-harmonic radiation properties of the particle. This method provides a theoretically well-founded approach for modelling nonlinear optical phenomena in nanoparticles.
NASA Technical Reports Server (NTRS)
Jin, Jian-Ming; Volakis, John L.; Collins, Jeffery D.
1991-01-01
A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-dimensional composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exact and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement. The paper begins with a general description of the method. A number of two- and three-dimensional applications are then given, including numerical computations which demonstrate the method's accuracy, efficiency, and capability.
Johnson, Anthony N; Hromadka, T V
2015-01-01
The Laplace equation that results from specifying either the normal or tangential force equilibrium equation in terms of the warping functions or its conjugate can be modeled as a complex variable boundary element method or CVBEM mixed boundary problem. The CVBEM is a well-known numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an approximation function that is derived from the Cauchy Integral in complex analysis. This paper highlights three customizations to the technique.•A least squares approach to modeling the complex-valued approximation function will be compared and analyzed to determine if modeling error on the boundary can be reduced without the need to find and evaluated additional linearly independent complex functions.•The nodal point locations will be moved outside the problem domain.•Contour and streamline plots representing the warping function and its complementary conjugate are generated simultaneously from the complex-valued approximating function.
Johnson, Anthony N.; Hromadka, T.V.
2015-01-01
The Laplace equation that results from specifying either the normal or tangential force equilibrium equation in terms of the warping functions or its conjugate can be modeled as a complex variable boundary element method or CVBEM mixed boundary problem. The CVBEM is a well-known numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an approximation function that is derived from the Cauchy Integral in complex analysis. This paper highlights three customizations to the technique.•A least squares approach to modeling the complex-valued approximation function will be compared and analyzed to determine if modeling error on the boundary can be reduced without the need to find and evaluated additional linearly independent complex functions.•The nodal point locations will be moved outside the problem domain.•Contour and streamline plots representing the warping function and its complementary conjugate are generated simultaneously from the complex-valued approximating function. PMID:26151000
COMGEN-BEM: Boundary element model generation for composite materials micromechanical analysis
NASA Technical Reports Server (NTRS)
Goldberg, Robert K.
1992-01-01
Composite Model Generation-Boundary Element Method (COMGEN-BEM) is a program developed in PATRAN command language (PCL) which generates boundary element models of continuous fiber composites at the micromechanical (constituent) scale. Based on the entry of a few simple parameters such as fiber volume fraction and fiber diameter, the model geometry and boundary element model are generated. In addition, various mesh densities, material properties, fiber orientation angles, loads, and boundary conditions can be specified. The generated model can then be translated to a format consistent with a boundary element analysis code such as BEST-CMS.
Bajaj, Chandrajit; Chen, Shun-Chuan; Rand, Alexander
2011-01-01
In order to compute polarization energy of biomolecules, we describe a boundary element approach to solving the linearized Poisson-Boltzmann equation. Our approach combines several important features including the derivative boundary formulation of the problem and a smooth approximation of the molecular surface based on the algebraic spline molecular surface. State of the art software for numerical linear algebra and the kernel independent fast multipole method is used for both simplicity and efficiency of our implementation. We perform a variety of computational experiments, testing our method on a number of actual proteins involved in molecular docking and demonstrating the effectiveness of our solver for computing molecular polarization energy. PMID:21660123
Koteras, J.R.
1993-07-01
Tunnels buried deep within the earth constitute an important class geomechanics problems. Two numerical techniques used for the analysis of geomechanics problems, the finite element method and the boundary element method, have complementary characteristics for applications to problems of this type. The usefulness of combining these two methods for use as a geomechanics analysis tool has been recognized for some time, and a number of coupling techniques have been proposed. However, not all of them lend themselves to efficient computational implementations for large-scale problems. This report examines a coupling technique that can form the basis for an efficient analysis tool for large scale geomechanics problems through the use of an iterative equation solver.
NASA Astrophysics Data System (ADS)
Javili, A.; Saeb, S.; Steinmann, P.
2017-01-01
In the past decades computational homogenization has proven to be a powerful strategy to compute the overall response of continua. Central to computational homogenization is the Hill-Mandel condition. The Hill-Mandel condition is fulfilled via imposing displacement boundary conditions (DBC), periodic boundary conditions (PBC) or traction boundary conditions (TBC) collectively referred to as canonical boundary conditions. While DBC and PBC are widely implemented, TBC remains poorly understood, with a few exceptions. The main issue with TBC is the singularity of the stiffness matrix due to rigid body motions. The objective of this manuscript is to propose a generic strategy to implement TBC in the context of computational homogenization at finite strains. To eliminate rigid body motions, we introduce the concept of semi-Dirichlet boundary conditions. Semi-Dirichlet boundary conditions are non-homogeneous Dirichlet-type constraints that simultaneously satisfy the Neumann-type conditions. A key feature of the proposed methodology is its applicability for both strain-driven as well as stress-driven homogenization. The performance of the proposed scheme is demonstrated via a series of numerical examples.
Massively parallel finite element computation of three dimensional flow problems
NASA Astrophysics Data System (ADS)
Tezduyar, T.; Aliabadi, S.; Behr, M.; Johnson, A.; Mittal, S.
1992-12-01
The parallel finite element computation of three-dimensional compressible, and incompressible flows, with emphasis on the space-time formulations, mesh moving schemes and implementations on the Connection Machines CM-200 and CM-5 are presented. For computation of unsteady compressible and incompressible flows involving moving boundaries and interfaces, the Deformable-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation that previously developed are employed. In this approach, the stabilized finite element formulations of the governing equations are written over the space-time domain of the problem; therefore, the deformation of the spatial domain with respect to time is taken into account automatically. This approach gives the capability to solve a large class of problems involving free surfaces, moving interfaces, and fluid-structure and fluid-particle interactions. By using special mesh moving schemes, the frequency of remeshing is minimized to reduce the projection errors involved in remeshing and also to increase the parallelization ease of the computations. The implicit equation systems arising from the finite element discretizations are solved iteratively by using the GMRES update technique with the diagonal and nodal-block-diagonal preconditioners. These formulations have all been implemented on the CM-200 and CM-5, and have been applied to several large-scale problems. The three-dimensional problems in this report were all computed on the CM-200 and CM-5.
NASA Astrophysics Data System (ADS)
Vu, Thu Hang; Deeks, Andrew J.
2014-04-01
This paper introduces a new technique for solving concentrated load problems in the scaled boundary finite element method (FEM). By employing fundamental solutions for the displacements and the stresses, the solution is computed as summation of a fundamental solution part and a regular part. The singularity at the point of load application is modelled exactly by the fundamental solution, and only the regular part, which enforces the boundary conditions of the domain onto the fundamental solution, needs to be approximated in the solution space of the scaled boundary FEM. Examples are provided illustrating that the new approach is much simpler to implement and more accurate than the method currently used for solving concentrated load problems with the scaled boundary method. In each illustration, solution convergence is examined. The relative error is described in terms of the scalar energy norm of the stress field. Mesh refinement is performed using p-refinement with high order element based on the Lobatto shape functions. The proposed technique is described for two-dimensional problems in this paper, but extension to any linear problem, for which fundamental solutions exist, is straightforward.
A new simple multidomain fast multipole boundary element method
NASA Astrophysics Data System (ADS)
Huang, S.; Liu, Y. J.
2016-09-01
A simple multidomain fast multipole boundary element method (BEM) for solving potential problems is presented in this paper, which can be applied to solve a true multidomain problem or a large-scale single domain problem using the domain decomposition technique. In this multidomain BEM, the coefficient matrix is formed simply by assembling the coefficient matrices of each subdomain and the interface conditions between subdomains without eliminating any unknown variables on the interfaces. Compared with other conventional multidomain BEM approaches, this new approach is more efficient with the fast multipole method, regardless how the subdomains are connected. Instead of solving the linear system of equations directly, the entire coefficient matrix is partitioned and decomposed using Schur complement in this new approach. Numerical results show that the new multidomain fast multipole BEM uses fewer iterations in most cases with the iterative equation solver and less CPU time than the traditional fast multipole BEM in solving large-scale BEM models. A large-scale fuel cell model with more than 6 million elements was solved successfully on a cluster within 3 h using the new multidomain fast multipole BEM.
Gumerov, Nail A; Duraiswami, Ramani
2009-01-01
The development of a fast multipole method (FMM) accelerated iterative solution of the boundary element method (BEM) for the Helmholtz equations in three dimensions is described. The FMM for the Helmholtz equation is significantly different for problems with low and high kD (where k is the wavenumber and D the domain size), and for large problems the method must be switched between levels of the hierarchy. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements), and these errors must be balanced against approximations introduced by the FMM and the convergence criterion for iterative solution. These different errors must all be chosen in a way that, on the one hand, excess work is not done and, on the other, that the error achieved by the overall computation is acceptable. Details of translation operators for low and high kD, choice of representations, and BEM quadrature schemes, all consistent with these approximations, are described. A novel preconditioner using a low accuracy FMM accelerated solver as a right preconditioner is also described. Results of the developed solvers for large boundary value problems with 0.0001 less, similarkD less, similar500 are presented and shown to perform close to theoretical expectations.
Programmable computing with a single magnetoresistive element
NASA Astrophysics Data System (ADS)
Ney, A.; Pampuch, C.; Koch, R.; Ploog, K. H.
2003-10-01
The development of transistor-based integrated circuits for modern computing is a story of great success. However, the proved concept for enhancing computational power by continuous miniaturization is approaching its fundamental limits. Alternative approaches consider logic elements that are reconfigurable at run-time to overcome the rigid architecture of the present hardware systems. Implementation of parallel algorithms on such `chameleon' processors has the potential to yield a dramatic increase of computational speed, competitive with that of supercomputers. Owing to their functional flexibility, `chameleon' processors can be readily optimized with respect to any computer application. In conventional microprocessors, information must be transferred to a memory to prevent it from getting lost, because electrically processed information is volatile. Therefore the computational performance can be improved if the logic gate is additionally capable of storing the output. Here we describe a simple hardware concept for a programmable logic element that is based on a single magnetic random access memory (MRAM) cell. It combines the inherent advantage of a non-volatile output with flexible functionality which can be selected at run-time to operate as an AND, OR, NAND or NOR gate.
Programmable computing with a single magnetoresistive element.
Ney, A; Pampuch, C; Koch, R; Ploog, K H
2003-10-02
The development of transistor-based integrated circuits for modern computing is a story of great success. However, the proved concept for enhancing computational power by continuous miniaturization is approaching its fundamental limits. Alternative approaches consider logic elements that are reconfigurable at run-time to overcome the rigid architecture of the present hardware systems. Implementation of parallel algorithms on such 'chameleon' processors has the potential to yield a dramatic increase of computational speed, competitive with that of supercomputers. Owing to their functional flexibility, 'chameleon' processors can be readily optimized with respect to any computer application. In conventional microprocessors, information must be transferred to a memory to prevent it from getting lost, because electrically processed information is volatile. Therefore the computational performance can be improved if the logic gate is additionally capable of storing the output. Here we describe a simple hardware concept for a programmable logic element that is based on a single magnetic random access memory (MRAM) cell. It combines the inherent advantage of a non-volatile output with flexible functionality which can be selected at run-time to operate as an AND, OR, NAND or NOR gate.
Synchrotron Imaging Computations on the Grid without the Computing Element
NASA Astrophysics Data System (ADS)
Curri, A.; Pugliese, R.; Borghes, R.; Kourousias, G.
2011-12-01
Besides the heavy use of the Grid in the Synchrotron Radiation Facility (SRF) Elettra, additional special requirements from the beamlines had to be satisfied through a novel solution that we present in this work. In the traditional Grid Computing paradigm the computations are performed on the Worker Nodes of the grid element known as the Computing Element. A Grid middleware extension that our team has been working on, is that of the Instrument Element. In general it is used to Grid-enable instrumentation; and it can be seen as a neighbouring concept to that of the traditional Control Systems. As a further extension we demonstrate the Instrument Element as the steering mechanism for a series of computations. In our deployment it interfaces a Control System that manages a series of computational demanding Scientific Imaging tasks in an online manner. The instrument control in Elettra is done through a suitable Distributed Control System, a common approach in the SRF community. The applications that we present are for a beamline working in medical imaging. The solution resulted to a substantial improvement of a Computed Tomography workflow. The near-real-time requirements could not have been easily satisfied from our Grid's middleware (gLite) due to the various latencies often occurred during the job submission and queuing phases. Moreover the required deployment of a set of TANGO devices could not have been done in a standard gLite WN. Besides the avoidance of certain core Grid components, the Grid Security infrastructure has been utilised in the final solution.
Brain-skull boundary conditions in a computational deformation model
NASA Astrophysics Data System (ADS)
Ji, Songbai; Liu, Fenghong; Roberts, David; Hartov, Alex; Paulsen, Keith
2007-03-01
Brain shift poses a significant challenge to accurate image-guided neurosurgery. To this end, finite element (FE) brain models have been developed to estimate brain motion during these procedures. The significance of the brain-skull boundary conditions (BCs) for accurate predictions in these models has been explored in dynamic impact and inertial rotation injury computational simulations where the results have shown that the brain mechanical response is sensitive to the type of BCs applied. We extend the study of brain-skull BCs to quasi-static brain motion simulations which prevail in neurosurgery. Specifically, a frictionless brain-skull BC using a contact penalty method master-slave paradigm is incorporated into our existing deformation forward model (forced displacement method). The initial brain-skull gap (CSF thickness) is assumed to be 2mm for demonstration purposes. The brain surface nodes are assigned as either fixed (at bottom along the gravity direction), free (at brainstem), with prescribed displacement (at craniotomy) or as slave nodes potentially in contact with the skull (all the remaining). Each slave node is assigned a penalty parameter (β=5) such that when the node penetrates the rigid body skull inner-surface (master surface), a contact force is introduced proportionally to the penetration. Effectively, brain surface nodes are allowed to move towards or away from the cranium wall, but are ultimately restricted from penetrating the skull. We show that this scheme improves the model's ability to represent the brain-skull interface.
On boundary-element models of elastic fault interaction
NASA Astrophysics Data System (ADS)
Becker, T. W.; Schott, B.
2002-12-01
We present the freely available, modular, and UNIX command-line based boundary-element program interact. It is yet another implementation of Crouch and Starfield's (1983) 2-D and Okada's (1992) half-space solutions for constant slip on planar fault segments in an elastic medium. Using unconstrained or non-negative, standard-package matrix routines, the code can solve for slip distributions on faults given stress boundary conditions, or vice versa, both in a local or global reference frame. Based on examples of complex fault geometries from structural geology, we discuss the effects of different stress boundary conditions on the predicted slip distributions of interacting fault systems. Such one-step calculations can be useful to estimate the moment-release efficiency of alternative fault geometries, and so to evaluate the likelihood which system may be realized in nature. A further application of the program is the simulation of cyclic fault rupture based on simple static-kinetic friction laws. We comment on two issues: First, that of the appropriate rupture algorithm. Cellular models of seismicity often employ an exhaustive rupture scheme: fault cells fail if some critical stress is reached, then cells slip once-only by a given amount, and subsequently the redistributed stress is used to check for triggered activations on other cells. We show that this procedure can lead to artificial complexity in seismicity if time-to-failure is not calculated carefully because of numerical noise. Second, we address the question if foreshocks can be viewed as direct expressions of a simple statistical distribution of frictional strength on individual faults. Repetitive failure models based on a random distribution of frictional coefficients initially show irregular seismicity. By repeatedly selecting weaker patches, the fault then evolves into a quasi-periodic cycle. Each time, the pre-mainshock events build up the cumulative moment release in a non-linear fashion. These
NASA Astrophysics Data System (ADS)
Ashbach, Jason A.
Periodic metallodielectric frequency selective surface (FSS) designs have historically seen widespread use in the microwave and radio frequency spectra. By scaling the dimensions of an FSS unit cell for use in a nano-fabrication process, these concepts have recently been adapted for use in optical applications as well. While early optical designs have been limited to wellunderstood geometries or optimized pixelated screens, nano-fabrication, lithographic and interconnect technology has progressed to a point where it is possible to fabricate metallic screens of arbitrary geometries featuring curvilinear or even three-dimensional characteristics that are only tens of nanometers wide. In order to design an FSS featuring such characteristics, it is important to have a robust numerical solver that features triangular elements in purely two-dimensional geometries and prismatic or tetrahedral elements in three-dimensional geometries. In this dissertation, a periodic finite element method code has been developed which features prismatic elements whose top and bottom boundaries are truncated by numerical integration of the boundary integral as opposed to an approximate representation found in a perfectly matched layer. However, since no exact solution exists for the calculation of triangular elements in a boundary integral, this process can be time consuming. To address this, these calculations were optimized for parallelization such that they may be done on a graphics processor, which provides a large increase in computational speed. Additionally, a simple geometrical representation using a Bezier surface is presented which provides generality with few variables. With a fast numerical solver coupled with a lowvariable geometric representation, a heuristic optimization algorithm has been used to develop several optical designs such as an absorber, a circular polarization filter, a transparent conductive surface and an enhanced, optical modulator.
Hypersonic turbulent wall boundary layer computations
NASA Astrophysics Data System (ADS)
Kim, S. C.; Harloff, G. J.
1988-05-01
The Baldwin-Lomax algebraic turbulence model was modified for hypersonic flow conditions. Two coefficients in the outer layer eddy viscosity model were determined as functions of Mach number and temperature ratio. By matching the solutions from the Baldwin-Lomax model to those from the Cebeci-Smith model for a flat plate at hypersonic speed, the new values of the coefficient were obtained. The results show that the values of C sub cp and C sub kleb are functions of both Mach number and wall temperature ratio. The C sub cp and C sub kleb variations with Mach number and wall temperature were used for the calculations of both a 4 deg wedge flow at Mach 18 and an axisymmetric Mach 20 nozzle flow. The Navier-Stokes equations with thin layer approximation were solved for the above hypersonic flow conditions and the results were compared with existing experimental data. The agreement between the numerical solutions and the existing experimental data were good. The modified Baldwin-Lomax model thus is useful in the computations of hypersonic flows.
Hypersonic turbulent wall boundary layer computations
NASA Technical Reports Server (NTRS)
Kim, S. C.; Harloff, G. J.
1988-01-01
The Baldwin-Lomax (1978) algebraic turbulence model was modified for hypersonic flow conditions. Two coefficients in the outer-layer eddy-viscosity model were determined as functions of Mach number and temperature ratio. By matching the solutions from the Baldwin-Lomax model to those from the Cebeci-Smith (1974) model for a flat plate at hypersonic speed, the new values of the coefficients were obtained. The results show that the values of C(cp) and C(kleb) are functions of both Mach number and wall temperature ratio. The C(cp) and C(kleb) variations with Mach number and wall temperature were used for the calculations of both a 4-deg wedge flow at Mach 18 and an axisymmetric Mach 20 nozzle flow. The Navier-Stokes equations with thin-layer approximation were solved for the above hypersonic flow conditions and the results were compared with existing experimental data. The agreement between the numerical solutions and the existing experimental data were good. The modified Baldwin-Lomax model thus is useful in the computations of hypersonic flows.
Hypersonic turbulent wall boundary layer computations
NASA Technical Reports Server (NTRS)
Kim, S. C.; Harloff, G. J.
1988-01-01
The Baldwin-Lomax algebraic turbulence model was modified for hypersonic flow conditions. Two coefficients in the outer layer eddy viscosity model were determined as functions of Mach number and temperature ratio. By matching the solutions from the Baldwin-Lomax model to those from the Cebeci-Smith model for a flat plate at hypersonic speed, the new values of the coefficient were obtained. The results show that the values of C sub cp and C sub kleb are functions of both Mach number and wall temperature ratio. The C sub cp and C sub kleb variations with Mach number and wall temperature were used for the calculations of both a 4 deg wedge flow at Mach 18 and an axisymmetric Mach 20 nozzle flow. The Navier-Stokes equations with thin layer approximation were solved for the above hypersonic flow conditions and the results were compared with existing experimental data. The agreement between the numerical solutions and the existing experimental data were good. The modified Baldwin-Lomax model thus is useful in the computations of hypersonic flows.
Ochiai, Yoshihiro
1995-09-01
Heat-conduction analysis under steady state without heat generation can easily be treated by the boundary element method. However, in the case with heat conduction with heat generation can approximately be solved without a domain integral by an improved multiple-reciprocity boundary element method. The convention multiple-reciprocity boundary element method is not suitable for complicated heat generation. In the improved multiple-reciprocity boundary element method, on the other hand, the domain integral in each step is divided into point, line, and area integrals. In order to solve the problem, the contour lines of heat generation, which approximate the actual heat generation, are used.
Novel TMS coils designed using an inverse boundary element method
NASA Astrophysics Data System (ADS)
Cobos Sánchez, Clemente; María Guerrero Rodriguez, Jose; Quirós Olozábal, Ángel; Blanco-Navarro, David
2017-01-01
In this work, a new method to design TMS coils is presented. It is based on the inclusion of the concept of stream function of a quasi-static electric current into a boundary element method. The proposed TMS coil design approach is a powerful technique to produce stimulators of arbitrary shape, and remarkably versatile as it permits the prototyping of many different performance requirements and constraints. To illustrate the power of this approach, it has been used for the design of TMS coils wound on rectangular flat, spherical and hemispherical surfaces, subjected to different constraints, such as minimum stored magnetic energy or power dissipation. The performances of such coils have been additionally described; and the torque experienced by each stimulator in the presence of a main magnetic static field have theoretically found in order to study the prospect of using them to perform TMS and fMRI concurrently. The obtained results show that described method is an efficient tool for the design of TMS stimulators, which can be applied to a wide range of coil geometries and performance requirements.
Completed double layer boundary element method for periodic suspensions
NASA Astrophysics Data System (ADS)
Fan, X.-J.; Phan-Thien, N.; Zheng, R.
In this paper, a traction-based boundary element method is formulated and implemented for periodic suspensions. Hydrodynamic interaction of particles at infinity is handled by O'Brien's method (1979), which is suitably modified for the adjoint double layer using the mean field values of the traction and the background flow. After a deflation of the extreme eigenvalue -1 of the adjoint double layer operator, an iterative solution strategy is implemented, which solves for the traction field on the surfaces of a group of near-by particles sequentially. Ewald's summation technique is employed, by expressing the adjoint double layer kernel in two sums, one converges rapidly in real space, and the other, in the reciprocal Fourier space. The implementation is tested on a periodic suspension of spheres and spheroids in simple and elongated face-centred cubic arrays, and proved to be very accurate when compared to established results. New results for the intrinsic viscosities of periodic suspensions of cubes and spheroids from moderate to high volume fractions are reported. Based on the numerical data for suspensions of spheroids, a simple modification of the constitutive equation of Hinch and Leal (1972), which was derived for dilute suspension of spheroids, is reported, allowing the constitutive equation to reasonably fit the numerical data at moderate to high concentrations.
Improvement in computational fluid dynamics through boundary verification and preconditioning
NASA Astrophysics Data System (ADS)
Folkner, David E.
This thesis provides improvements to computational fluid dynamics accuracy and efficiency through two main methods: a new boundary condition verification procedure and preconditioning techniques. First, a new verification approach that addresses boundary conditions was developed. In order to apply the verification approach to a large range of arbitrary boundary conditions, it was necessary to develop unifying mathematical formulation. A framework was developed that allows for the application of Dirichlet, Neumann, and extrapolation boundary condition, or in some cases the equations of motion directly. Verification of boundary condition techniques was performed using exact solutions from canonical fluid dynamic test cases. Second, to reduce computation time and improve accuracy, preconditioning algorithms were applied via artificial dissipation schemes. A new convective upwind and split pressure (CUSP) scheme was devised and was shown to be more effective than traditional preconditioning schemes in certain scenarios. The new scheme was compared with traditional schemes for unsteady flows for which both convective and acoustic effects dominated. Both boundary conditions and preconditioning algorithms were implemented in the context of a "strand grid" solver. While not the focus of this thesis, strand grids provide automatic viscous quality meshing and are suitable for moving mesh overset problems.
The case for biological quantum computer elements
NASA Astrophysics Data System (ADS)
Baer, Wolfgang; Pizzi, Rita
2009-05-01
An extension to vonNeumann's analysis of quantum theory suggests self-measurement is a fundamental process of Nature. By mapping the quantum computer to the brain architecture we will argue that the cognitive experience results from a measurement of a quantum memory maintained by biological entities. The insight provided by this mapping suggests quantum effects are not restricted to small atomic and nuclear phenomena but are an integral part of our own cognitive experience and further that the architecture of a quantum computer system parallels that of a conscious brain. We will then review the suggestions for biological quantum elements in basic neural structures and address the de-coherence objection by arguing for a self- measurement event model of Nature. We will argue that to first order approximation the universe is composed of isolated self-measurement events which guaranties coherence. Controlled de-coherence is treated as the input/output interactions between quantum elements of a quantum computer and the quantum memory maintained by biological entities cognizant of the quantum calculation results. Lastly we will present stem-cell based neuron experiments conducted by one of us with the aim of demonstrating the occurrence of quantum effects in living neural networks and discuss future research projects intended to reach this objective.
A novel periodic boundary condition for computational hemodynamics studies.
Bahramian, Fereshteh; Mohammadi, Hadi
2014-07-01
In computational fluid dynamics models for hemodynamics applications, boundary conditions remain one of the major issues in obtaining accurate fluid flow predictions. For major cardiovascular models, the realistic boundary conditions are not available. In order to address this issue, the whole computational domain needs to be modeled, which is practically impossible. For simulating fully developed turbulent flows using the large eddy simulation and dynamic numerical solution methods, which are very popular in hemodynamics studies, periodic boundary conditions are suitable. This is mainly because the computational domain can be reduced considerably. In this study, a novel periodic boundary condition is proposed, which is based on mass flow condition. The proposed boundary condition is applied on a square duct for the sake of validation. The mass-based condition was shown to obtain the solution in 15% less time. As such, the mass-based condition has two decisive advantages: first, the solution for a given Reynolds number can be obtained in a single simulation because of the direct specification of the mass flow, and second, simulations can be made more quickly.
NASA Astrophysics Data System (ADS)
Chu, Yuchuan; Cao, Yong; He, Xiaoming; Luo, Min
2011-11-01
Many of the magnetostatic/electrostatic field problems encountered in aerospace engineering, such as plasma sheath simulation and ion neutralization process in space, are not confined to finite domain and non-interface problems, but characterized as open boundary and interface problems. Asymptotic boundary conditions (ABC) and immersed finite elements (IFE) are relatively new tools to handle open boundaries and interface problems respectively. Compared with the traditional truncation approach, asymptotic boundary conditions need a much smaller domain to achieve the same accuracy. When regular finite element methods are applied to an interface problem, it is necessary to use a body-fitting mesh in order to obtain the optimal convergence rate. However, immersed finite elements possess the same optimal convergence rate on a Cartesian mesh, which is critical to many applications. This paper applies immersed finite element methods and asymptotic boundary conditions to solve an interface problem arising from electric field simulation in composite materials with open boundary. Numerical examples are provided to demonstrate the high global accuracy of the IFE method with ABC based on Cartesian meshes, especially around both interface and boundary. This algorithm uses a much smaller domain than the truncation approach in order to achieve the same accuracy.
Finite element concepts in computational aerodynamics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1978-01-01
Finite element theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the finite element concept for computational aerodynamics is made.
High-Speed Boundary-Layer Transition Induced by an Isolated Roughness Element
NASA Technical Reports Server (NTRS)
Kegerise, Michael A.; Owens, Lewis R.; King, Rudolph A.
2010-01-01
Progress on an experimental effort to quantify the instability mechanisms associated with roughness-induced transition in a high-speed boundary layer is reported in this paper. To simulate the low-disturbance environment encountered during high-altitude flight, the experimental study was performed in the NASA-Langley Mach 3.5 Supersonic Low-Disturbance Tunnel. A flat plate trip sizing study was performed first to identify the roughness height required to force transition. That study, which included transition onset measurements under both quiet and noisy freestream conditions, confirmed the sensitivity of roughness-induced transition to freestream disturbance levels. Surveys of the laminar boundary layer on a 7deg half-angle sharp-tipped cone were performed via hot-wire anemometry and pitot-pressure measurements. The measured mean mass-flux and Mach-number profiles agreed very well with computed mean-flow profiles. Finally, surveys of the boundary layer developing downstream of an isolated roughness element on the cone were performed. The measurements revealed an instability in the far wake of the roughness element that grows exponentially and has peak frequencies in the 150 to 250 kHz range.
NASA Astrophysics Data System (ADS)
Gu, Yan; Gao, Hongwei; Chen, Wen; Wang, Huijuan; Zhang, Chuanzeng
2017-05-01
One of the typical and most significant issues of almost all boundary element analyses is the accurate evaluation of nearly singular boundary element integrals. In this study, we review some numerical techniques used currently to calculate nearly singular integrals and propose an improved algorithm to calculate integrals with nearly strong (and beyond) singularities. This new method has full generally and can be easily included in any existing computer code. The method is tested in general three-dimensional boundary element analysis. Comparison of this method with some of the existing methods is also presented. It is shown that several orders of magnitude improvement in relative errors can be obtained using the proposed method when compared to a straightforward implementation of Gaussian quadrature.
Massively parallel computation of RCS with finite elements
NASA Technical Reports Server (NTRS)
Parker, Jay
1993-01-01
One of the promising combinations of finite element approaches for scattering problems uses Whitney edge elements, spherical vector wave-absorbing boundary conditions, and bi-conjugate gradient solution for the frequency-domain near field. Each of these approaches may be criticized. Low-order elements require high mesh density, but also result in fast, reliable iterative convergence. Spherical wave-absorbing boundary conditions require additional space to be meshed beyond the most minimal near-space region, but result in fully sparse, symmetric matrices which keep storage and solution times low. Iterative solution is somewhat unpredictable and unfriendly to multiple right-hand sides, yet we find it to be uniformly fast on large problems to date, given the other two approaches. Implementation of these approaches on a distributed memory, message passing machine yields huge dividends, as full scalability to the largest machines appears assured and iterative solution times are well-behaved for large problems. We present times and solutions for computed RCS for a conducting cube and composite permeability/conducting sphere on the Intel ipsc860 with up to 16 processors solving over 200,000 unknowns. We estimate problems of approximately 10 million unknowns, encompassing 1000 cubic wavelengths, may be attempted on a currently available 512 processor machine, but would be exceedingly tedious to prepare. The most severe bottlenecks are due to the slow rate of mesh generation on non-parallel machines and the large transfer time from such a machine to the parallel processor. One solution, in progress, is to create and then distribute a coarse mesh among the processors, followed by systematic refinement within each processor. Elimination of redundant node definitions at the mesh-partition surfaces, snap-to-surface post processing of the resulting mesh for good modelling of curved surfaces, and load-balancing redistribution of new elements after the refinement are auxiliary
Fast iterative boundary element methods for high-frequency scattering problems in 3D elastodynamics
NASA Astrophysics Data System (ADS)
Chaillat, Stéphanie; Darbas, Marion; Le Louër, Frédérique
2017-07-01
The fast multipole method is an efficient technique to accelerate the solution of large scale 3D scattering problems with boundary integral equations. However, the fast multipole accelerated boundary element method (FM-BEM) is intrinsically based on an iterative solver. It has been shown that the number of iterations can significantly hinder the overall efficiency of the FM-BEM. The derivation of robust preconditioners for FM-BEM is now inevitable to increase the size of the problems that can be considered. The main constraint in the context of the FM-BEM is that the complete system is not assembled to reduce computational times and memory requirements. Analytic preconditioners offer a very interesting strategy by improving the spectral properties of the boundary integral equations ahead from the discretization. The main contribution of this paper is to combine an approximate adjoint Dirichlet to Neumann (DtN) map as an analytic preconditioner with a FM-BEM solver to treat Dirichlet exterior scattering problems in 3D elasticity. The approximations of the adjoint DtN map are derived using tools proposed in [40]. The resulting boundary integral equations are preconditioned Combined Field Integral Equations (CFIEs). We provide various numerical illustrations of the efficiency of the method for different smooth and non-smooth geometries. In particular, the number of iterations is shown to be completely independent of the number of degrees of freedom and of the frequency for convex obstacles.
NASA Astrophysics Data System (ADS)
Bozkaya, C.; Tezer-Sezgin, M.
2006-06-01
A numerical scheme which is a combination of the dual reciprocity boundary element method (DRBEM) and the differential quadrature method (DQM), is proposed for the solution of unsteady magnetohydrodynamic (MHD) flow problem in a rectangular duct with insulating walls. The coupled MHD equations in velocity and induced magnetic field are transformed first into the decoupled time-dependent convection-diffusion-type equations. These equations are solved by using DRBEM which treats the time and the space derivatives as nonhomogeneity and then by using DQM for the resulting system of initial value problems. The resulting linear system of equations is overdetermined due to the imposition of both boundary and initial conditions. Employing the least square method to this system the solution is obtained directly at any time level without the need of step-by-step computation with respect to time. Computations have been carried out for moderate values of Hartmann number (M50) at transient and the steady-state levels. As M increases boundary layers are formed for both the velocity and the induced magnetic field and the velocity becomes uniform at the centre of the duct. Also, the higher the value of M is the smaller the value of time for reaching steady-state solution.
GPU-accelerated indirect boundary element method for voxel model analyses with fast multipole method
NASA Astrophysics Data System (ADS)
Hamada, Shoji
2011-05-01
An indirect boundary element method (BEM) that uses the fast multipole method (FMM) was accelerated using graphics processing units (GPUs) to reduce the time required to calculate a three-dimensional electrostatic field. The BEM is designed to handle cubic voxel models and is specialized to consider square voxel walls as boundary surface elements. The FMM handles the interactions among the surface charge elements and directly outputs surface integrals of the fields over each individual element. The CPU code was originally developed for field analysis in human voxel models derived from anatomical images. FMM processes are programmed using the NVIDIA Compute Unified Device Architecture (CUDA) with double-precision floating-point arithmetic on the basis of a shared pseudocode template. The electric field induced by DC-current application between two electrodes is calculated for two models with 499,629 (model 1) and 1,458,813 (model 2) surface elements. The calculation times were measured with a four-GPU configuration (two NVIDIA GTX295 cards) with four CPU cores (an Intel Core i7-975 processor). The times required by a linear system solver are 31 s and 186 s for models 1 and 2, respectively. The speed-up ratios of the FMM range from 5.9 to 8.2 for model 1 and from 5.0 to 5.6 for model 2. The calculation speed for element-interaction in this BEM analysis was comparable to that of particle-interaction using FMM on a GPU.
Boundary element method applied to a gas-fired pin-fin-enhanced heat pipe
Andraka, C.E.; Knorovsky, G.A.; Drewien, C.A.
1998-02-01
The thermal conduction of a portion of an enhanced surface heat exchanger for a gas fired heat pipe solar receiver was modeled using the boundary element and finite element methods (BEM and FEM) to determine the effect of weld fillet size on performance of a stud welded pin fin. A process that could be utilized by others for designing the surface mesh on an object of interest, performing a conversion from the mesh into the input format utilized by the BEM code, obtaining output on the surface of the object, and displaying visual results was developed. It was determined that the weld fillet on the pin fin significantly enhanced the heat performance, improving the operating margin of the heat exchanger. The performance of the BEM program on the pin fin was measured (as computational time) and used as a performance comparison with the FEM model. Given similar surface element densities, the BEM method took longer to get a solution than the FEM method. The FEM method creates a sparse matrix that scales in storage and computation as the number of nodes (N), whereas the BEM method scales as N{sup 2} in storage and N{sup 3} in computation.
T.F. Eibert; J.L. Volakis; Y.E. Erdemli
2002-03-03
Hybrid finite element (FE)--boundary integral (BI) analysis of infinite periodic arrays is extended to include planar multilayered Green's functions. In this manner, a portion of the volumetric dielectric region can be modeled via the finite element method whereas uniform multilayered regions can be modeled using a multilayered Green's function. As such, thick uniform substrates can be modeled without loss of efficiency and accuracy. The multilayered Green's function is analytically computed in the spectral domain and the resulting BI matrix-vector products are evaluated via the fast spectral domain algorithm (FSDA). As a result, the computational cost of the matrix-vector products is kept at O(N). Furthermore, the number of Floquet modes in the expansion are kept very few by placing the BI surfaces within the computational unit cell. Examples of frequency selective surface (FSS) arrays are analyzed with this method to demonstrate the accuracy and capability of the approach. One example involves complicated multilayered substrates above and below an inhomogeneous filter element and the other is an optical ring-slot array on a substrate several hundred wavelengths in thickness. Comparisons with measurements are included.
NASA Astrophysics Data System (ADS)
Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin; Auken, Esben; Han, Muran; Li, Jianhui
2017-10-01
We implemented an edge-based finite element time domain (FETD) modeling algorithm for simulating controlled-source electromagnetic (CSEM) data. The modeling domain is discretized using unstructured tetrahedral mesh and we consider a finite difference discretization of time using the backward Euler method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping method with trivial computation cost once the matrix is factorized. We try to keep the same time step size for a fixed number of steps using an adaptive time step doubling (ATSD) method. The finite element modeling domain is also truncated using a semi-adaptive method. We proposed a new boundary condition based on approximating the total field on the modeling boundary using the primary field corresponding to a layered background model. We validate our algorithm using several synthetic model studies.
NASA Technical Reports Server (NTRS)
Seybert, A. F.; Wu, T. W.; Wu, X. F.
1994-01-01
This research report is presented in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing and the radiation efficiency of each mode. The radiation efficiency of each of the transmission housing modes was then compared to theoretical results for a finite baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis; noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: sound power predicted by the BEM model using vibration data measured on the surface of the box; sound power predicted by the FEM/BEM model; and sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. The predicted vibration and radiated noise were then validated through experimentation.
NASA Astrophysics Data System (ADS)
Wu, Xuefeng
1992-01-01
The research presented in this dissertation is reported in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing, and the radiation efficiency of each mode. The radiation efficiency of the transmission housing modes was then compared to theoretical results for finite, baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level expected to be radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis, noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: (1) sound power predicted by the BEM model using vibration data measured on the surface of the box; (2) sound power predicted by the FEM/BEM model; and (3) sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. The predicted vibration and radiated noise were then validated through experimentation.
Koteras, J.R.
1996-01-01
The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region.
Boundary element modeling of earthquake site effects including the complete incident wavefield
NASA Astrophysics Data System (ADS)
Kim, Kyoung-Tae
Numerical modeling of earthquake site effects in realistic, three-dimensional structures, including high frequencies, low surface velocities and surface topography, has not been possible simply because the amount of computer memory constrains the number of grid points available. In principle, this problem is reduced in the Boundary Element Method (BEM) since only the surface of the velocity discontinuity is discretized; wave propagation both inside and outside this boundary is computed analytically. Equivalent body forces are determined on the boundary by solving a matrix equation containing frequency-domain displacement and stress Green's functions from every point on the boundary to every other point. This matrix problem has imposed a practical limit on the size or maximum frequency of previous BEM models. Although the matrix can be quite large, it also seems to be fairly sparse. We have used iterative matrix algorithms of the PETSc package and direct solution algorithms of the ScaLAPACK on the massively parallel supercomputers at Cornell, San Diego and Michigan. Preconditioning has been applied using blockwise ILU decomposition for the iterative approach or LU decomposition for the direct approach. The matrix equation is solved using the GMRES method for the iterative approach and a tri-diagonal solver for the direct approach. Previous BEM applications typically have assumed a single, incident plane wave. However, it is clear that for more realistic ground motion simulations, we need to consider the complete incident wavefield. If we assume that the basin or three-dimensional structure of interest is embedded in a surrounding plane-layered medium, we may use the propagator matrix method to solve for the displacements and stresses at depth on the boundary. This is done in the frequency domain with integration over wavenumber so that all P, S, mode conversions, reverberations and surface waves are included. The Boundary Element Method succeeds in modeling
BEST3D user's manual: Boundary Element Solution Technology, 3-Dimensional Version 3.0
NASA Technical Reports Server (NTRS)
1991-01-01
The theoretical basis and programming strategy utilized in the construction of the computer program BEST3D (boundary element solution technology - three dimensional) and detailed input instructions are provided for the use of the program. An extensive set of test cases and sample problems is included in the manual and is also available for distribution with the program. The BEST3D program was developed under the 3-D Inelastic Analysis Methods for Hot Section Components contract (NAS3-23697). The overall objective of this program was the development of new computer programs allowing more accurate and efficient three-dimensional thermal and stress analysis of hot section components, i.e., combustor liners, turbine blades, and turbine vanes. The BEST3D program allows both linear and nonlinear analysis of static and quasi-static elastic problems and transient dynamic analysis for elastic problems. Calculation of elastic natural frequencies and mode shapes is also provided.
Artificial Boundary Conditions for Computation of Oscillating External Flows
NASA Technical Reports Server (NTRS)
Tsynkov, S. V.
1996-01-01
In this paper, we propose a new technique for the numerical treatment of external flow problems with oscillatory behavior of the solution in time. Specifically, we consider the case of unbounded compressible viscous plane flow past a finite body (airfoil). Oscillations of the flow in time may be caused by the time-periodic injection of fluid into the boundary layer, which in accordance with experimental data, may essentially increase the performance of the airfoil. To conduct the actual computations, we have to somehow restrict the original unbounded domain, that is, to introduce an artificial (external) boundary and to further consider only a finite computational domain. Consequently, we will need to formulate some artificial boundary conditions (ABC's) at the introduced external boundary. The ABC's we are aiming to obtain must meet a fundamental requirement. One should be able to uniquely complement the solution calculated inside the finite computational domain to its infinite exterior so that the original problem is solved within the desired accuracy. Our construction of such ABC's for oscillating flows is based on an essential assumption: the Navier-Stokes equations can be linearized in the far field against the free-stream back- ground. To actually compute the ABC's, we represent the far-field solution as a Fourier series in time and then apply the Difference Potentials Method (DPM) of V. S. Ryaben'kii. This paper contains a general theoretical description of the algorithm for setting the DPM-based ABC's for time-periodic external flows. Based on our experience in implementing analogous ABC's for steady-state problems (a simpler case), we expect that these boundary conditions will become an effective tool for constructing robust numerical methods to calculate oscillatory flows.
The simulation of Lamb waves in a cracked plate using the scaled boundary finite element method.
Gravenkamp, Hauke; Prager, Jens; Saputra, Albert A; Song, Chongmin
2012-09-01
The scaled boundary finite element method is applied to the simulation of Lamb waves for ultrasonic testing applications. With this method, the general elastodynamic problem is solved, while only the boundary of the domain under consideration has to be discretized. The reflection of the fundamental Lamb wave modes from cracks of different geometry in a steel plate is modeled. A test problem is compared with commercial finite element software, showing the efficiency and convergence of the scaled boundary finite element method. A special formulation of this method is utilized to calculate dispersion relations for plate structures. For the discretization of the boundary, higher-order elements are employed to improve the efficiency of the simulations. The simplicity of mesh generation of a cracked plate for a scaled boundary finite element analysis is illustrated.
Linear and nonlinear dynamic analysis by boundary element method. Ph.D. Thesis, 1986 Final Report
NASA Technical Reports Server (NTRS)
Ahmad, Shahid
1991-01-01
An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons
Open Rotor Computational Aeroacoustic Analysis with an Immersed Boundary Method
NASA Technical Reports Server (NTRS)
Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.
2016-01-01
Reliable noise prediction capabilities are essential to enable novel fuel efficient open rotor designs that can meet the community and cabin noise standards. Toward this end, immersed boundary methods have reached a level of maturity so that they are being frequently employed for specific real world applications within NASA. This paper demonstrates that our higher-order immersed boundary method provides the ability for aeroacoustic analysis of wake-dominated flow fields generated by highly complex geometries. This is the first of a kind aeroacoustic simulation of an open rotor propulsion system employing an immersed boundary method. In addition to discussing the peculiarities of applying the immersed boundary method to this moving boundary problem, we will provide a detailed aeroacoustic analysis of the noise generation mechanisms encountered in the open rotor flow. The simulation data is compared to available experimental data and other computational results employing more conventional CFD methods. The noise generation mechanisms are analyzed employing spectral analysis, proper orthogonal decomposition and the causality method.
Open Rotor Computational Aeroacoustic Analysis with an Immersed Boundary Method
NASA Technical Reports Server (NTRS)
Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.
2016-01-01
Reliable noise prediction capabilities are essential to enable novel fuel efficient open rotor designs that can meet the community and cabin noise standards. Toward this end, immersed boundary methods have reached a level of maturity where more and more complex flow problems can be tackled with this approach. This paper demonstrates that our higher-order immersed boundary method provides the ability for aeroacoustic analysis of wake-dominated flow fields generated by a contra-rotating open rotor. This is the first of a kind aeroacoustic simulation of an open rotor propulsion system employing an immersed boundary method. In addition to discussing the methodologies of how to apply the immersed boundary method to this moving boundary problem, we will provide a detailed validation of the aeroacoustic analysis approach employing the Launch Ascent and Vehicle Aerodynamics (LAVA) solver. Two free-stream Mach numbers with M=0.2 and M=0.78 are considered in this analysis that are based on the nominally take-off and cruise flow conditions. The simulation data is compared to available experimental data and other computational results employing more conventional CFD methods. Spectral analysis is used to determine the dominant wave propagation pattern in the acoustic near-field.
LES of turbulent boundary layer flow over urban-like roughness elements
NASA Astrophysics Data System (ADS)
Tamura, Tetsuro; Tsubokura, Makoto; Nozu, Tsuyoshi; Onishi, Keiji
2014-11-01
LES of turbulent boundary layer flow over urban-like roughness elements has been performed. Final goal of this paper is to elucidate the availability of LES on the wind flow within the canopy among buildings in cities. Firstly rectangular blocks, definitely larger than those on conventional rough wall such as grain or sand, are homogeneously arrayed and above-region equilibrium profiles of mean velocity and turbulent statistics are investigated. Also, in order to predict the fluctuating velocity characteristics of urban boundary layer, actual complicated-shaped buildings are used for reproducing the surface shape in cities. For numerical modeling, this study employs the unstructured-grid system where grid lines correctly fit to the building shape and BCM (Building Cube Method) which is formulated on very fine Cartesian mesh system. Based on the GIS data, BCM employs the external forcing technique named IBM (Immersed Boundary Method). Also, in BCM, computational process is so simple that the parallel algorithm and the memory access obtain the perfect efficiency. Using both the LES results, turbulence structures in the urban canopy are discussed. Appropriate 3D vortical structures can be recognized at inflow, along the street and among a pack of tall buildings.
Conserved boundary elements from the Hox complex of mosquito, Anopheles gambiae
Ahanger, Sajad H.; Srinivasan, Arumugam; Vasanthi, Dasari; Shouche, Yogesh S.; Mishra, Rakesh K.
2013-01-01
The conservation of hox genes as well as their genomic organization across the phyla suggests that this system of anterior–posterior axis formation arose early during evolution and has come under strong selection pressure. Studies in the split Hox cluster of Drosophila have shown that proper expression of hox genes is dependent on chromatin domain boundaries that prevent inappropriate interactions among different types of cis-regulatory elements. To investigate whether boundary function and their role in regulation of hox genes is conserved in insects with intact Hox clusters, we used an algorithm to locate potential boundary elements in the Hox complex of mosquito, Anopheles gambiae. Several potential boundary elements were identified that could be tested for their functional conservation. Comparative analysis revealed that like Drosophila, the bithorax region in A. gambiae contains an extensive array of boundaries and enhancers organized into domains. We analysed a subset of candidate boundary elements and show that they function as enhancer blockers in Drosophila. The functional conservation of boundary elements from mosquito in fly suggests that regulation of hox genes involving chromatin domain boundaries is an evolutionary conserved mechanism and points to an important role of such elements in key developmentally regulated loci. PMID:23221647
NASA Technical Reports Server (NTRS)
Seybert, A. F.; Wu, X. F.; Oswald, Fred B.
1992-01-01
Analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise radiated from the box. The FEM was used to predict the vibration, and the surface vibration was used as input to the BEM to predict the sound intensity and sound power. Vibration predicted by the FEM model was validated by experimental modal analysis. Noise predicted by the BEM was validated by sound intensity measurements. Three types of results are presented for the total radiated sound power: (1) sound power predicted by the BEM modeling using vibration data measured on the surface of the box; (2) sound power predicted by the FEM/BEM model; and (3) sound power measured by a sound intensity scan. The sound power predicted from the BEM model using measured vibration data yields an excellent prediction of radiated noise. The sound power predicted by the combined FEM/BEM model also gives a good prediction of radiated noise except for a shift of the natural frequencies that are due to limitations in the FEM model.
Computer constructed imagery of distant plasma interaction boundaries
NASA Technical Reports Server (NTRS)
Greenstadt, E. W.; Schurr, H. D.; Tsugawa, R. K.
1982-01-01
Computer constructed sketches of plasma boundaries arising from the interaction between the solar wind and the magnetosphere can serve as both didactic and research tools. In particular, the structure of the earth's bow shock can be represented as a nonuniform surfce according to the instantaneous orientation of the IMF, and temporal changes in structural distribution can be modeled as a sequence of sketches based on observed sequences of spacecraft-based measurements. Viewed rapidly, such a sequence of sketches can be the basis for representation of plasma processes by computer animation.
Computational quantum-classical boundary of noisy commuting quantum circuits
Fujii, Keisuke; Tamate, Shuhei
2016-01-01
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region. PMID:27189039
Computational quantum-classical boundary of noisy commuting quantum circuits.
Fujii, Keisuke; Tamate, Shuhei
2016-05-18
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.
Computational quantum-classical boundary of noisy commuting quantum circuits
NASA Astrophysics Data System (ADS)
Fujii, Keisuke; Tamate, Shuhei
2016-05-01
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.
Dual Reciprocity Boundary Element Method for studying thermal flow in cooling Magma Oceans
NASA Astrophysics Data System (ADS)
Drombosky, T.; Hier-Majumder, S.
2011-12-01
Earth's early history is marked by a giant impact with a Mars-sized object which lead to the formation of the moon. This impact event likely led to a substantial amount of melting of the Earth's interior. Subsequent cooling of the Earth involved extensive crystallization in this "magma ocean" over a relatively short period of time. While chemical evidence from ancient sources provides some clues on the rate of cooling, computational models of such phenomena are sparse. Modeling the crystal settling behavior requires solving a coupled system of partial differential equations, specifically the Stokes flow equation coupled with the heat equation through an advection term. Our work uses the dual reciprocity boundary element method (DRBEM) to model such a system. DRBEM extends on the boundary element method (BEM) to solve the heat equation for a multiparticle system in an infinite suspension fluid while avoiding the expensive rediscretization inherit in other methods. In DRBEM, terms arising from the material time derivative of temperature are expanded in a series of function, known as radial basis functions. By modeling this system we are able to simulate thermal interactions among an arbitrary number of crystals settling in a magma ocean. The types of interactions include the enhanced cooling of the magma due to an advecting matrix of cold crystal particles. We are also able to observe the interactions of the crystals' thermal profiles. As a crystal settles, it leaves behind a trail of lower temperature suspension fluid, which then interacts with surrounding particles.
Acoustic scattering for 3D multi-directional periodic structures using the boundary element method.
Karimi, Mahmoud; Croaker, Paul; Kessissoglou, Nicole
2017-01-01
An efficient boundary element formulation is proposed to solve three-dimensional exterior acoustic scattering problems with multi-directional periodicity. The multi-directional periodic acoustic problem is represented as a multilevel block Toeplitz matrix. By exploiting the Toeplitz structure, the computational time and storage requirements to construct and to solve the linear system of equations arising from the boundary element formulation are significantly reduced. The generalized minimal residual method is implemented to solve the linear system of equations. To efficiently calculate the matrix-vector product in the iterative algorithm, the original matrix is embedded into a multilevel block circulant matrix. A multi-dimensional discrete Fourier transform is then employed to accelerate the matrix-vector product. The proposed approach is applicable to a periodic acoustic problem for any arbitrary shape of the structure in both full space and half space. Two case studies involving sonic crystal barriers are presented. In the first case study, a sonic crystal barrier comprising rigid cylindrical scatterers is modeled. To demonstrate the effectiveness of the proposed technique, periodicity in one, two, or three directions is examined. In the second case study, the acoustic performance of a sonic crystal barrier with locally resonant C-shaped scatterers is studied.
Prediction of sound fields in acoustical cavities using the boundary element method. M.S. Thesis
NASA Technical Reports Server (NTRS)
Kipp, C. R.; Bernhard, R. J.
1985-01-01
A method was developed to predict sound fields in acoustical cavities. The method is based on the indirect boundary element method. An isoparametric quadratic boundary element is incorporated. Pressure, velocity and/or impedance boundary conditions may be applied to a cavity by using this method. The capability to include acoustic point sources within the cavity is implemented. The method is applied to the prediction of sound fields in spherical and rectangular cavities. All three boundary condition types are verified. Cases with a point source within the cavity domain are also studied. Numerically determined cavity pressure distributions and responses are presented. The numerical results correlate well with available analytical results.
White, D; Fasenfest, B; Rieben, R; Stowell, M
2006-09-08
We are concerned with the solution of time-dependent electromagnetic eddy current problems using a finite element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. We propose a Biot-Savart law based volume-to-surface boundary condition to meet this requirement. This Biot-Savart approach is demonstrated to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretized Biot-Savart law.
A time-domain finite element boundary integral approach for elastic wave scattering
NASA Astrophysics Data System (ADS)
Shi, F.; Lowe, M. J. S.; Skelton, E. A.; Craster, R. V.
2017-08-01
The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach.
Frayce, D.; Khayat, R.E.; Derdouri, A.
1996-02-23
The dual reciprocity boundary element method (DRBEM) is implemented to solve three-dimensional transient heat conduction problems in the presence of arbitrary sources, typically as these problems arise in materials processing. The DRBEM has a major advantage over conventional BEM, since it avoids the computation of volume integrals. These integrals stem from transient, nonlinear, and/or source terms. Thus there is no need to discretize the inner domain, since only a number of internal points are needed for the computation. The validity of the method is assessed upon comparison with results from benchmark problems where analytical solutions exist. There is generally good agreement. Comparison against finite element results is also favorable. Calculations are carried out in order to assess the influence of the number and location of internal nodes. The influence of the ratio of the numbers of internal to boundary nodes is also examined.
JCMmode: an adaptive finite element solver for the computation of leaky modes
NASA Astrophysics Data System (ADS)
Zschiedrich, Lin W.; Burger, Sven; Klose, Roland; Schaedle, Achim; Schmidt, Frank
2005-03-01
We present our simulation tool JCMmode for calculating propagating modes of an optical waveguide. As ansatz functions we use higher order, vectorial elements (Nedelec elements, edge elements). Further we construct transparent boundary conditions to deal with leaky modes even for problems with inhomogeneous exterior domains as for integrated hollow core Arrow waveguides. We have implemented an error estimator which steers the adaptive mesh refinement. This allows the precise computation of singularities near the metal's corner of a Plasmon-Polariton waveguide even for irregular shaped metal films on a standard personal computer.
Power throttling of collections of computing elements
Bellofatto, Ralph E.; Coteus, Paul W.; Crumley, Paul G.; Gara, Alan G.; Giampapa, Mark E.; Gooding; Thomas M.; Haring, Rudolf A.; Megerian, Mark G.; Ohmacht, Martin; Reed, Don D.; Swetz, Richard A.; Takken, Todd
2011-08-16
An apparatus and method for controlling power usage in a computer includes a plurality of computers communicating with a local control device, and a power source supplying power to the local control device and the computer. A plurality of sensors communicate with the computer for ascertaining power usage of the computer, and a system control device communicates with the computer for controlling power usage of the computer.
Computation of dispersion curves for embedded waveguides using a dashpot boundary condition.
Gravenkamp, Hauke; Birk, Carolin; Song, Chongmin
2014-03-01
In this paper a numerical approach is presented to compute dispersion curves for solid waveguides coupled to an infinite medium. The derivation is based on the scaled boundary finite element method that has been developed previously for waveguides with stress-free surfaces. The effect of the surrounding medium is accounted for by introducing a dashpot boundary condition at the interface between the waveguide and the adjoining medium. The damping coefficients are derived from the acoustic impedances of the surrounding medium. Results are validated using an improved implementation of an absorbing region. Since no discretization of the surrounding medium is required for the dashpot approach, the required number of degrees of freedom is typically 10 to 50 times smaller compared to the absorbing region. When compared to other finite element based results presented in the literature, the number of degrees of freedom can be reduced by as much as a factor of 4000.
Otani, Makoto; Ise, Shiro
2006-05-01
Recently, development of a numerical calculation of the head-related transfer function (HRTF) has been conducted using a computer model of a human head and the boundary element method. The reciprocity theorem is incorporated into the computational process in order to shorten the computational time, which is otherwise very long. On the other hand, another fast HRTF calculation method for any source position, which is realized by calculating factors independent of the source position in advance, has been suggested by the authors. Using this algorithm, the HRTF for any source position can be obtained in a few seconds with a common PC. The resulting HRTFs are more precise and are calculated faster than those by using the reciprocity theorem. However, speeding the process up even further is required in order to respond to a head movement and rotation or to moving sources during binaural sound reproduction. In this paper, a faster calculation method by incorporating a time domain operation into the authors' previous algorithm is proposed. Additionally, the new formulation, which eliminates the extra computational time in the preprocess, is proposed. This method is shown to be faster than the previous ones, but there are some discrepancies at higher frequencies.
NASA Astrophysics Data System (ADS)
Gartling, D. K.; Hickox, C. E.
1982-10-01
The theoretical background for the finite element computer program MARIAH is presented. The MARIAH code is designed for the analysis of incompressible fluid flow and heat transfer in saturated porous media. A description of the fluid/thermal boundary value problem treated by the program is presented and the finite element method and associated numerical methods used in MARIAH are discussed. Instructions for use of the program are documented in the Sandia National Laboratories report, SAND79-1623.
An improved boundary element method for realistic volume-conductor modeling.
Fuchs, M; Drenckhahn, R; Wischmann, H A; Wagner, M
1998-08-01
An improved boundary element method (BEM) with a virtual triangle refinement using the vertex normals, an optimized auto solid angle approximation, and a weighted isolated problem approach is presented. The performance of this new approach is compared to analytically solvable spherical shell models and highly refined reference BEM models for tangentially and radially oriented dipoles at different eccentricities. The lead fields of several electroencephalography (EEG) and magnetoencephalography (MEG) setups are analyzed by singular-value decompositions for realistically shaped volume-conductor models. Dipole mislocalizations due to simplified volume-conductor models are investigated for EEG and MEG examinations for points on a three dimensional (3-D) grid with 10-mm spacing inside the conductor and all principal dipole orientations. The applicability of the BEM in view of the computational effort is tested with a standard workstation. Finally, an application of the new method to epileptic spike data is studied and the results are compared to the spherical-shells approximation.
NASA Astrophysics Data System (ADS)
Scheiber, D.; Pippan, R.; Puschnig, P.; Romaner, L.
2016-12-01
We report high throughput density functional theory (DFT) calculations to simulate segregation of s- and p-elements in Mo and W. First, the preference of solutes for interstitial or substitutional positions in the bulk is evaluated and then the segregation energies for the solutes to interstitial and different substitutional sites at a grain boundary (GB) and a free surface (FS) are computed. We show that several solutes change their site preference from substitutional to interstitial position upon segregation to the GB. With the segregation energies to GB and FS, the changes in cohesion can be calculated and GB cohesion enhancing solutes can be identified. The results show striking similarity for both W and Mo. In addition, we collected the available literature data from experimental and theoretical side, which we consequently compare to our results. From our results and the comparison to literature, we identify B, C and Be as potential alloying additions for an increased GB cohesion in Mo and W.
NASA Astrophysics Data System (ADS)
Wagenhoffer, Nathan; Moored, Keith; Jaworski, Justin
2016-11-01
The design of quiet and efficient bio-inspired propulsive concepts requires a rapid, unified computational framework that integrates the coupled fluid dynamics with the noise generation. Such a framework is developed where the fluid motion is modeled with a two-dimensional unsteady boundary element method that includes a vortex-particle wake. The unsteady surface forces from the potential flow solver are then passed to an acoustic boundary element solver to predict the radiated sound in low-Mach-number flows. The use of the boundary element method for both the hydrodynamic and acoustic solvers permits dramatic computational acceleration by application of the fast multiple method. The reduced order of calculations due to the fast multipole method allows for greater spatial resolution of the vortical wake per unit of computational time. The coupled flow-acoustic solver is validated against canonical vortex-sound problems. The capability of the coupled solver is demonstrated by analyzing the performance and noise production of an isolated bio-inspired swimmer and of tandem swimmers.
Cutanda-Henríquez, Vicente; Juhl, Peter Møller
2013-11-01
The formulation presented in this paper is based on the boundary element method (BEM) and implements Kirchhoff's decomposition into viscous, thermal, and acoustic components, which can be treated independently everywhere in the domain except on the boundaries. The acoustic variables with losses are solved using extended boundary conditions that assume (i) negligible temperature fluctuations at the boundary and (ii) normal and tangential matching of the boundary's particle velocity. The proposed model does not require constructing a special mesh for the viscous and thermal boundary layers as is the case with the existing finite element method (FEM) implementations with losses. The suitability of this approach is demonstrated using an axisymmetrical BEM and two test cases where the numerical results are compared with analytical solutions.
NASA Technical Reports Server (NTRS)
Tamma, Kumar K.; Railkar, Sudhir B.
1988-01-01
This paper represents an attempt to apply extensions of a hybrid transfinite element computational approach for accurately predicting thermoelastic stress waves. The applicability of the present formulations for capturing the thermal stress waves induced by boundary heating for the well known Danilovskaya problems is demonstrated. A unique feature of the proposed formulations for applicability to the Danilovskaya problem of thermal stress waves in elastic solids lies in the hybrid nature of the unified formulations and the development of special purpose transfinite elements in conjunction with the classical Galerkin techniques and transformation concepts. Numerical test cases validate the applicability and superior capability to capture the thermal stress waves induced due to boundary heating.
Application of the Boundary Element Method to Fatigue Crack Growth Analysis
1988-09-01
III, and Noetic PROBE in Section IV. Correlation of the boundary element method and modeling techniques employed in this study were shown with the...distribution unlimited I I I Preface! 3 The purpose of this study was to apply the boundary element method (BEM) to two dimensional fracture mechanics...problems, and to use the BEM to analyze the interference effects of holes on cracks through a parametric study of a two hole 3 tension strip. The study
Improved design of special boundary elements for T-shaped reinforced concrete walls
NASA Astrophysics Data System (ADS)
Ji, Xiaodong; Liu, Dan; Qian, Jiaru
2017-01-01
This study examines the design provisions of the Chinese GB 50011-2010 code for seismic design of buildings for the special boundary elements of T-shaped reinforced concrete walls and proposes an improved design method. Comparison of the design provisions of the GB 50011-2010 code and those of the American code ACI 318-14 indicates a possible deficiency in the T-shaped wall design provisions in GB 50011-2010. A case study of a typical T-shaped wall designed in accordance with GB 50011-2010 also indicates the insufficient extent of the boundary element at the non-flange end and overly conservative design of the flange end boundary element. Improved designs for special boundary elements of T-shaped walls are developed using a displacement-based method. The proposed design formulas produce a longer boundary element at the non-flange end and a shorter boundary element at the flange end, relative to those of the GB 50011-2010 provisions. Extensive numerical analysis indicates that T-shaped walls designed using the proposed formulas develop inelastic drift of 0.01 for both cases of the flange in compression and in tension.
Evidence for a single impact at the Cretaceous-Tertiary boundary from trace elements
NASA Technical Reports Server (NTRS)
Gilmour, Iain; Anders, Edward
1988-01-01
Not only meteoritic elements (Ir, Ni, Au, Pt metals), but also some patently non-meteoritic elements (As, Sb) are enriched at the K-T boundary. Eight enriched elements at 7 K-T sites were compared and it was found that: All have fairly constant proportions to Ir and Kilauea (invoked as an example of a volcanic source of Ir by opponents of the impact theory) has too little of 7 of these 8 elements to account for the boundary enrichments. The distribution of trace elements at the K-T boundary was reexamined using data from 11 sites for which comprehensive are available. The meteoritic component can be assessed by first normalizing the data to Ir, the most obviously extraterrestrial element, and then to Cl chondrites. The double normalization reduces the concentration range from 11 decades to 5 and also facilitates the identification of meteoritic elements. At sites where trace elements were analyzed in sub-divided samples of boundary clay, namely, Caravaca (SP), Stevns Klint (DK), Flaxbourne River (NZ) and Woodside Creek (NZ), Sb, As and Zn are well correlated with Ir across the boundary implying a common deposition mechanism. Elemental carbon is also enriched by up to 10,000 x in boundary clay from 5 K-T sides and is correlated with Ir across the boundary at Woodside Creek. While biomass would appear to be the primary fuel source for this carbon a contribution from a fossil fuel source may be necessary in order to account for the observed C abundance.
NASA Astrophysics Data System (ADS)
Watson, E. B.
2009-12-01
Historically, studies of grain-boundary diffusion have focused on elements that are compatible in the lattices of the crystals forming the grain boundary. This has been the case mainly because the mathematical basis for interpreting experimental results relies upon lattice compatibility to detect and characterize grain-boundary transport. The recently-introduced “detector particle” method (Hayden & Watson 2007; 2008), in contrast, enables estimation of grain-boundary diffusivities of elements that are totally incompatible in the crystal lattice. The technique involves “seeding” the polycrystalline material with isolated, small grains of a minor phase (“detector particles” or sinks) in which the element of interest is compatible. A source of the element is placed at some distance from the sinks, such that the source and sink can “communicate” only by diffusion along the major-phase grain boundaries. Although demonstrably effective, the technique suffers from the shortcoming that analysis of the sink particles alone (e.g., by EPMA) yields only qualitative results. The ion probe may hold the key to quantitative implementation. Computer simulations reveal that when the sink particles are uniformly dispersed in a polycrystalline material and a source of the diffusant is placed at the polycrystal surface, the grain-boundary diffusivity is given simply by Dgb = (Cprt×Vprt)/(Csrf×δ×t), where Cprt is the concentration of the diffusant in the sink particles near the source, Vprt is the particle volume, δ is the grain-boundary width, t is time and Csrf is the concentration in the grain boundary at the diffusant source. Most of the quantities in this relationship can be readily estimated, and Cprt is measurable by electron microprobe. It is Csrf that is elusive, but potentially accessible by ion microprobe. Future collaborations between experimentalists and ion-probe analysts may be able to exploit the detector-particle technique and the simple
Nummenmaa, Aapo; Stenroos, Matti; Ilmoniemi, Risto J.; Okada, Yoshio C.; Hämäläinen, Matti S.; Raij, Tommi
2013-01-01
Objective MRI-guided real-time transcranial magnetic stimulation (TMS) navigators that apply electromagnetic modeling have improved the utility of TMS. However, their accuracy and speed depends on the assumed volume conductor geometry. Spherical models found in present navigators are computationally fast but may be inaccurate in some areas. Realistically-shaped boundary-element models (BEMs) could increase accuracy at a moderate computational cost, but it is unknown which model features have the largest influence on accuracy. Thus, we compared different types of spherical models and BEMs. Methods Globally and locally fitted spherical models and different BEMs with either one or three compartments and with different skull-to-brain conductivity ratios (1/1 – 1/80) were compared against a reference BEM. Results The one-compartment BEM at inner skull surface was almost as accurate as the reference BEM. Skull/brain conductivity ratio in the range 1/10 – 1/80 had only a minor influence. BEMs were superior to spherical models especially in frontal and temporal areas (up to 20 mm localization and 40% intensity improvement); in motor cortex all models provided similar results. Conclusions One-compartment BEMs offer a good balance between accuracy and computational cost. Significance Realistically-shaped BEMs may increase TMS navigation accuracy in several brain areas, such as in prefrontal regions often targeted in clinical applications. PMID:23890512
An Adaptive Fast Multipole Boundary Element Method for Poisson−Boltzmann Electrostatics
2009-01-01
The numerical solution of the Poisson−Boltzmann (PB) equation is a useful but a computationally demanding tool for studying electrostatic solvation effects in chemical and biomolecular systems. Recently, we have described a boundary integral equation-based PB solver accelerated by a new version of the fast multipole method (FMM). The overall algorithm shows an order N complexity in both the computational cost and memory usage. Here, we present an updated version of the solver by using an adaptive FMM for accelerating the convolution type matrix-vector multiplications. The adaptive algorithm, when compared to our previous nonadaptive one, not only significantly improves the performance of the overall memory usage but also remarkably speeds the calculation because of an improved load balancing between the local- and far-field calculations. We have also implemented a node-patch discretization scheme that leads to a reduction of unknowns by a factor of 2 relative to the constant element method without sacrificing accuracy. As a result of these improvements, the new solver makes the PB calculation truly feasible for large-scale biomolecular systems such as a 30S ribosome molecule even on a typical 2008 desktop computer. PMID:19517026
An Adaptive Fast Multipole Boundary Element Method for Poisson-Boltzmann Electrostatics.
Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, J Andrew
2009-06-09
The numerical solution of the Poisson-Boltzmann (PB) equation is a useful but a computationally demanding tool for studying electrostatic solvation effects in chemical and biomolecular systems. Recently, we have described a boundary integral equation-based PB solver accelerated by a new version of the fast multipole method (FMM). The overall algorithm shows an order N complexity in both the computational cost and memory usage. Here, we present an updated version of the solver by using an adaptive FMM for accelerating the convolution type matrix-vector multiplications. The adaptive algorithm, when compared to our previous nonadaptive one, not only significantly improves the performance of the overall memory usage but also remarkably speeds the calculation because of an improved load balancing between the local- and far-field calculations. We have also implemented a node-patch discretization scheme that leads to a reduction of unknowns by a factor of 2 relative to the constant element method without sacrificing accuracy. As a result of these improvements, the new solver makes the PB calculation truly feasible for large-scale biomolecular systems such as a 30S ribosome molecule even on a typical 2008 desktop computer.
An Adaptive Fast Multipole Boundary Element Method for Poisson-Boltzmann Electrostatics
Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, Jonathan
2009-01-01
The numerical solution of the Poisson Boltzmann (PB) equation is a useful but a computationally demanding tool for studying electrostatic solvation effects in chemical and biomolecular systems. Recently, we have described a boundary integral equation-based PB solver accelerated by a new version of the fast multipole method (FMM). The overall algorithm shows an order N complexity in both the computational cost and memory usage. Here, we present an updated version of the solver by using an adaptive FMM for accelerating the convolution type matrix-vector multiplications. The adaptive algorithm, when compared to our previous nonadaptive one, not only significantly improves the performance of the overall memory usage but also remarkably speeds the calculation because of an improved load balancing between the local- and far-field calculations. We have also implemented a node-patch discretization scheme that leads to a reduction of unknowns by a factor of 2 relative to the constant element method without sacrificing accuracy. As a result of these improvements, the new solver makes the PB calculation truly feasible for large-scale biomolecular systems such as a 30S ribosome molecule even on a typical 2008 desktop computer.
Boundary element method for 3-D cracks in a plate
NASA Technical Reports Server (NTRS)
Fares, N.; Li, V. C.
1988-01-01
Fundamental solutions which automatically satisfy boundary conditions at the interfaces of an elastic plate perfectly bonded to two elastic halfspaces are implemented in a three-dimensional BEM for crack problems. The BEM features a new integration scheme for highly singular kernels. The capability is achieved through a part analytic and part numerical integration procedure, such that the analytic part of the integration is similar for all slip/opening variations. Part-through elliptic cracks in an elastic plate with traction-free surfaces are analyzed and the SIF values along the crack front are found to compare favorably with the numerical SIF results of Raju and Newman (1979).
Generalized Transition Finite-Boundary Elements for high speed flight structures
NASA Technical Reports Server (NTRS)
Sarigul-Klijn, Nesrin; Odabas, Onur
1990-01-01
A new class of 'Generalized Transition Finite-Boundary Elements' formulation is presented to predict temperature and/or stress distribution of flight structures at high speeds. A tweleve-noded three-dimensional transition element and a variable degree of freedom eight-noded element are formulated. These elements are incorporated into the formulation of the heat transfer and structural analysis problems by utilizing a newly introduced 'material approximation functions' concept. Results obtained from limited examples compared with the solutions from analytical and other finite element analysis solution. Numerical examples presented illustrate the effectiveness of these elements.
NASA Astrophysics Data System (ADS)
Kim, H.; Ryue, J.; Thompson, D. J.; Müller, A. D.
2016-09-01
Recently, complex shaped aluminium panels have been adopted in many structures to make them lighter and stronger. The vibro-acoustic behaviour of these complex panels has been of interest for many years but conventional finite element and boundary element methods are not efficient to predict their performance at higher frequencies. Where the cross-sectional properties of the panels are constant in one direction, wavenumber domain numerical analysis can be applied and this becomes more suitable for panels with complex cross-sectional geometries. In this paper, a coupled wavenumber domain finite element and boundary element method is applied to predict the sound radiation from and sound transmission through a double-layered aluminium extruded panel, having a typical shape used in railway carriages. The predicted results are compared with measured ones carried out on a finite length panel and good agreement is found.
A Galerkin symmetric boundary-element method in elasticity - Formulation and implementation
NASA Astrophysics Data System (ADS)
Sirtori, S.; Maier, G.; Novati, G.; Miccoli, S.
1992-08-01
Both static and kinematic fictitious discontinuities are considered as sources on the boundary of a homogeneous linear elastic body embedded in the unbounded elastic space. A set of algebraic linear equations is generated by modeling the boundary variables and enforcing Betti's equation in a weighted-residual sense. Particular attention is given to reciprocity relations among kernels focusing on the role of singularities; conditions to be satisfied by the boundary field modeling to achieve symmetry of the coefficient matrix; and variational properties of the solution. For 2D problems, a technique based on a complex-variable formalism is proposed to perform double integrations involved in the boundary-element approach.
A Global Interpolation Function (GIF) boundary element code for viscous flows
NASA Technical Reports Server (NTRS)
Reddy, D. R.; Lafe, O.; Cheng, A. H-D.
1995-01-01
Using global interpolation functions (GIF's), boundary element solutions are obtained for two- and three-dimensional viscous flows. The solution is obtained in the form of a boundary integral plus a series of global basis functions. The unknown coefficients of the GIF's are determined to ensure the satisfaction of the governing equations at selected collocation points. The values of the coefficients involved in the boundary integral equations are determined by enforcing the boundary conditions. Both primitive variable and vorticity-velocity formulations are examined.
NASA Technical Reports Server (NTRS)
Collins, Jeffery D.; Volakis, John L.
1989-01-01
A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principle advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.
GHARAKHANI,ADRIN; WOLFE,WALTER P.
1999-10-01
The prediction of potential flow about zero thickness membranes by the boundary element method constitutes an integral component of the Lagrangian vortex-boundary element simulation of flow about parachutes. To this end, the vortex loop (or the panel) method has been used, for some time now, in the aerospace industry with relative success [1, 2]. Vortex loops (with constant circulation) are equivalent to boundary elements with piecewise constant variation of the potential jump. In this case, extending the analysis in [3], the near field potential velocity evaluations can be shown to be {Omicron}(1). The accurate evaluation of the potential velocity field very near the parachute surface is particularly critical to the overall accuracy and stability of the vortex-boundary element simulations. As we will demonstrate in Section 3, the boundary integral singularities, which arise due to the application of low order boundary elements, may lead to severely spiked potential velocities at vortex element centers that are near the boundary. The spikes in turn cause the erratic motion of the vortex elements, and the eventual loss of smoothness of the vorticity field and possible numerical blow up. In light of the arguments above, the application of boundary elements with (at least) a linear variation of the potential jump--or, equivalently, piecewise constant vortex sheets--would appear to be more appropriate for vortex-boundary element simulations. For this case, two strategies are possible for obtaining the potential flow field. The first option is to solve the integral equations for the (unknown) strengths of the surface vortex sheets. As we will discuss in Section 2.1, the challenge in this case is to devise a consistent system of equations that imposes the solenoidality of the locally 2-D vortex sheets. The second approach is to solve for the unknown potential jump distribution. In this case, for commonly used C{sup o} shape functions, the boundary integral is singular at
Stenroos, Matti
2016-11-21
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from the standard formulation. The approach and resulting solver are verified in four ways, including comparisons of volume and surface potentials to those obtained using the finite element method (FEM), and the effect of a hole in skull on electroencephalographic scalp potentials is demonstrated.
NASA Astrophysics Data System (ADS)
Stenroos, Matti
2016-11-01
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from the standard formulation. The approach and resulting solver are verified in four ways, including comparisons of volume and surface potentials to those obtained using the finite element method (FEM), and the effect of a hole in skull on electroencephalographic scalp potentials is demonstrated.
Ooi, E H; Ang, W T; Ng, E Y K
2009-08-01
A three-dimensional boundary element model of the human eye is developed to investigate the thermal effects of eye tumor on the ocular temperature distribution. The human eye is modeled as comprising several regions which have different thermal properties. The tumor is one of these regions. The thermal effects of the tumor are simulated by taking it to have a very high metabolic heat generation and blood perfusion rate. Inside the tumor, the steady state temperature is governed by the Pennes bioheat equation. Elsewhere, in normal tissues of the eye, the temperature satisfies the Laplace's equation. To compute the temperature on the corneal surface, the surface boundary of each region is divided into triangular elements.
Lu, Benzhuo; McCammon, J Andrew
2007-05-01
A patch representation differing from the traditional treatments in the boundary element method (BEM) is presented, which we call the constant "node patch" method. Its application to solving the Poisson-Boltzmann equation (PBE) demonstrates considerable improvement in speed compared with the constant element and linear element methods. In addition, for the node-based BEMs, we propose an efficient interpolation method for the calculation of the electrostatic stress tensor and PB force on the solvated molecular surface. This force calculation is simply an O(N) algorithm (N is the number of elements). Moreover, our calculations also show that the geometric factor correction in the boundary integral equations significantly increases the accuracy of the potential solution on the boundary, and thereby the PB force calculation.
Image-guided near infrared spectroscopy using boundary element method: phantom validation
Srinivasan, Subhadra; Carpenter, Colin; Pogue, Brian W.; Paulsen, Keith D.
2010-01-01
Image-guided near infrared spectroscopy (IG-NIRS) can provide high-resolution vascular, metabolic and molecular characterization of localized tissue volumes in-vivo. The approach for IG-NIRS uses hybrid systems where the spatial anatomical structure of tissue obtained from standard imaging modalities (such as MRI) is combined with tissue information from diffuse optical imaging spectroscopy. There is need to optimize these hybrid systems for large-scale clinical trials anticipated in the near future in order to evaluate the feasibility of this technology across a larger population. However, existing computational methods such as the finite element method mesh arbitrary image volumes, which inhibit automation, especially with large numbers of datasets. Circumventing this issue, a boundary element method (BEM) for IG-NIRS systems in 3–D is presented here using only surface rendering and discretization. The process of surface creation and meshing is faster, more reliable, and is easily generated automatically as compared to full volume meshing. The proposed method has been implemented here for multi-spectral non-invasive characterization of tissue. In phantom experiments, 3–D spectral BEM-based spectroscopy recovered the oxygen dissociation curve with mean error of 6.6% and tracked variation in total hemoglobin linearly. PMID:20445830
NASA Astrophysics Data System (ADS)
Contreras Zazueta, M. A.; Perton, M.; Sanchez-Sesma, F. J.; Sánchez-Alvaro, E.
2013-12-01
The seismic hazard assessment of extended developments, such as a dam, a bridge or a pipeline, needs the strong ground motion simulation taking into account the effects of surface geology. In many cases the incoming wave field can be obtained from attenuation relations or simulations for layered media using Discrete Wave Number (DWN). Sometimes there is a need to include in simulations the seismic source as well. A number of methods to solve these problems have been developed. Among them the Finite Element and Finite Difference Methods (FEM and FDM) are generally preferred because of the facility of use. Nevertheless, the analysis of realistic dynamic loading induced by earthquakes requires a thinner mesh of the entire domain to consider high frequencies. Consequently this may imply a high computational cost. The Indirect Boundary Element Method (IBEM) can also be employed. Here it is used to study the response of a site to historical seismic activity. This method is particularly suited to model wave propagation through wide areas as it requires only the meshing of boundaries. Moreover, it is well suited to represent finely the diffraction that can occur on a fault. However, the IBEM has been applied mainly to simple geometrical configurations. In this communication significant refinements of the formulation are presented. Using IBEM we can simulate wave propagation in complex geometrical configurations such as a stratified medium crossed by thin faults or having a complex topography. Two main developments are here described; one integrates the DWN method inside the IBEM in order to represent the Green's functions of stratified media with relatively low computational cost but assuming unbounded parallel flat layers, and the other is the extension of IBEM to deal with multi-regions in contact which allows more versatility with a higher computational cost compared to the first one but still minor to an equivalent FEM formulation. The two approaches are fully
Axisymmetric Boundary Element Method for vesicles in a capillary
NASA Astrophysics Data System (ADS)
Trozzo, R.; Boedec, G.; Leonetti, M.; Jaeger, M.
2015-05-01
The problem of a vesicle transported by a fluid flow can present a large range of length scales. One example is the case of a vesicle producing a tether, and eventually pearls, in an elongational flow. Another case occurs when a lubrication film is formed, such as during the short range interaction between two vesicles. Such problems are still challenging for 3D simulations. On the other hand, a good understanding could be obtained by first considering the axisymmetric regime when such a regime exists. An axisymmetric model could then be used, without the criticisms that can be made of a 2D approach. We propose such a model, primarily interested in flows through narrow cylindrical capillaries. Two options are compared, with and without explicit representation of the capillary boundaries by a mesh. The numerical effort is characterized as a function of the vesicle's initial shape, the flow magnitude and the confinement. The model is able to treat typical configurations of red blood cells flowing through very narrow pores with extremely thin lubrication films.
Elemental anomalies at the cretaceous-tertiary boundary, woodside creek, new zealand.
Brooks, R R; Reeves, R D; Yang, X H; Ryan, D E; Holzbecher, J; Collen, J D; Neall, V E; Lee, J
1984-11-02
Iridium and 26 other elements were determined in shale from the Cretaceous-Tertiary boundary at the locus classicus (for iridium anomalies) at Woodside Creek, New Zealand. Iridium, gold, copper, cobalt, chromium, nickel, arsenic, molybdenum, and iron were enriched in the basal 2 millimeters of the 8-millimeter shale parting as compared with the rest of the stratigraphic column. No other shale partings in the column had anomalous concentrations of any element when the data were expressed on a carbonate-free basis. The boundary material showed striking compositional similarities with the Stevns Klint Danish boundary shale. Elemental concentrations were in general much higher in the New Zealand material than in nonboundary shales from elsewhere in the world. The high concentration of iridium (153 nanograms per gram) in the basal layer of the boundary, together with the enrichment of other siderophile elements supports the idea of an extraterrestrial source for much of the material. The iridium/gold ratio of 2.1 is also in accordance with such a source. The iridium content of the basal layer is higher than for any other marine boundary shale obtained on land. The integrated iridium value is 187 nanograms per square centimeter of boundary surface.
Experience with automatic, dynamic load balancing and adaptive finite element computation
Wheat, S.R.; Devine, K.D.; Maccabe, A.B.
1993-10-01
Distributed memory, Massively Parallel (MP), MIMD technology has enabled the development of applications requiring computational resources previously unobtainable. Structural mechanics and fluid dynamics applications, for example, are often solved by finite element methods (FEMs) requiring, millions of degrees of freedom to accurately simulate physical phenomenon. Adaptive methods, which automatically refine or coarsen meshes and vary the order of accuracy of the numerical solution, offer greater robustness and computational efficiency than traditional FEMs by reducing the amount of computation required away from physical structures such as shock waves and boundary layers. On MP computers, FEMs frequently result in distributed processor load imbalances. To overcome load imbalance, many MP FEMs use static load balancing as a preprocessor to the finite element calculation. Adaptive methods complicate the load imbalance problem since the work per element is not uniform across the solution domain and changes as the computation proceeds. Therefore, dynamic load balancing is required to maintain global load balance. We describe a dynamic, fine-grained, element-based data migration system that maintains global load balance and is effective in the presence of changing work loads. Global load balance is achieved by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. The method utilizes an automatic element management system library to which a programmer integrates the application`s computational description. The library`s flexibility supports a large class of finite element and finite difference based applications.
System, Subsystem, Hive: Boundary Problems in Computational Theories of Consciousness
Fekete, Tomer; van Leeuwen, Cees; Edelman, Shimon
2016-01-01
A computational theory of consciousness should include a quantitative measure of consciousness, or MoC, that (i) would reveal to what extent a given system is conscious, (ii) would make it possible to compare not only different systems, but also the same system at different times, and (iii) would be graded, because so is consciousness. However, unless its design is properly constrained, such an MoC gives rise to what we call the boundary problem: an MoC that labels a system as conscious will do so for some—perhaps most—of its subsystems, as well as for irrelevantly extended systems (e.g., the original system augmented with physical appendages that contribute nothing to the properties supposedly supporting consciousness), and for aggregates of individually conscious systems (e.g., groups of people). This problem suggests that the properties that are being measured are epiphenomenal to consciousness, or else it implies a bizarre proliferation of minds. We propose that a solution to the boundary problem can be found by identifying properties that are intrinsic or systemic: properties that clearly differentiate between systems whose existence is a matter of fact, as opposed to those whose existence is a matter of interpretation (in the eye of the beholder). We argue that if a putative MoC can be shown to be systemic, this ipso facto resolves any associated boundary issues. As test cases, we analyze two recent theories of consciousness in light of our definitions: the Integrated Information Theory and the Geometric Theory of consciousness. PMID:27512377
Comparing Experiment and Computation of Hypersonic Laminar Boundary Layers with Isolated Roughness
NASA Technical Reports Server (NTRS)
Bathel, Brett F.; Iyer, Prahladh S.; Mahesh, Krishnan; Danehy, Paul M.; Inman, Jennifer A.; Jones, Stephen B.; Johansen, Craig T.
2014-01-01
Streamwise velocity profile behavior in a hypersonic laminar boundary layer in the presence of an isolated roughness element is presented for an edge Mach number of 8.2. Two different roughness element types are considered: a 2-mm tall, 4-mm diameter cylinder, and a 2-mm radius hemisphere. Measurements of the streamwise velocity behavior using nitric oxide (NO) planar laser-induced fluorescence (PLIF) molecular tagging velocimetry (MTV) have been performed on a 20-degree wedge model. The top surface of this model acts as a flat-plate and is oriented at 5 degrees with respect to the freestream flow. Computations using direct numerical simulation (DNS) of these flows have been performed and are compared to the measured velocity profiles. Particular attention is given to the characteristics of velocity profiles immediately upstream and downstream of the roughness elements. In these regions, the streamwise flow can experience strong deceleration or acceleration. An analysis in which experimentally measured MTV profile displacements are compared with DNS particle displacements is performed to determine if the assumption of constant velocity over the duration of the MTV measurement is valid. This assumption is typically made when reporting MTV-measured velocity profiles, and may result in significant errors when comparing MTV measurements to computations in regions with strong deceleration or acceleration. The DNS computations with the cylindrical roughness element presented in this paper were performed with and without air injection from a rectangular slot upstream of the cylinder. This was done to determine the extent to which gas seeding in the MTV measurements perturbs the boundary layer flowfield.
Computers in the Library: The Human Element.
ERIC Educational Resources Information Center
Magrath, Lynn L.
1982-01-01
Discusses library staff and public reaction to the computerization of library operations at the Pikes Peak Library District in Colorado Springs. An outline of computer applications implemented since the inception of the program in 1975 is included. (EJS)
Exterior optical cloaking and illusions by using active sources: A boundary element perspective
NASA Astrophysics Data System (ADS)
Zheng, H. H.; Xiao, J. J.; Lai, Y.; Chan, C. T.
2010-05-01
Recently, it was demonstrated that active sources can be used to cloak any objects that lie outside the cloaking devices [F. Guevara Vasquez, G. W. Milton, and D. Onofrei, Phys. Rev. Lett. 103, 073901 (2009)]. Here, we propose that active sources can create illusion effects so that an object outside the cloaking device can be made to look like another object. Invisibility is a special case in which the concealed object is transformed to a volume of air. From a boundary element perspective, we show that active sources can create a nearly “silent” domain which can conceal any objects inside and at the same time make the whole system look like an illusion of our choice outside a virtual boundary. The boundary element method gives the fields and field gradients, which can be related to monopoles and dipoles, on continuous curves which define the boundary of the active devices. Both the cloaking and illusion effects are confirmed by numerical simulations.
Ultraconserved Elements: Analyses of Dosage Sensitivity, Motifs and Boundaries
Chiang, Charleston W. K.; Derti, Adnan; Schwartz, Daniel; Chou, Michael F.; Hirschhorn, Joel N.; Wu, C.-ting
2008-01-01
Ultraconserved elements (UCEs) are sequences that are identical between reference genomes of distantly related species. As they are under negative selection and enriched near or in specific classes of genes, one explanation for their ultraconservation may be their involvement in important functions. Indeed, many UCEs can drive tissue-specific gene expression. We have demonstrated that nonexonic UCEs are depleted among segmental duplications (SDs) and copy number variants (CNVs) and proposed that their ultraconservation may reflect a mechanism of copy counting via comparison. Here, we report that nonexonic UCEs are also depleted among 10 of 11 recent genomewide data sets of human CNVs, including 3 obtained with strategies permitting greater precision in determining the extents of CNVs. We further present observations suggesting that nonexonic UCEs per se may contribute to this depletion and that their apparent dosage sensitivity was in effect when they became fixed in the last common ancestor of mammals, birds, and reptiles, consistent with dosage sensitivity contributing to ultraconservation. Finally, in searching for the mechanism(s) underlying the function of nonexonic UCEs, we have found that they are enriched in TAATTA, which is also the recognition sequence for the homeodomain DNA-binding module, and bounded by a change in A + T frequency. PMID:18957701
Carpenter, D.C.
1998-01-01
This bibliography provides a list of references on finite element and related methods analysis in reactor physics computations. These references have been published in scientific journals, conference proceedings, technical reports, thesis/dissertations and as chapters in reference books from 1971 to the present. Both English and non-English references are included. All references contained in the bibliography are sorted alphabetically by the first author`s name and a subsort by date of publication. The majority of the references relate to reactor physics analysis using the finite element method. Related topics include the boundary element method, the boundary integral method, and the global element method. All aspects of reactor physics computations relating to these methods are included: diffusion theory, deterministic radiation and neutron transport theory, kinetics, fusion research, particle tracking in finite element grids, and applications. For user convenience, many of the listed references have been categorized. The list of references is not all inclusive. In general, nodal methods were purposely excluded, although a few references do demonstrate characteristics of finite element methodology using nodal methods (usually as a non-conforming element basis). This area could be expanded. The author is aware of several other references (conferences, thesis/dissertations, etc.) that were not able to be independently tracked using available resources and thus were not included in this listing.
NASA Astrophysics Data System (ADS)
Li, Yuan; Dang, HuaYang; Xu, GuangTao; Fan, CuiYing; Zhao, MingHao
2016-08-01
The extended displacement discontinuity boundary integral equation (EDDBIE) and boundary element method is developed for the analysis of planar cracks of arbitrary shape in the isotropic plane of three-dimensional (3D) transversely isotropic thermo-magneto-electro-elastic (TMEE) media. The extended displacement discontinuities (EDDs) include conventional displacement discontinuity, electric potential discontinuity, magnetic potential discontinuity, as well as temperature discontinuity across crack faces; correspondingly, the extended stresses represent conventional stress, electric displacement, magnetic induction and heat flux. Employing a Hankel transformation, the fundamental solutions for unit point EDDs in 3D transversely isotropic TMEE media are derived. The EDDBIEs for a planar crack of arbitrary shape in the isotropic plane of a 3D transversely isotropic TMEE medium are then established. Using the boundary integral equation method, the singularities of near-crack border fields are obtained and the extended stress field intensity factors are expressed in terms of the EDDs on crack faces. According to the analogy between the EDDBIEs for an isotropic thermoelastic material and TMEE medium, an analogical solution method for crack problems of a TMEE medium is proposed for coupled multi-field loadings. Employing constant triangular elements, the EDDBIEs are discretized and numerically solved. As an application, the problems of an elliptical crack subjected to combined mechanical-electric-magnetic-thermal loadings are investigated.
Numerical simulation of the non-Newtonian fluid flow using the indirect boundary element method
NASA Astrophysics Data System (ADS)
Bessonova, M. P.; Yakutenok, V. A.
2017-02-01
The indirect boundary element method is formulated for a two-dimensional Stokes flow with the moving boundary when gravity force aids the flow. The governing equations of low Reynolds flow are formulated. The numerical technique is described. Two regimes of the fluid flow depending on the Stokes number value were detected: the regime of full filling and the jet flow regime. The comparison of obtained results with data of other authors is presented.
E-coil: an inverse boundary element method for a quasi-static problem.
Sanchez, Clemente Cobos; Garcia, Salvador Gonzalez; Power, Henry
2010-06-07
Boundary element methods represent a valuable approach for designing gradient coils; these methods are based on meshing the current carrying surface into an array of boundary elements. The temporally varying magnetic fields produced by gradient coils induce electric currents in conducting tissues and so the exposure of human subjects to these magnetic fields has become a safety concern, especially with the increase in the strength of the field gradients used in magnetic resonance imaging. Here we present a boundary element method for the design of coils that minimize the electric field induced in prescribed conducting systems. This work also details some numerical examples of the application of this coil design method. The reduction of the electric field induced in a prescribed region inside the coils is also evaluated.
Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity
Atroshchenko, Elena; Bordas, Stéphane P. A.
2015-01-01
In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate the analogue of Somigliana stress identity, which can be used to obtain the stress and couple-stress fields inside the domain from the boundary values of the displacements, microrotation and stress and couple-stress tractions. Using these newly derived fundamental solutions, the boundary integral equations of both types are formulated and solved by the boundary element method. Simultaneous use of both types of equations (approach known as the dual boundary element method (BEM)) allows problems where parts of the boundary are overlapping, such as crack problems, to be treated and to do this for general geometry and loading conditions. The high accuracy of the boundary element method for both types of equations is demonstrated for a number of benchmark problems, including a Griffith crack problem and a plate with an edge crack. The detailed comparison of the BEM results and the analytical solution for a Griffith crack and an edge crack is given, particularly in terms of stress and couple-stress intensity factors, as well as the crack opening displacements and microrotations on the crack faces and the angular distributions of stresses and couple-stresses around the crack tip. PMID:26345089
Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity.
Atroshchenko, Elena; Bordas, Stéphane P A
2015-07-08
In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate the analogue of Somigliana stress identity, which can be used to obtain the stress and couple-stress fields inside the domain from the boundary values of the displacements, microrotation and stress and couple-stress tractions. Using these newly derived fundamental solutions, the boundary integral equations of both types are formulated and solved by the boundary element method. Simultaneous use of both types of equations (approach known as the dual boundary element method (BEM)) allows problems where parts of the boundary are overlapping, such as crack problems, to be treated and to do this for general geometry and loading conditions. The high accuracy of the boundary element method for both types of equations is demonstrated for a number of benchmark problems, including a Griffith crack problem and a plate with an edge crack. The detailed comparison of the BEM results and the analytical solution for a Griffith crack and an edge crack is given, particularly in terms of stress and couple-stress intensity factors, as well as the crack opening displacements and microrotations on the crack faces and the angular distributions of stresses and couple-stresses around the crack tip.
NASA Astrophysics Data System (ADS)
Gwinner, Joachim
2016-12-01
This contribution deals with unilateral contact problems with Tresca friction (given friction model) in hemitropic mi-cropolar elasticity. Based on a boundary integral approach such problems can be reduced to boundary variational inequalities. This suggests the use of boundary element methods for their numerical treatment. With higher order approximation this leads to a nonconforming approximation what can numerically be realized by means of Gauss-Lobatto quadrature. The contribution is based on the recent papers [7, 8] of the author and on joint work [3] with A. Gachechiladze, R. Gachechi-ladze, and D. Natroshvili.
Multidimensional phase change problems by the dual-reciprocity boundary-element method
Jo, J.C.; Shin, W.K.; Choi, C.Y.
1999-07-01
Transient heat transfer problems with phase changes (Stefan problems) occur in many engineering situations, including potential core melting and solidification during pressurized-water-reactor severe accidents, ablation of thermal shields, melting and solidification of alloys, and many others. This article addresses the numerical analysis of nonlinear transient heat transfer with melting or solidification. An effective and simple procedure is presented for the simulation of the motion of the boundary and the transient temperature field during the phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual-reciprocity boundary-element method. The dual-reciprocity boundary-element approach provided in this article is much simpler than the usual boundary-element method in applying a reciprocity principle and an available technique for dealing with the domain integral of the boundary element formulation simultaneously. In this article, attention is focused on two-dimensional melting (ablation)/solidification problems for simplicity. The accuracy and effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of some examples of one-phase ablation/solidification problems with their known semianalytical or numerical solutions where available.
NASA Astrophysics Data System (ADS)
Maerten, F.; Maerten, L.; Pollard, D. D.
2014-11-01
Most analytical solutions to engineering or geological problems are limited to simple geometries. For example, analytical solutions have been found to solve for stresses around a circular hole in a plate. To solve more complex problems, mathematicians and engineers have developed powerful computer-aided numerical methods, which can be categorized into two main types: differential methods and integral methods. The finite element method (FEM) is a differential method that was developed in the 1950s and is one of the most commonly used numerical methods today. Since its development, other differential methods, including the boundary element method (BEM), have been developed to solve different types of problems. The purpose of this paper is to describe iBem3D, formally called Poly3D, a C++ and modular 3D boundary element computer program based on the theory of angular dislocations for modeling three-dimensional (3D) discontinuities in an elastic, heterogeneous, isotropic whole- or half-space. After 20 years and more than 150 scientific publications, we present in detail the formulation behind this method, its enhancements over the years as well as some important applications in several domains of the geosciences. The main advantage of using this formulation, for describing geological objects such as faults, resides in the possibility of modeling complex geometries without gaps and overlaps between adjacent triangular dislocation elements, which is a significant shortcoming for models using rectangular dislocation elements. Reliability, speed, simplicity, and accuracy are enhanced in the latest version of the computer code. Industrial applications include subseismic fault modeling, fractured reservoir modeling, interpretation and validation of fault connectivity and reservoir compartmentalization, depleted area and fault reactivation, and pressurized wellbore stability. Academic applications include earthquake and volcano monitoring, hazard mitigation, and slope
A boundary element-Random walk model of mass transport in groundwater
Kemblowski, M.
1986-01-01
A boundary element solution to the convective mass transport in groundwater is presented. This solution produces a continuous velocity field and reduces the amount of data preparation time and bookkeeping. By combining this solution and the random walk procedure, a convective-dispersive mass transport model is obtained. This model may be easily used to simulate groundwater contamination problems. The accuracy of the boundary element model has been verified by reproducing the analytical solution to a two-dimensional convective mass transport problem. The method was also used to simulate a convective-dispersive problem. ?? 1986.
Roughness receptivity studies in a 3-D boundary layer - Flight tests and computations
NASA Astrophysics Data System (ADS)
Carpenter, Andrew L.; Saric, William S.; Reed, Helen L.
The receptivity of 3-D boundary layers to micron-sized, spanwise-periodic Discrete Roughness Elements (DREs) was studied. The DREs were applied to the leading edge of a 30-degree swept-wing at the wavelength of the most unstable disturbance. In this case, calibrated, multi-element hotfilm sensors were used to measure disturbance wall shear stress. The roughness height was varied from 0 to 50 microns. Thus, the disturbance-shear-stress amplitude variations were determined as a function of modulated DRE heights. The computational work was conducted parallel to the flight experiments. The complete viscous flowfield over the O-2 aircraft with the SWIFT model mounted on the port wing store pylon was successfully modeled and validated with the flight data. This highly accurate basic-state solution was incorporated into linear stability calculations and the wave growth associated with the crossflow instability was calculated.
Grain Boundary Transport of Siderophile Elements in MgO at High Pressure
NASA Astrophysics Data System (ADS)
Watson, H. C.; Siebert, J.; Ryerson, F. J.; Roberts, J. J.; Hayden, L.; Watson, E. B.
2007-12-01
The extent of interaction between the Earth's core and mantle remains an actively debated question. Siderophile element signatures in rocks that can be observed at the surface indicate that the mantle and core may have exchanged material over the history of the Earth. Here, a potential physical mechanism to facilitate this communication is considered. It has recently been shown that grain boundaries in lower mantle analog materials at 2.5 GPa act as reservoirs and fast transport pathways for incompatible elements, specifically siderophile elements [1]. In the present study, we conducted multi-anvil experiments held at 10 GPa and 1600°C for 5 hours to examine the persistence of fast grain boundary transport at higher pressures. Thin layers of Os and Au powders were loaded in a standard 10/5 multi-anvil assembly and separated from a Pt foil by a cylindrical MgO plug approximately 1mm long. These two elements were expected to be among the slowest and fastest diffusers respectively. The final composition of the Pt foil was measured by electron microprobe. The presence of measurable siderophile element "blebs" in the Pt foil indicates substantial grain boundary diffusion. Our preliminary results suggest that siderophile element mobility and presence on grain boundaries may be affected slightly with increased pressure, but could remain a viable mechanism for transport on length scales applicable to communication within the deeper Earth over it's history. The effect of pressure and grain size on grain boundary diffusion, and potential reasons for a large variation between diffusivities of different siderophile elements will be discussed. [1] Hayden, L., and Watson, E.B., 2006. GCA Supp., v. 70, iss. 18, p. 238
Higher-Order Finite Elements for Computing Thermal Radiation
NASA Technical Reports Server (NTRS)
Gould, Dana C.
2004-01-01
Two variants of the finite-element method have been developed for use in computational simulations of radiative transfers of heat among diffuse gray surfaces. Both variants involve the use of higher-order finite elements, across which temperatures and radiative quantities are assumed to vary according to certain approximations. In this and other applications, higher-order finite elements are used to increase (relative to classical finite elements, which are assumed to be isothermal) the accuracies of final numerical results without having to refine computational meshes excessively and thereby incur excessive computation times. One of the variants is termed the radiation sub-element (RSE) method, which, itself, is subject to a number of variations. This is the simplest and most straightforward approach to representation of spatially variable surface radiation. Any computer code that, heretofore, could model surface-to-surface radiation can incorporate the RSE method without major modifications. In the basic form of the RSE method, each finite element selected for use in computing radiative heat transfer is considered to be a parent element and is divided into sub-elements for the purpose of solving the surface-to-surface radiation-exchange problem. The sub-elements are then treated as classical finite elements; that is, they are assumed to be isothermal, and their view factors and absorbed heat fluxes are calculated accordingly. The heat fluxes absorbed by the sub-elements are then transferred back to the parent element to obtain a radiative heat flux that varies spatially across the parent element. Variants of the RSE method involve the use of polynomials to interpolate and/or extrapolate to approximate spatial variations of physical quantities. The other variant of the finite-element method is termed the integration method (IM). Unlike in the RSE methods, the parent finite elements are not subdivided into smaller elements, and neither isothermality nor other
Second-Order Far Field Computational Boundary Conditions for Inviscid Duct Flow Problems
1990-03-01
COMPUTATIONAL BOUNDARY CONDITIONS INTERNAL FLOW COMPUTATIONS EULER METHODS 19. ABSTRACT (Continue on reverse if necessary and identify by block number...SOLUTIONS OF THE LINEARIZED, SECOND-ORDER EULER EQUATIONS. THE EULER EQUATIONS ARE LINEARIZED ABOUT A CONSTANT PRESSURE, RECTILINEAR FLOW C)NDITION...THE BOUNDARY PROCEDURE CAN BE USED WITH ANY NUMERICAL EULER SOLUTION METHOD AND ALLOWS COMPUTATIONAL BOUNDARIES TO BE LOCATED EXTREMELY CLOSE TO THE
Adaptive Finite-Element Computation In Fracture Mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1995-01-01
Report discusses recent progress in use of solution-adaptive finite-element computational methods to solve two-dimensional problems in linear elastic fracture mechanics. Method also shown extensible to three-dimensional problems.
Combined Finite- and Boundary-Element Analysis of SCC Crack Growth
NASA Astrophysics Data System (ADS)
Nikishkov, Gennadiy
2010-05-01
Modeling of stress corrosion cracking (SCC) is performed using the combination of the finite element method and the symmetric Galerkin boundary element method. The uncracked structural component is represented with finite elements. The crack is simulated using the boundary element method. The superposition principle is employed for combining two solutions. The equilibrium state for the system of the structural component and the crack is reached after several iterations that alternate between two methods. It is adopted that the crack develops in the direction of the J-integral vector and the crack growth rate is determined by the mechanochemical model using the effective stress intensity factor based on the J-integral value. Results of SCC crack growth modeling are presented for inclined semi-elliptical surface cracks under tensile loading.
Application of a boundary element method to the study of dynamical torsion of beams
NASA Technical Reports Server (NTRS)
Czekajski, C.; Laroze, S.; Gay, D.
1982-01-01
During dynamic torsion of beam elements, consideration of nonuniform warping effects involves a more general technical formulation then that of Saint-Venant. Nonclassical torsion constants appear in addition to the well known torsional rigidity. The adaptation of the boundary integral element method to the calculation of these constants for general section shapes is described. The suitability of the formulation is investigated with some examples of thick as well as thin walled cross sections.
Application of a boundary element method to the study of dynamical torsion of beams
NASA Technical Reports Server (NTRS)
Czekajski, C.; Laroze, S.; Gay, D.
1982-01-01
During dynamic torsion of beam elements, consideration of nonuniform warping effects involves a more general technical formulation then that of Saint-Venant. Nonclassical torsion constants appear in addition to the well known torsional rigidity. The adaptation of the boundary integral element method to the calculation of these constants for general section shapes is described. The suitability of the formulation is investigated with some examples of thick as well as thin walled cross sections.
Optically intraconnected computer employing dynamically reconfigurable holographic optical element
NASA Technical Reports Server (NTRS)
Bergman, Larry A. (Inventor)
1992-01-01
An optically intraconnected computer and a reconfigurable holographic optical element employed therein. The basic computer comprises a memory for holding a sequence of instructions to be executed; logic for accessing the instructions in sequence; logic for determining for each the instruction the function to be performed and the effective address thereof; a plurality of individual elements on a common support substrate optimized to perform certain logical sequences employed in executing the instructions; and, element selection logic connected to the logic determining the function to be performed for each the instruction for determining the class of each function and for causing the instruction to be executed by those the elements which perform those associated the logical sequences affecting the instruction execution in an optimum manner. In the optically intraconnected version, the element selection logic is adapted for transmitting and switching signals to the elements optically.
Solution-adaptive finite element method in computational fracture mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1993-01-01
Some recent results obtained using solution-adaptive finite element method in linear elastic two-dimensional fracture mechanics problems are presented. The focus is on the basic issue of adaptive finite element method for validating the applications of new methodology to fracture mechanics problems by computing demonstration problems and comparing the stress intensity factors to analytical results.
A computer graphics program for general finite element analyses
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Sawyer, L. M.
1978-01-01
Documentation for a computer graphics program for displays from general finite element analyses is presented. A general description of display options and detailed user instructions are given. Several plots made in structural, thermal and fluid finite element analyses are included to illustrate program options. Sample data files are given to illustrate use of the program.
Boundary element model for simulating sound propagation and source localization within the lungs.
Ozer, M B; Acikgoz, S; Royston, T J; Mansy, H A; Sandler, R H
2007-07-01
An acoustic boundary element (BE) model is used to simulate sound propagation in the lung parenchyma. It is computationally validated and then compared with experimental studies on lung phantom models. Parametric studies quantify the effect of different model parameters on the resulting acoustic field within the lung phantoms. The BE model is then coupled with a source localization algorithm to predict the position of an acoustic source within the phantom. Experimental studies validate the BE-based source localization algorithm and show that the same algorithm does not perform as well if the BE simulation is replaced with a free field assumption that neglects reflections and standing wave patterns created within the finite-size lung phantom. The BE model and source localization procedure are then applied to actual lung geometry taken from the National Library of Medicine's Visible Human Project. These numerical studies are in agreement with the studies on simpler geometry in that use of a BE model in place of the free field assumption alters the predicted acoustic field and source localization results. This work is relevant to the development of advanced auscultatory techniques that utilize multiple noninvasive sensors to construct acoustic images of sound generation and transmission to identify pathologies.
Analysis of the role of diffraction in topographic site effects using boundary element techniques
NASA Astrophysics Data System (ADS)
Gomez, Juan; Restrepo, Doriam; Jaramillo, Juan; Valencia, Camilo
2013-10-01
The role played by the diffraction field on the problem of seismic site effects is studied. For that purpose we solve and analyze simple scattering problems under P and SV in-plane wave assumptions, using two well known direct boundary-element-based numerical methods. After establishing the difference between scattered and diffracted motions, and introducing the concept of artificious and physically based incoming fields, we obtain the amplitude of the Fourier spectra for the diffracted part of the response: this is achieved after establishing the connection between the spatial distribution of the transfer function over the studied simple topographies and the diffracted field. From the numerical simulations it is observed that this diffracted part of the response is responsible for the amplification of the surface ground motions due to the geometric effect. Furthermore, it is also found that the diffraction field sets in a fingerprint of the topographic effect in the total ground motions. These conclusions are further supported by observations in the time-domain in terms of snapshots of the propagation patterns over the complete computational model. In this sense the geometric singularities are clearly identified as sources of diffraction and for the considered range of dimensionless frequencies it is evident that larger amplifications are obtained for the geometries containing a larger number of diffraction sources thus resulting in a stronger topographic effect. The need for closed-form solutions of canonical problems to construct a robust analysis method based on the diffraction field is identified.
Hirosawa, Kunikazu; Ishizuka, Takashi; Fujiwara, Kyoji
2009-05-01
The boundary element method (BEM) is widely used for sound field analysis problems; however, it has a non-uniqueness problem in the exterior domain. Various methods to avoid this problem have been developed; however, these are not easily applied to the BEM. In this paper, a simple method called the "ICA-Ring (inner cavity ringing) method" is proposed for avoiding the non-uniqueness problem, and this method is applied to the BEM in both single and plural domains. The concept of the ICA-Ring method is that a scatterer in free space is hollowed as a shell and the volume is smaller; the eigenfrequencies are shifted to a higher range. Next, the mechanism of the non-uniqueness problem in plural domains and a reason of the application of the ICA-Ring method to the case of plural domains are explained. Finally, some results calculated by the BEM using the ICA-Ring method are shown. The calculational condition is that a cylinder with radius 0.125 m floats in two-dimensional free space. In this case, no calculational errors exist in 1-6000 Hz in both single and plural domains, when the thickness of the shell is 20 mm. The ICA-Ring method does not need to modify an existing computer program of conventional BEM.
NASA Astrophysics Data System (ADS)
Wagenhoffer, Nathan; Moored, Keith; Jaworski, Justin
2015-11-01
Animals have evolved flexible wings and fins to efficiently and quietly propel themselves through the air and water. The design of quiet and efficient bio-inspired propulsive concepts requires a rapid, unified computational framework that integrates three essential features: the fluid mechanics, the elastic structural response, and the noise generation. This study focuses on the development, validation, and demonstration of a transient, two-dimensional acoustic boundary element solver accelerated by a fast multipole algorithm. The resulting acoustic solver is used to characterize the acoustic signature produced by a vortex street advecting over a NACA 0012 airfoil, which is representative of vortex-body interactions that occur in schools of swimming fish. Both 2S and 2P canonical vortex streets generated by fish are investigated over the range of Strouhal number 0 . 2 < St < 0 . 4 , and the acoustic signature of the airfoil is quantified. This study provides the first estimate of the noise signature of a school of swimming fish. Lehigh University CORE Grant.
A Boundary Element Model of Microbubble Sticking and Sliding in the Microcirculation
Eshpuniyani, Brijesh; Fowlkes, J. Brian; Bull, Joseph L.
2009-01-01
A pressure driven 2-D channel flow at very low Reynolds numbers (Stokes flow) with a bubble sticking and sliding along one of the walls is studied computationally using the boundary element method (BEM). The moving three phase contact lines are modeled using a Tanner law wherein the contact line speed is linearly proportional to the deviation of the contact angle from its equilibrium value. Results are presented with and without the effect of contact angle hysteresis. Including contact angle hysteresis allows us to predict the stick-slide behavior of bubbles, which in turn affects the long term evolution and dynamics of the bubbles. It is shown that the initial rapid contraction or expansion of the bubbles to achieve local equilibrium with the surrounding pressure field results in cusps and bulges in the wall normal stress profiles. The wall shear stress also increases (with opposite signs upstream and downstream of the bubble) as the fluid rushes in or out of the channel inlet and outlet. In the long term, bubbles slowly expand as they slide along the channel wall. Contact lines are found to correspond to peaks in the wall normal and shear stress profiles at all times. The effectiveness of bubbles in occluding flow through the channel is also examined. PMID:19885367
Mäkitalo, Jouni; Suuriniemi, Saku; Kauranen, Martti
2014-12-01
The study of metal nanoparticles and metamaterials has increased the demand for accurate and efficient numerical methods for solving electromagnetic scattering problems. The boundary element method, and especially its Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation, has received growing interest lately due to its accuracy and stability at plasmon resonance conditions. Consequently, this formulation has been used to model second-harmonic generation (SHG) in plasmonic nanoparticles, which is an area of increasing importance. Many nanostructures exhibit geometrical symmetries, whose identification is often crucial for the qualitative understanding of SHG. In this work, we present the theory and details to take advantage of these symmetries in the PMCHWT formulation. We show that, importantly, the symmetry of the medium can be exploited even though the excitation source does not exhibit a well-defined symmetry. We estimate the obtainable computational benefits and apply the method to the study of the linear and second-order nonlinear properties of multiply split gold ring resonators.
In this study, gas-phase elemental mercury (Hg0) and related species (including inorganic reactive gaseous mercury (RGM) and particulate mercury (PHg)) were measured at Cheeka Peak Observatory (CPO), Washington State, in the marine boundary layer (MBL) during 2001-2002. Air of...
In this study, gas-phase elemental mercury (Hg0) and related species (including inorganic reactive gaseous mercury (RGM) and particulate mercury (PHg)) were measured at Cheeka Peak Observatory (CPO), Washington State, in the marine boundary layer (MBL) during 2001-2002. Air of...
NASA Astrophysics Data System (ADS)
Zhang, Pengchong; Liu, Jun; Lin, Gao
2017-04-01
The scaled boundary finite element method (SBFEM) and the precise integration algorithm (PIA) are utilized to analyze the extended displacement field in clamped or simple-supported magneto-electro-elastic plates produced by external transverse loadings. There are no limitation on boundary conditions and types of external forces. Only the in-plane dimensions are divided into 2D elements. By introducing a set of scaled boundary local coordinates, 3D governing partial differential equations are converted into the second order ordinary differential matrix equation. By means of the internal nodal force, a first order ordinary differential equation is obtained and its general solution is a matrix exponential. The PIA is introduced to calculate the matrix exponential and any desired accuracy can be obtained. Finally, several numerical examples are provided to validate the versatility of the proposed technique.
NASA Technical Reports Server (NTRS)
Oliver, A. B.; Lillard, R. P.; Blaisdell, G. A.; Lyrintizis, A. S.
2006-01-01
The capability of the OVERFLOW code to accurately compute high-speed turbulent boundary layers and turbulent shock-boundary layer interactions is being evaluated. Configurations being investigated include a Mach 2.87 flat plate to compare experimental velocity profiles and boundary layer growth, a Mach 6 flat plate to compare experimental surface heat transfer,a direct numerical simulation (DNS) at Mach 2.25 for turbulent quantities, and several Mach 3 compression ramps to compare computations of shock-boundary layer interactions to experimental laser doppler velocimetry (LDV) data and hot-wire data. The present paper describes outlines the study and presents preliminary results for two of the flat plate cases and two small-angle compression corner test cases.
The Impact of Instructional Elements in Computer-Based Instruction
ERIC Educational Resources Information Center
Martin, Florence; Klein, James D.; Sullivan, Howard
2007-01-01
This study investigated the effects of several elements of instruction (objectives, information, practice, examples and review) when they were combined in a systematic manner. College students enrolled in a computer literacy course used one of six different versions of a computer-based lesson delivered on the web to learn about input, processing,…
Gartling, D.K.; Hogan, R.E.
1994-10-01
The theoretical and numerical background for the finite element computer program, COYOTE II, is presented in detail. COYOTE II is designed for the multi-dimensional analysis of nonlinear heat conduction problems and other types of diffusion problems. A general description of the boundary value problems treated by the program is presented. The finite element formulation and the associated numerical methods used in COYOTE II are also outlined. Instructions for use of the code are documented in SAND94-1179; examples of problems analyzed with the code are provided in SAND94-1180.
Bramble, J.H.; King, J.T.
1994-07-01
In this paper the authors consider a simple finite element method on an approximately polygonal domain using linear elements. The Dirichlet data are transferred in a natural way and the resulting linear system can be solved using multigrid techniques. Their analysis takes into account the change in domain and data transfer, and optimal-error estimates are obtained that are robust in the regularity of the boundary data provided they are at least square integrable. It is proved that the natural extension of this finite element approximation to the original domain is optimal-order accurate.
Phan, Anh-Vu; Gray, Leonard J; Salvadori, Alberto
2011-01-01
A dynamic analysis of crack-inclusion interaction is described in this paper. The analysis employs a two-dimensional symmetric-Galerkin boundary integral formulation for multi-domain elastodynamic fracture analysis in the frequency domain. The multi-domain technique is based on the assumption of perfectly bonded inclusions. The numerical implementation of this boundary integral formulation is carried out with standard quadratic elements, allowing the use of an improved quarter-point element for accurately determining frequency responses of the dynamic stress intensity factors (DSIFs). To deal with singular and hypersingular integrals, the formulation is decomposed into two parts: the rst part is identical to that for elastostatics while the second part contains at most logarithmic singularities. The treatment of the elastostatic singular and hypersingular singular integrals employs an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Time histories (transient responses) of the DSIFs are obtained in a post-processing step by applying the fast Fourier transform (FFT) and inverse FFT to the frequency responses of these DSIFs. Two numerical examples are presented for the computation of the DSIFs due to crack-inclusion interaction under two types of impact loading: Heaviside step loading and blast loading. The numerical results are consistent and con rm the well known crack tip shielding mechanism observed during the interaction between a crack and a much stiffer inclusion.
Acceleration of matrix element computations for precision measurements
Brandt, Oleg; Gutierrez, Gaston; Wang, M. H.L.S.; Ye, Zhenyu
2014-11-25
The matrix element technique provides a superior statistical sensitivity for precision measurements of important parameters at hadron colliders, such as the mass of the top quark or the cross-section for the production of Higgs bosons. The main practical limitation of the technique is its high computational demand. Using the example of the top quark mass, we present two approaches to reduce the computation time of the technique by a factor of 90. First, we utilize low-discrepancy sequences for numerical Monte Carlo integration in conjunction with a dedicated estimator of numerical uncertainty, a novelty in the context of the matrix element technique. We then utilize a new approach that factorizes the overall jet energy scale from the matrix element computation, a novelty in the context of top quark mass measurements. The utilization of low-discrepancy sequences is of particular general interest, as it is universally applicable to Monte Carlo integration, and independent of the computing environment.
Application of the boundary element method to the micromechanical analysis of composite materials
NASA Technical Reports Server (NTRS)
Goldberg, R. K.; Hopkins, D. A.
1995-01-01
A new boundary element formulation for the micromechanical analysis of composite materials is presented in this study. A unique feature of the formulation is the use of circular shape functions to convert the two-dimensional integrations of the composite fibers to one-dimensional integrations. To demonstrate the applicability of the formulations, several example problems including elastic and thermal analysis of laminated composites and elastic analyses of woven composites are presented and the boundary element results compared to experimental observations and/or results obtained through alternate analytical procedures. While several issues remain to be addressed in order to make the methodology more robust, the formulations presented here show the potential in providing an alternative to traditional finite element methods, particularly for complex composite architectures.
Finite Element Method for Thermal Analysis. [with computer program
NASA Technical Reports Server (NTRS)
Heuser, J.
1973-01-01
A two- and three-dimensional, finite-element thermal-analysis program which handles conduction with internal heat generation, convection, radiation, specified flux, and specified temperature boundary conditions is presented. Elements used in the program are the triangle and tetrahedron for two- and three-dimensional analysis, respectively. The theory used in the program is developed, and several sample problems demonstrating the capability and reliability of the program are presented. A guide to using the program, description of the input cards, and program listing are included.
Anaf, Willemien; Horemans, Benjamin; Van Grieken, René; De Wael, Karolien
2012-11-15
A method for the classification of individual aerosol particles using computer controlled electron probe microanalysis is presented. It is based on chemical boundary conditions (CBC) and enables quick and easy processing of a large set of elemental concentration data (mass%), derived from the X-ray spectra of individual particles. The particles are first classified into five major classes (sea salt related, secondary inorganic, minerals, iron-rich and carbonaceous), after which advanced data mining can be performed by examining the elemental composition of particles within each class into more detail (e.g., by ternary diagrams). The CBC method is validated and evaluated by comparing its results with the output obtained with hierarchical cluster analysis (HCA) for well-known standard particles as well as real aerosol particles collected with a cascade impactor. The CBC method gives reliable results and has a major advantage compared to HCA. CBC is based on boundary conditions that are derived from chemical logical thinking and does not require a translation of a mathematical algorithm output as does HCA. Therefore, the CBC method is more objective and enables comparison between samples without intermediate steps.
Scattering of elastic waves by a 2-D crack using the Indirect Boundary Element Method (IBEM)
NASA Astrophysics Data System (ADS)
Iturrarán-Viveros, Ursula; Vai, Rossana; Sánchez-Sesma, Francisco J.
2005-09-01
The scattering of elastic waves by cracks is an old problem and various ways to solve it have been proposed in the last decades. One approach is using dual integral equations, another useful and common formulation is the Boundary Element Method (BEM). With the last one, the boundary conditions of the crack lead to hyper-singularities and particular care should be taken to regularize and solve the resulting integral equations. In this work, instead, the Indirect Boundary Element Method (IBEM) is applied to study problems of zero-thickness 2-D cracks. The IBEM yields the Crack Opening Displacement (COD) which is used to evaluate the solution away from the crack. We use a multiregional approach which consists of splitting a boundary S into two identical boundaries S+ and S- chosen such that the cracks lie in the interface. The resulting integral equations are not hyper-singular and wave propagation within media that contain zero-thickness cracks can be rigorously solved. In order to validate the method, we deal with the scalar case, namely the scattering of antiplane SH waves by a 2-D crack. We compare results against a recently published analytic solution, obtaining an excellent agreement. This comparison gives us confidence to study cases where no analytic solutions exist. Some examples of incidence of P- or SV waves are depicted and the salient aspects of the method are also discussed.
Near shore seismic movements induced by seaquakes using the boundary element method
NASA Astrophysics Data System (ADS)
Rodríguez-Castellanos, Alejandro; Carbajal-Romero, Manuel; Flores-Guzmán, Norberto; Rodríguez-Sánchez, J. Efraín; Kryvko, Andriy
2017-07-01
This study quantifies seismic amplifications in near-shore arising from seaquakes. Within the Boundary Element Method, boundary elements are used to irradiate waves and force densities obtained for each element. Huygenś Principle is implemented since the diffracted waves are constructed at the boundary from which they are radiated, which is equivalent to Somiglianás theorem. Application of boundary conditions leads to a system of integral equations of the Fredholm type of second kind and zero order. Several numerical configurations are analyzed: The first is used to verify the present formulation with ideal sea floor configurations to estimate seismic amplifications. With the formulation verified, simple slope configurations are studied to estimate spectra of seismic motions. It is found that P-waves can produce seismic amplifications from 1.2 to 3.9 times the amplitude of the incident wave. SV-waves can generate seismic amplifications up to 4.5 times the incident wave. Another relevant finding is that the highest amplifications are at the shore compared to the ones at the sea floor.
An emulator for minimizing computer resources for finite element analysis
NASA Technical Reports Server (NTRS)
Melosh, R.; Utku, S.; Islam, M.; Salama, M.
1984-01-01
A computer code, SCOPE, has been developed for predicting the computer resources required for a given analysis code, computer hardware, and structural problem. The cost of running the code is a small fraction (about 3 percent) of the cost of performing the actual analysis. However, its accuracy in predicting the CPU and I/O resources depends intrinsically on the accuracy of calibration data that must be developed once for the computer hardware and the finite element analysis code of interest. Testing of the SCOPE code on the AMDAHL 470 V/8 computer and the ELAS finite element analysis program indicated small I/O errors (3.2 percent), larger CPU errors (17.8 percent), and negligible total errors (1.5 percent).
NASA Astrophysics Data System (ADS)
Takinoue, Masahiro; Kiga, Daisuke; Shohda, Koh-Ichiroh; Suyama, Akira
2008-10-01
Autonomous DNA computers have been attracting much attention because of their ability to integrate into living cells. Autonomous DNA computers can process information through DNA molecules and their molecular reactions. We have already proposed an idea of an autonomous molecular computer with high computational ability, which is now named Reverse-transcription-and-TRanscription-based Autonomous Computing System (RTRACS). In this study, we first report an experimental demonstration of a basic computation element of RTRACS and a mathematical modeling method for RTRACS. We focus on an AND gate, which produces an output RNA molecule only when two input RNA molecules exist, because it is one of the most basic computation elements in RTRACS. Experimental results demonstrated that the basic computation element worked as designed. In addition, its behaviors were analyzed using a mathematical model describing the molecular reactions of the RTRACS computation elements. A comparison between experiments and simulations confirmed the validity of the mathematical modeling method. This study will accelerate construction of various kinds of computation elements and computational circuits of RTRACS, and thus advance the research on autonomous DNA computers.
Takinoue, Masahiro; Kiga, Daisuke; Shohda, Koh-Ichiroh; Suyama, Akira
2008-10-01
Autonomous DNA computers have been attracting much attention because of their ability to integrate into living cells. Autonomous DNA computers can process information through DNA molecules and their molecular reactions. We have already proposed an idea of an autonomous molecular computer with high computational ability, which is now named Reverse-transcription-and-TRanscription-based Autonomous Computing System (RTRACS). In this study, we first report an experimental demonstration of a basic computation element of RTRACS and a mathematical modeling method for RTRACS. We focus on an AND gate, which produces an output RNA molecule only when two input RNA molecules exist, because it is one of the most basic computation elements in RTRACS. Experimental results demonstrated that the basic computation element worked as designed. In addition, its behaviors were analyzed using a mathematical model describing the molecular reactions of the RTRACS computation elements. A comparison between experiments and simulations confirmed the validity of the mathematical modeling method. This study will accelerate construction of various kinds of computation elements and computational circuits of RTRACS, and thus advance the research on autonomous DNA computers.
Trace and Major Element Chemistry Across the Cretaceous/Tertiary Boundary at Stevns Klint
NASA Astrophysics Data System (ADS)
Graup, G.; Spettel, B.
1992-07-01
INAA measurements of samples obtained by high-resolution stratigraphy on a mm scale reveal considerable variations in element concentrations across the boundary with their respective maxima stratified in distinct sublayers (Graup et al., 1992). These results suggest that measurements of bulk boundary samples a few cm thick may be inappropriate as concentration variations and element ratios would be leveled out pretending a single geochemical signal. Having investigated a sample comprising sublayers B, C, and D (Fig. 1), Alvarez et al.(1980) acknowledge that "no information is available on the chemical variations within the boundary." This kind of information is given below and shown in Fig. 1 (sublayers A and B are drafted in double scale). From the main lithologic characteristics of Maastrichtian to Paleocene sediments (Schmitz, 1988; Graup et al., 1992) it is readily deduced that Eh and pH conditions in the marine environment changed from oxic-mildly alkaline with normal carbonate sedimentation (Q-M) to anoxic-(mildly) acid with deposition of pyrite spherules (A3), organic material, and clay minerals in the Fish Clay (A-D), followed by a restoration of oxic-alkaline conditions depositing the Cerithium limestone (E- I). The element distribution across the boundary obviously mirrors these alternating environmental conditions: compounds soluble under acid and reducing conditions like Ca-carbonate and Mn are strongly depleted in the Fish Clay (Fig. 1A), whereas compounds stable and insoluble under these conditions are highly enriched (Fig. 1B). The opposite holds true for the calcareous sediments. Across the boundary, enhanced element concentrations are not evenly distributed but appear to be stratified with maximum concentrations in three distinct sublayers for the following elements: (1) A1 (hard clay): peak concentrations for REE (La 72 ppm) and U (45.5 ppm) as compared to 13 ppm La and 2 ppm U in sublayer A2 immediately above. (2) A3 (pyrite spherules): peak
3-D Image-guided diffuse optical tomography using boundary element method and MPI implementation.
Srinivasan, Subhadra; Ghadyani, Hamid
2011-01-01
Boundary elements provide an attractive method for image-guided multi-modality near infrared spectroscopy in three dimensions using only surface discretization. This method operates under the assumption that the underlying tissue contains piece-wise constant domains whose boundaries are known a priori from an alternative imaging modality such as MRI or microCT. This significantly simplifies the meshing process providing both speed-up and accuracy in the forward solution. Challenges with this method are in solving dense matrices, and working with complex heterogeneous domains. Solutions to these problems are presented here, with applications in breast cancer imaging and small - animal molecular imaging.
Computer simulation of grain boundary self-diffusion in aluminum
Dragunov, Andrei S.; Weckman, A. V.; Demyanov, B. F.
2014-10-06
In the work study the process of self-diffusion in symmetric tilt grain boundaries (GB) with the axes misorientation [100], [110] and [111]. The research was carried out by the methods of computer simulation The objects of the research are the three GB of common and special type for each axis misorientation. The angles of misorientation of the common GB is amounted to 10°, 30° and 50°. The simulation was performed by the method of molecular dynamics in the temperature range from 600 to 1000 K, with an interval of 50 K. For research on the direction jumps atoms were built tracks the movement of atoms in the process of self-diffusion. The calculations have shown, that for all of GB is characterized by pronounced anisotropy of the jumps at low temperatures (< 700K). At temperatures near to the melting point directions of the jumps are isotropic only for three GB (Θ=30°[100], Θ=50=[100] and Σ5(013)[100]). For other GB such as [100] and [110] remains priority direction of diffusion along the nuclei GB dislocations. Arrenius curves have from one to three linear plots with different tilt. Change the tilt of Arrenius dependences testifies to the change in the mechanism of self-diffusion. The parameters of grainboundary self-diffusion were determined The activation energy of grainboundary diffusion in 4–5 times lower than the energy of activation of a volume self-diffusion of aluminum (about 200 KJ/mol). The minimum value of activation energy has GB 10° with the axis misorientation [100] (10,15 KJ/mol), maximum (104.12 Kj/mol) - a special GB Σ11(113)
A fast multipole boundary element method for solving two-dimensional thermoelasticity problems
NASA Astrophysics Data System (ADS)
Liu, Y. J.; Li, Y. X.; Huang, S.
2014-09-01
A fast multipole boundary element method (BEM) for solving general uncoupled steady-state thermoelasticity problems in two dimensions is presented in this paper. The fast multipole BEM is developed to handle the thermal term in the thermoelasticity boundary integral equation involving temperature and heat flux distributions on the boundary of the problem domain. Fast multipole expansions, local expansions and related translations for the thermal term are derived using complex variables. Several numerical examples are presented to show the accuracy and effectiveness of the developed fast multipole BEM in calculating the displacement and stress fields for 2-D elastic bodies under various thermal loads, including thin structure domains that are difficult to mesh using the finite element method (FEM). The BEM results using constant elements are found to be accurate compared with the analytical solutions, and the accuracy of the BEM results is found to be comparable to that of the FEM with linear elements. In addition, the BEM offers the ease of use in generating the mesh for a thin structure domain or a domain with complicated geometry, such as a perforated plate with randomly distributed holes for which the FEM fails to provide an adequate mesh. These results clearly demonstrate the potential of the developed fast multipole BEM for solving 2-D thermoelasticity problems.
Advanced development of the boundary element method for steady-state heat conduction
NASA Technical Reports Server (NTRS)
Dargush, G. F.; Banerjee, Prasanta K.
1989-01-01
Considerable progress has been made in recent years toward advancing the state-of-the-art in solid mechanics boundary element technology. In the present work, much of this new technology is applied in the development of a general-purpose boundary element method (BEM) for steady-state heat conduction. In particular, the BEM implementation involves the use of higher-order conforming elements, self-adaptive integration and multi-region capability. Two- and three-dimensional, as well as axisymmetric analysis, are incorporated within a unified framework. In addition, techniques are introduced for the calculation of boundary flux, and for the inclusion of thermal resistance across interfaces. As a final extension, an efficient formulation is developed for the analysis of solid three-dimensional bodies with embedded holes. For this last class of problems, the new BEM formulation is particularly attractive, since use of the alternatives (i.e. finite element or finite difference methods) is not practical. A number of detailed examples illustrate the suitability and robustness of the present approach for steady-state heat conduction.
Advanced development of the boundary element method for steady-state heat conduction
NASA Technical Reports Server (NTRS)
Dargush, G. F.; Banerjee, Prasanta K.
1989-01-01
Considerable progress has been made in recent years toward advancing the state-of-the-art in solid mechanics boundary element technology. In the present work, much of this new technology is applied in the development of a general-purpose boundary element method (BEM) for steady-state heat conduction. In particular, the BEM implementation involves the use of higher-order conforming elements, self-adaptive integration and multi-region capability. Two- and three-dimensional, as well as axisymmetric analysis, are incorporated within a unified framework. In addition, techniques are introduced for the calculation of boundary flux, and for the inclusion of thermal resistance across interfaces. As a final extension, an efficient formulation is developed for the analysis of solid three-dimensional bodies with embedded holes. For this last class of problems, the new BEM formulation is particularly attractive, since use of the alternatives (i.e. finite element or finite difference methods) is not practical. A number of detailed examples illustrate the suitability and robustness of the present approach for steady-state heat conduction.
NASA Astrophysics Data System (ADS)
Xu, Kai-Jiang; Pan, Xiao-Min; Li, Ren-Xian; Sheng, Xin-Qing
2017-07-01
In optical trapping applications, the optical force should be investigated within a wide range of parameter space in terms of beam configuration to reach the desirable performance. A simple but reliable way of conducting the related investigation is to evaluate optical forces corresponding to all possible beam configurations. Although the optical force exerted on arbitrarily shaped particles can be well predicted by boundary element method (BEM), such investigation is time costing because it involves many repetitions of expensive computation, where the forces are calculated from the equivalent surface currents. An algorithm is proposed to alleviate the difficulty by exploiting our previously developed skeletonization framework. The proposed algorithm succeeds in reducing the number of repetitions. Since the number of skeleton beams is always much less than that of beams in question, the computation can be very efficient. The proposed algorithm is accurate because the skeletonization is accuracy controllable.
Finite element dynamic analysis on CDC STAR-100 computer
NASA Technical Reports Server (NTRS)
Noor, A. K.; Lambiotte, J. J., Jr.
1978-01-01
Computational algorithms are presented for the finite element dynamic analysis of structures on the CDC STAR-100 computer. The spatial behavior is described using higher-order finite elements. The temporal behavior is approximated by using either the central difference explicit scheme or Newmark's implicit scheme. In each case the analysis is broken up into a number of basic macro-operations. Discussion is focused on the organization of the computation and the mode of storage of different arrays to take advantage of the STAR pipeline capability. The potential of the proposed algorithms is discussed and CPU times are given for performing the different macro-operations for a shell modeled by higher order composite shallow shell elements having 80 degrees of freedom.
Mixed Element Formulation for the Finite Element-Boundary Integral Method
2006-03-01
bottom) of the prism. For conjunction with other elements. The edges the vertical edges, k1 and k2 are defined in in the extrusion direction are orthogonal...are the vertical prism expansion functions, important because they have the ability to X ki k2 model irregular surface geometries with 7 2 3...3.2 3!4 3!6 38 4 4. 4.4 4 4 5 wher p dnote thefac theeithr th tes orFrequ-n,¢[GHzI source edge are associated with a test Figure 4: Radar Cross
Computer simulation of functioning of elements of security systems
NASA Astrophysics Data System (ADS)
Godovykh, A. V.; Stepanov, B. P.; Sheveleva, A. A.
2017-01-01
The article is devoted to issues of development of the informational complex for simulation of functioning of the security system elements. The complex is described from the point of view of main objectives, a design concept and an interrelation of main elements. The proposed conception of the computer simulation provides an opportunity to simulate processes of security system work for training security staff during normal and emergency operation.
NASA Astrophysics Data System (ADS)
Metz, P. D.
A FORTRAN computer program called GROCS (GRound Coupled Systems) has been developed to study 3-dimensional underground heat flow. Features include the use of up to 30 finite elements or blocks of Earth which interact via finite difference heat flow equations and a subprogram which sets realistic time and depth dependent boundary conditions. No explicit consideration of mositure movement or freezing is given. GROCS has been used to model the thermal behavior of buried solar heat storage tanks (with and without insulation) and serpentine pipe fields for solar heat pump space conditioning systems. The program is available independently or in a form compatible with specially written TRNSYS component TYPE subroutines. The approach taken in the design of GROCS, the mathematics contained and the program architecture, are described. Then, the operation of the stand-alone version is explained. Finally, the validity of GROCS is discussed.
NASA Technical Reports Server (NTRS)
Liepmann, Hans W; Fila, Gertrude H
1947-01-01
The laminar boundary layer and the position of the transition point were investigated on a heated flat plate. It was found that the Reynolds number of transition decreased as the temperature of the plate is increased. It is shown from simple qualitative analytical considerations that the effect of variable viscosity in the boundary layer due to the temperature difference produces a velocity profile with an inflection point if the wall temperature is higher than the free-stream temperature. This profile is confirmed by measurements. The instability of inflection-point profiles is discussed. Studies of the flow in the wake of large, two-dimensional roughness elements are presented. It is shown that a boundary-layer can separate and reattach itself to the wall without having transition take place.
Saigal, S. ); Chandra, A. )
1991-05-01
Design sensitivity analysis, along with the shape optimization of heat diffusion problems using the boundary element method (BEM), is presented in this paper. The present approach utilizes the implicit differentiation of discretized boundary integral equations with respect to the design variables to yield the sensitivity equations. A technique based on the response of an object to a constant boundary temperature is presented for the evaluation of singular terms in the thermal sensitivity kernels. A procedure for the design sensitivity analysis of a reduced system of equations obtained via substructuring and condensation is also presented. The BEM formulations are implemented for both two-dimensional and axisymmetric objects. A number of sample problems are solved to demonstrate the accuracy of the present sensitivity formulation and to obtain optimal configurations of some mechanical components of practical interest, which are subjected to different thermal environments.
Boundary element analysis of unilateral supported Reissner plates on elastic foundations
NASA Astrophysics Data System (ADS)
Xiao, J. R.
A boundary element-linear complementary equation method (BE-LCEM) is developed for the bending of thick plates with free edges on unilateral elastic foundations with particular emphasis on the non-contact phenomenon between the plates and the subgrades. The theory of thick plate was used, and three boundary conditions on free edge have been adopted. Following numerical discretization by using the boundary integral equation method for this contact problem, an effective linear complementary equation is then established with two complementary variables for each contact node. Complementary variables are taken as the normal contact force and the relative deflection between the plate and the foundation. The solution of which can be obtained using mathematical programming. A number of examples are presented to demonstrate the effectiveness of the features as implemented. Two types of foundations (Winkler and half-space) are examined and the method is shown to provide good agreement with available analytical solutions obtained by other investigators.
Immersed boundary-finite element model of fluid-structure interaction in the aortic root
NASA Astrophysics Data System (ADS)
Flamini, Vittoria; DeAnda, Abe; Griffith, Boyce E.
2016-04-01
It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to evolve as increasingly detailed in vivo imaging data become available. Herein, we describe a fluid-structure interaction model of the aortic root, including the aortic valve leaflets, the sinuses of Valsalva, the aortic annulus, and the sinotubular junction, that employs a version of Peskin's immersed boundary (IB) method with a finite element description of the structural elasticity. As in earlier work, we use a fiber-based model of the valve leaflets, but this study extends earlier IB models of the aortic root by employing an incompressible hyperelastic model of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backward displacement method that determines the unloaded configuration of the root model. Our model yields realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations indicate that although the detailed leaflet and root kinematics show some grid sensitivity, our IB model of the aortic root nonetheless produces essentially grid-converged flow rates and pressures at practical grid spacings for the high Reynolds number flows of the aortic root. These results thereby clarify minimum grid resolutions required by such models when used as stand-alone models of the aortic valve as well as when used to provide models of the outflow valves in models of left-ventricular fluid dynamics.
Finite and Boundary Element Modeling of the NASA Langley Aluminum Testbed Cylinder (ATC)
NASA Technical Reports Server (NTRS)
Grosveld, Ferdinand W.
2006-01-01
The NASA Langley Aluminum Testbed Cylinder (ATC) was designed to serve as a universal structure for evaluating structural acoustic codes, modeling techniques and optimization methods used in the prediction of aircraft interior noise. Finite element models were developed for the components of the ATC based on the geometric, structural and material properties of the physical test structure. Numerically predicted modal frequencies for the longitudinal stringer, ring frame and dome component models, and six assembled ATC arrangements were in good agreement with experimental modal survey data. Finite element modal analyses were performed for 3 psi and 6 psi internal pressurization conditions. Acoustic cylinder modes for the interior of the ATC were calculated with an acoustic finite element model. Frequency transfer functions between a unit force on the structure and the acoustic response inside the ATC cylinder were measured and were compared with predictions based on a boundary element model. Comparisons between predicted and experimental results are presented and discussed.
Stress and strength analysis of composite joints using direct boundary element method
NASA Astrophysics Data System (ADS)
Lin, Chien-Chang; Lin, Chuen-Horng
The stress distribution and the strength of bolted joints of orthotropic composite plates under uniform loading are investigated. A direct boundary element method with quadratic isoparametric elements in conjunction with a fundamental solution derived by Rizzo and Shippy (1970) is used. Plates with rigid bolts are treated as 2D plane stress problems, and the bolt size is considered to be identical to the hole dimension. The prediction of the laminate strength is based on the Yamada-Sun (1978) failure criterion. Some numerical results for various edge distances and material properties are presented for illustrative purposes.
Coupling finite and boundary element methods for 2-D elasticity problems
NASA Technical Reports Server (NTRS)
Krishnamurthy, T.; Raju, I. S.; Sistla, R.
1993-01-01
A finite element-boundary element (FE-BE) coupling method for two-dimensional elasticity problems is developed based on a weighted residual variational method in which a portion of the domain of interest is modeled by FEs and the remainder of the region by BEs. The performance of the FE-BE coupling method is demonstrated via applications to a simple 'patch test' problem and three-crack problems. The method passed the patch tests for various modeling configurations and yielded accurate strain energy release rates for the crack problems studied.
ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve☆
Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk
2014-01-01
In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu (1987) [52] are mathematically well-established and widely used in practice. In this work, we propose and analyze ZZ-type error estimators for the adaptive boundary element method (BEM). We consider weakly singular and hyper-singular integral equations and prove, in particular, convergence of the related adaptive mesh-refining algorithms. Throughout, the theoretical findings are underlined by numerical experiments. PMID:24748725
Altman, Michael D; Bardhan, Jaydeep P; White, Jacob K; Tidor, Bruce
2009-01-15
We present a boundary-element method (BEM) implementation for accurately solving problems in biomolecular electrostatics using the linearized Poisson-Boltzmann equation. Motivating this implementation is the desire to create a solver capable of precisely describing the geometries and topologies prevalent in continuum models of biological molecules. This implementation is enabled by the synthesis of four technologies developed or implemented specifically for this work. First, molecular and accessible surfaces used to describe dielectric and ion-exclusion boundaries were discretized with curved boundary elements that faithfully reproduce molecular geometries. Second, we avoided explicitly forming the dense BEM matrices and instead solved the linear systems with a preconditioned iterative method (GMRES), using a matrix compression algorithm (FFTSVD) to accelerate matrix-vector multiplication. Third, robust numerical integration methods were employed to accurately evaluate singular and near-singular integrals over the curved boundary elements. Fourth, we present a general boundary-integral approach capable of modeling an arbitrary number of embedded homogeneous dielectric regions with differing dielectric constants, possible salt treatment, and point charges. A comparison of the presented BEM implementation and standard finite-difference techniques demonstrates that for certain classes of electrostatic calculations, such as determining absolute electrostatic solvation and rigid-binding free energies, the improved convergence properties of the BEM approach can have a significant impact on computed energetics. We also demonstrate that the improved accuracy offered by the curved-element BEM is important when more sophisticated techniques, such as nonrigid-binding models, are used to compute the relative electrostatic effects of molecular modifications. In addition, we show that electrostatic calculations requiring multiple solves using the same molecular geometry, such as
NASA Astrophysics Data System (ADS)
Zheng, Chang-Jun; Chen, Hai-Bo; Chen, Lei-Lei
2013-04-01
This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/plane-symmetric acoustic wave problems. The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only. Moreover, a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived, and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating, translating and saving the multipole/local expansion coefficients of the image domain. The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems. As for exterior acoustic problems, the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method. Details on the implementation of the present method are described, and numerical examples are given to demonstrate its accuracy and efficiency.
Comparison of the constant and linear boundary element method for EEG and MEG forward modeling
Mosher, J.C.; Chang, C.H.; Leahy, R.M.
1996-07-01
We present a comparison of boundary element methods for solving the forward problem in EEG and MEG. We use the method of weighted residuals and focus on the collocation and Galerkin forms for constant and linear basis functions. We also examine the effect of the isolated skull approach for reducing numerical errors due to the low conductivity of the skull. We demonstrate the improvement that a linear Galerkin approach may yield in solving the forward problem.
An enriched finite element model with q-refinement for radiative boundary layers in glass cooling
Mohamed, M. Shadi; Seaid, Mohammed; Trevelyan, Jon; Laghrouche, Omar
2014-02-01
Radiative cooling in glass manufacturing is simulated using the partition of unity finite element method. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary simplified P{sub 1} approximation for the radiation in non-grey semitransparent media. To integrate the coupled equations in time we consider a linearly implicit scheme in the finite element framework. A class of hyperbolic enrichment functions is proposed to resolve boundary layers near the enclosure walls. Using an industrial electromagnetic spectrum, the proposed method shows an immense reduction in the number of degrees of freedom required to achieve a certain accuracy compared to the conventional h-version finite element method. Furthermore the method shows a stable behaviour in treating the boundary layers which is shown by studying the solution close to the domain boundaries. The time integration choice is essential to implement a q-refinement procedure introduced in the current study. The enrichment is refined with respect to the steepness of the solution gradient near the domain boundary in the first few time steps and is shown to lead to a further significant reduction on top of what is already achieved with the enrichment. The performance of the proposed method is analysed for glass annealing in two enclosures where the simplified P{sub 1} approximation solution with the partition of unity method, the conventional finite element method and the finite difference method are compared to each other and to the full radiative heat transfer as well as the canonical Rosseland model.
NASA Astrophysics Data System (ADS)
Hilson, Christopher William
Following the February 27, 2010 Mw 8.8 Maule earthquake, an international effort was undertaken to better understand reasons for observed damage to concrete structural walls in buildings located in the affected region of Chile and to address potential design implications. The Chilean building code for concrete structures is based on the U.S. ACI 318 building code; however, based on the observed performance of over 400 buildings in the March 1985 earthquake-impacted Vina del Mar, Chilean Code NCh433.Of96 included an exception that special boundary elements (SBEs)---which are commonly required for walls in U.S. buildings---need not be provided. By taking exception to the special boundary element detailing provisions, the Chilean code allowed thin wall boundary zones with relatively large (typically 20 cm) spacing of transverse reinforcement (essentially unconfined) to be constructed. Given these differences, the 2010 earthquake is an excellent opportunity to assess the performance of reinforced concrete buildings designed using modern codes similar to those used in the United States. Data from damaged and undamaged buildings, as well as from parametric and experimental studies, are used to provide recommendations to improve the efficacy of U.S. provisions designed to inhibit structural damage at wall boundaries. Seven Chilean buildings were selected to investigate the performance of boundary elements during the 2010 earthquake. Several walls from each of the seven buildings were chosen to evaluate the ACI 318-11 Section 21.9.6.2 displacement-based trigger equation for determining if SBEs would have been required and if observed damage was consistent with the evaluation result (i.e., SBE required, no damage; SBE required, damage observed). The propensity of boundary longitudinal reinforcement to buckle was also investigated, taking into consideration the influence of boundary transverse reinforcement configuration and longitudinal reinforcement strain history. In
Gertsman, V.Y. |; Tangri, K.
1995-06-01
Microstructures formed as a result of multiple twinning have been simulated by means of computer modeling. Grain boundary misorientation (character) and triple junction distributions have been studied with the emphasis on the effect of initial texture and multiple twinning process. Although grain boundary distributions are similar in all the microstructures modeled, sharp initial texture leads to a somewhat enhanced amount of {Sigma}3 boundaries and to a considerable increase in the number of triple junctions containing two {Sigma}3 boundaries. The impact of these parameters on the material susceptibility to intergranular crack propagation has been analyzed and implications for grain boundary engineering has been discussed.
Simulation of electrochemical machining using the boundary element method with no saturation
NASA Astrophysics Data System (ADS)
Petrov, A. G.; Sanduleanu, S. V.
2016-10-01
The simulation of electrochemical machining (ECM) is based on determining the surface shape at each point in time. The change in the shape of the surface depends on the rate of the electrochemical dissolution of the metal (conducting material), which is assumed to be proportional to the electric field strength on the boundary of the workpiece. The potential of the electric field is a harmonic function outside the two domains—the tool electrode and the workpiece. Constant potentials are specified on the boundaries of the tool electrode and the workpiece. A scheme with no saturation in which the strength of the electric field created by the potential difference on the boundary of the workpiece is proposed. The scheme converges exponentially in the number of grid elements on the workpiece boundary. Given the rate of electrochemical dissolution, the workpiece boundary, which depends on time, is found. The numerical solutions are compared with exact solutions, examples of the ECM simulation are discussed, and the results are compared with those obtained by other numerical methods and the ones obtained using ECM machines.
Numerical algorithms for finite element computations on arrays of microprocessors
NASA Technical Reports Server (NTRS)
Ortega, J. M.
1981-01-01
The development of a multicolored successive over relaxation (SOR) program for the finite element machine is discussed. The multicolored SOR method uses a generalization of the classical Red/Black grid point ordering for the SOR method. These multicolored orderings have the advantage of allowing the SOR method to be implemented as a Jacobi method, which is ideal for arrays of processors, but still enjoy the greater rate of convergence of the SOR method. The program solves a general second order self adjoint elliptic problem on a square region with Dirichlet boundary conditions, discretized by quadratic elements on triangular regions. For this general problem and discretization, six colors are necessary for the multicolored method to operate efficiently. The specific problem that was solved using the six color program was Poisson's equation; for Poisson's equation, three colors are necessary but six may be used. In general, the number of colors needed is a function of the differential equation, the region and boundary conditions, and the particular finite element used for the discretization.
Computer programs for the Boltzmann collision matrix elements
NASA Astrophysics Data System (ADS)
Das, P.
1989-09-01
When the distribution function in the kinetic theory of gases is expanded in a basis of orthogonal functions, the Boltzmann collision operators can be evaluated in terms of appropriate matrix elements. These matrix elements are usually given in terms of highly complex algebraic expressions. When Burnett functions, which consist of Sonine polynomials and spherical harmonics, are used as the basis, the irreducible tensor formalism provides expressions for the matrix elements that are algebraically simple, possess high symmetry, and are computationally more economical than in any other basis. The package reported here consists of routines to compute such matrix elements in a Burnett function basis for a mixture of hard sphere gases, as also the loss integral of a Burnett mode and the functions themselves. The matrix elements involve the Clebsch-Gordan and Brody-Moshinsky coefficients, both of which are used here for unusually high values of their arguments. For the purpose of validation both coefficients are computed using two different methods. Though written for hard sphere molecules the package can, with only slight modification, be adapted to more general molecular models as well.
Rad-hard computer elements for space applications
NASA Technical Reports Server (NTRS)
Krishnan, G. S.; Longerot, Carl D.; Treece, R. Keith
1993-01-01
Space Hardened CMOS computer elements emulating a commercial microcontroller and microprocessor family have been designed, fabricated, qualified, and delivered for a variety of space programs including NASA's multiple launch International Solar-Terrestrial Physics (ISTP) program, Mars Observer, and government and commercial communication satellites. Design techniques and radiation performance of the 1.25 micron feature size products are described.
NASA Astrophysics Data System (ADS)
Aristovich, K. Y.; Khan, S. H.
2010-07-01
Realistic computer modelling of biological objects requires building of very accurate and realistic computer models based on geometric and material data, type, and accuracy of numerical analyses. This paper presents some of the automatic tools and algorithms that were used to build accurate and realistic 3D finite element (FE) model of whole-brain. These models were used to solve the forward problem in magnetic field tomography (MFT) based on Magnetoencephalography (MEG). The forward problem involves modelling and computation of magnetic fields produced by human brain during cognitive processing. The geometric parameters of the model were obtained from accurate Magnetic Resonance Imaging (MRI) data and the material properties - from those obtained from Diffusion Tensor MRI (DTMRI). The 3D FE models of the brain built using this approach has been shown to be very accurate in terms of both geometric and material properties. The model is stored on the computer in Computer-Aided Parametrical Design (CAD) format. This allows the model to be used in a wide a range of methods of analysis, such as finite element method (FEM), Boundary Element Method (BEM), Monte-Carlo Simulations, etc. The generic model building approach presented here could be used for accurate and realistic modelling of human brain and many other biological objects.
Modeling of rolling element bearing mechanics. Computer program user's manual
NASA Technical Reports Server (NTRS)
Greenhill, Lyn M.; Merchant, David H.
1994-01-01
This report provides the user's manual for the Rolling Element Bearing Analysis System (REBANS) analysis code which determines the quasistatic response to external loads or displacement of three types of high-speed rolling element bearings: angular contact ball bearings, duplex angular contact ball bearings, and cylindrical roller bearings. The model includes the defects of bearing ring and support structure flexibility. It is comprised of two main programs: the Preprocessor for Bearing Analysis (PREBAN) which creates the input files for the main analysis program, and Flexibility Enhanced Rolling Element Bearing Analysis (FEREBA), the main analysis program. This report addresses input instructions for and features of the computer codes. A companion report addresses the theoretical basis for the computer codes. REBANS extends the capabilities of the SHABERTH (Shaft and Bearing Thermal Analysis) code to include race and housing flexibility, including such effects as dead band and preload springs.
A non-reflecting boundary for use in a finite element beam model of a railway track
NASA Astrophysics Data System (ADS)
Yang, Jiannan; Thompson, David J.
2015-02-01
Some beam-like structures such as a railway track are effectively infinite in nature. Analytical solutions exist for simple structures but numerical methods like the finite element (FE) method are often employed to study more complicated problems. However, when the FE method is used for structures of infinite extent it is essential to introduce artificial boundaries to limit the area of computation. Here, a non-reflecting boundary is developed using a damped tapered tip for application in a finite element model representing an infinite supported beam. The FE model of the tapered tip is validated against an analytical model based on Bessel functions. The reflection characteristics of the FE tapered tip are quantified using a wave/FE superposition method. It is shown that the damped tapered tip is much more effective than its constant counterpart and achieves reduction of the model size. The damped tapered tip is applied to a simple FE railway track model and good agreement is found when its point mobility is compared with an analytical infinite track model.
Trace-element anomalies at the Mississippian/Pennsylvanian boundary in Oklahoma and Texas
NASA Astrophysics Data System (ADS)
Orth, Charles J.; Quintana, Leonard R.; Gilmore, James S.; Grayson, Robert C., Jr.; Westergaard, Edwin H.
1986-12-01
Trace-element abundance anomalies have been found at the Mississippian/Pennsylvania boundary at sites in Oklahoma and Texas where the boundary has been precisely located on the basis of an abrupt change in conodont diversity and species composition. Enriched elements include osmium, indium, platinum, chromium, most chalcophiles, rare earths, and uranium. The anomalies are more intense (e.g., Os = 4 ppb, Ir = 0.38 ppb, Pt = 6 ppb, Cr = 12000 ppm, U = 380 ppm) and peisist through a thicker interval at the south-central Texas locality than in Oklahoma, and in bolh locations the anomalies are associated with an increase in phosphate content of the rocks. There is no tangible evidence of an asteroid or comet impact source for the excess Pt-group elements and fauna! crisis. The cause of the elemental enrichments and the biological disturbance may possibly be related to a change in the ocean chemistry of the Paleozoic seaway, such as increased upwelling, stagnation, or nearby submarine volcanism.
NASA Astrophysics Data System (ADS)
Velichko, A.; Wilcox, P. D.
2012-05-01
An efficient technique for predicting the complete scattering behavior for an arbitrarily-shaped scatterer is presented. The spatial size of the modeling domain around the scatterer is as small as possible to minimize computational expense and a minimum number of models are executed. This model uses non-reflecting boundary conditions on the surface surrounding the scatterer which are non-local in space. Example results for 2D and 3D scattering in isotropic material and guided wave scattering are presented.
NASA Technical Reports Server (NTRS)
Sistla, R.; Raju, I. S.; Krishnamurthy, T.
1993-01-01
A displacement gradient method for 2D anisotropic elasticity problems is presented, which effectively minimizes the boundary layer effect through a two-step procedure. First, the boundary integral equations are solved for the unknown boundary displacements and tractions. Second, a direct integral equation for displacement gradients is developed in terms of boundary tractions. Three methods based on different evaluation procedures and locations for determining the displacement gradients are proposed. In the first method the displacement gradients are averaged at nodes common to adjacent elements. The second method stores the gradients element-wise. In the third method, the gradients are evaluated at the nodes of discontinuous elements. The three methods are applied to near-isotropic plates with circular and elliptic cutouts. It is concluded that all three methods can yield accurate stress distributions.
NASA Technical Reports Server (NTRS)
Albers, J. A.; Gregg, J. L.
1974-01-01
Finite-difference computer program calculates viscous compressible boundary layer flow over either planar or axisymmetric surfaces. Flow may be initially laminar and progress through transitional zone to fully turbulent flow, or it may remain laminar, depending on imposed boundary conditions, laws of viscosity, and numerical solution of momentum and energy equations.
A multiple flux boundary element method applied to the description of surface water waves
NASA Astrophysics Data System (ADS)
Hague, C. H.; Swan, C.
2009-08-01
This paper concerns a two dimensional numerical model based on a high-order boundary element method with fully nonlinear free surface boundary conditions. Multiple fluxes are applied as a method of removing the so-called “corner problem”, whereby the direction of the outward normal at geometric discontinuities is ill-defined. In the present method, both fluxes associated with differing directions of the outward normal at a corner are considered, allowing a single node to be placed at that position. This prevents any loss of information at what can be an important part of the boundary, especially if considering simulations of wave reflection and wave run-up. The method is compared to both the double node approach and the use of discontinuous elements and is shown to be a more accurate technique. The success of the method is further demonstrated by its ability to accurately simulate various problems involving wave transmission and wave-structure interactions at domain corners; the results being achieved without the need for filtering, smoothing or re-gridding of any kind.
Lyard, F.; Genco, M.L.
1994-10-01
A bidimensional, spectral in time, quasi-linearised hydrodynamic ocean tide model has been developed at the Institut de Mecanique de Grenoble. This model is derived from the classical shallow water equations by removing the velocity unknowns in the continuity equation, that leads to an elliptic, second-order differential equation where tide denivellation remains the only unknown quantity. The problem is solved in its variational formulation and the finite elements method is used to discretise the equations in the spatial domain with a Lagrange-P2 approximation. Bottom topography has to be known at the integration points of the elements. In the case of the large oceanic basins, a specific method, called the bathymetry optimisation method, is needed to correctly take into account the bottom topography inside the model. The accuracy of the model`s solutions is also strongly dependent on the quality of the open boundary conditions because of the elliptic characteristics of the problem. The optimisation method for open boundary conditions relies on the use of the in situ data available in the modelled domain. The aim of this paper is to present the basis of these optimisations of bathymetry and open boundary conditions. An illustration of the related improvements is presented on the North Atlantic Basin. 36 refs., 10 figs., 5 tabs.
Jang, Hae-Won; Ih, Jeong-Guon
2013-03-01
The time domain boundary element method (TBEM) to calculate the exterior sound field using the Kirchhoff integral has difficulties in non-uniqueness and exponential divergence. In this work, a method to stabilize TBEM calculation for the exterior problem is suggested. The time domain CHIEF (Combined Helmholtz Integral Equation Formulation) method is newly formulated to suppress low order fictitious internal modes. This method constrains the surface Kirchhoff integral by forcing the pressures at the additional interior points to be zero when the shortest retarded time between boundary nodes and an interior point elapses. However, even after using the CHIEF method, the TBEM calculation suffers the exponential divergence due to the remaining unstable high order fictitious modes at frequencies higher than the frequency limit of the boundary element model. For complete stabilization, such troublesome modes are selectively adjusted by projecting the time response onto the eigenspace. In a test example for a transiently pulsating sphere, the final average error norm of the stabilized response compared to the analytic solution is 2.5%.
STARS: A general-purpose finite element computer program for analysis of engineering structures
NASA Technical Reports Server (NTRS)
Gupta, K. K.
1984-01-01
STARS (Structural Analysis Routines) is primarily an interactive, graphics-oriented, finite-element computer program for analyzing the static, stability, free vibration, and dynamic responses of damped and undamped structures, including rotating systems. The element library consists of one-dimensional (1-D) line elements, two-dimensional (2-D) triangular and quadrilateral shell elements, and three-dimensional (3-D) tetrahedral and hexahedral solid elements. These elements enable the solution of structural problems that include truss, beam, space frame, plane, plate, shell, and solid structures, or any combination thereof. Zero, finite, and interdependent deflection boundary conditions can be implemented by the program. The associated dynamic response analysis capability provides for initial deformation and velocity inputs, whereas the transient excitation may be either forces or accelerations. An effective in-core or out-of-core solution strategy is automatically employed by the program, depending on the size of the problem. Data input may be at random within a data set, and the program offers certain automatic data-generation features. Input data are formatted as an optimal combination of free and fixed formats. Interactive graphics capabilities enable convenient display of nodal deformations, mode shapes, and element stresses.
Hromadka, T.V.; Guymon, G.L.
1985-01-01
An algorithm is presented for the numerical solution of the Laplace equation boundary-value problem, which is assumed to apply to soil freezing or thawing. The Laplace equation is numerically approximated by the complex-variable boundary-element method. The algorithm aids in reducing integrated relative error by providing a true measure of modeling error along the solution domain boundary. This measure of error can be used to select locations for adding, removing, or relocating nodal points on the boundary or to provide bounds for the integrated relative error of unknown nodal variable values along the boundary.
Supplement to the ICRPG turbulent boundary layer nozzle analysis computer program
NASA Technical Reports Server (NTRS)
Omori, S.; Gross, K. W.
1972-01-01
A supplement is presented for a turbulent boundary layer nozzle analysis computer program. It describes the program calculation sequence and presents a detailed documentation of each subroutine. Important equations are derived explicitly, and improvements to the program are discussed.
Yamaguchi, Tohru F; Okamoto, Yoshiwo
2017-06-14
Abdominal fat accumulation is considered an essential indicator of human health. Electrical impedance tomography has considerable potential for abdominal fat imaging because of the low specific conductivity of human body fat. In this paper, we propose a robust reconstruction method for high-fidelity conductivity imaging by abstraction of the abdominal cross section using a relatively small number of parameters. Toward this end, we assume homogeneous conductivity in the abdominal subcutaneous fat area and characterize its geometrical shape by parameters defined as the ratio of the distance from the center to boundary of subcutaneous fat to the distance from the center to outer boundary in 64 equiangular directions. To estimate the shape parameters, the sensitivity of the noninvasively measured voltages with respect to the shape parameters is formulated for numerical optimization. Numerical simulations are conducted to demonstrate the validity of the proposed method. A 3-dimensional finite element method is used to construct a computer model of the human abdomen. The inverse problems of shape parameters and conductivities are solved concurrently by iterative forward and inverse calculations. As a result, conductivity images are reconstructed with a small systemic error of less than 1% for the estimation of the subcutaneous fat area. A novel method is devised for estimating the boundary of the abdominal subcutaneous fat. The fidelity of the overall reconstructed image to the reference image is significantly improved. The results demonstrate the possibility of realization of an abdominal fat scanner as a low-cost, radiation-free medical device. Copyright © 2017 John Wiley & Sons, Ltd.
An algebraic way to compute boundary layer's sizes
NASA Astrophysics Data System (ADS)
GRENIER, E.
2001-05-01
The aim of the talk is to describe a simple way to recover the classical boundary layers' sizes in rotating fluids and MHD problems, to derive there equations and to simply investigate some of there stability property. This gives a new view on classical Fourier Laplace methods, using modern mathematical tools (pseudodifferential operators) adapted to complex geometries (spheres, between two spheres, non flat boundaries), and greatly simplifies the classical derivations of Proudman and Stewartson (rotating fluids between two spheres), Hartmann... We will give a special stress on equatorial singularities and on the various sizes which appear near the equator, both with and without the magnetic field and make a short review of the mathematical (partial differential equation's type) literature on the subject.
NASA Astrophysics Data System (ADS)
Thompson, T. B.; Meade, B. J.
2015-12-01
The Himalayas are the tallest mountains on Earth with ten peaks exceeding 8000 meters, including Mt. Everest. The geometrically complex fault system at the Himalayan Range Front produces both great relief and great earthquakes, like the recent Mw=7.8 Nepal rupture. Here, we develop geometrically accurate elastic boundary element models of the fault system at the Himalayan Range Front including the Main Central Thrust, South Tibetan Detachment, Main Frontal Thrust, Main Boundary Thrust, the basal detachment, and surface topography. Using these models, we constrain the tectonic driving forces and frictional fault strength required to explain Quaternary fault slip rate estimates. These models provide a characterization of the heterogeneity of internal stress in the region surrounding the 2015 Nepal earthquake.
Uranus, Henri; Hoekstra, H
2004-06-14
A finite-element-based vectorial optical mode solver is used to analyze microstructured optical waveguides. By employing 1st-order Bayliss-Gunzburger-Turkel-like transparent boundary conditions, both the real and imaginary part of the modal indices can be calculated in a relatively small computational domain. Results for waveguides with either circular or non-circular microstructured holes, solid- or air-core will be presented, including the silica-air Bragg fiber recently demonstrated by Vienne et al. (Post-deadline Paper PDP25, OFC 2004). The results of solid-core structures are in good agreement with the results of other methods while the results of air-core structure agree to the experimental results.
Computation of Three-Dimensional Boundary Layers Including Separation
1987-02-01
BOUNDARY LAYERS INCLUDING SEPARATION The material assembled in this book was prepared under the combined sponsorship of the Fluid Dynamics Panel, the...publication has been reproduced directly from material supplied by AGARD or the authors. Published February 1987 Copyright© AGARD 1987 All Rights...precisely, T is proportional to v ’z. Using (1.19), the ratios of scales characterizing the energy-containing eddies (u, 1, 8 ) and the dissipative
Computation of three-dimensional mixed convective boundary layer flow
NASA Technical Reports Server (NTRS)
Gadepalli, Prashandt; Rahman, Muhammad M.
1995-01-01
The paper presents the numerical solution of heat and mass transfer during cross-flow (orthogonal) mixed convection. In this class of flow, a buoyancy-driven transport in the vertical direction and a forced convective flow in the horizontal direction results in a three-dimensional boundary layer structure adjacent to the plate. The rates of heat and mass transfer are determined by a combined influence of the two transport processes. The equations for the conservation of mass, momentum, energy, and species concentration were solved along with appropriate boundary conditions to determine the distributions of velocity components, temperature, and concentration across the thickness of the boundary layer at different locations on the plate. Results were expressed in dimensionless form using Reynolds number, Richardson number for heat transfer, Richardson number for mass transfer, Prandtl number, and Schmidt number as parameters. It was found that the transport is dominated by buoyancy at smaller vertical locations and at larger distances away from the forced convection leading edge. Effects of forced convection appeared to be very strong at smaller horizontal distances from the leading edge. The cross stream forced convection enhanced the rate of heat and mass transfer by a very significant amount.
NASA Astrophysics Data System (ADS)
Takahashi, Toru; Coulier, Pieter; Darve, Eric
2017-07-01
We investigate an efficient preconditioning of iterative methods (such as GMRES) for solving dense linear systems Ax = b that follow from a boundary element method (BEM) for the 3D Helmholtz equation, focusing on the low-frequency regime. While matrix-vector products in GMRES can be accelerated through the low-frequency fast multipole method (LFFMM), the BEM often remains computationally expensive due to the large number of GMRES iterations. We propose the application of the inverse fast multipole method (IFMM) as a preconditioner to accelerate the convergence of GMRES. The IFMM is in essence an approximate direct solver that uses a multilevel hierarchical decomposition and low-rank approximations. The proposed IFMM-based preconditioning has a tunable parameter ε that balances the cost to construct a preconditioner M, which is an approximation of A-1, and the cost to perform the iterative process by means of M. Namely, using a small (respectively, large) value of ε takes a long (respectively, short) time to construct M, while the number of iterations can be small (respectively, large). A comprehensive set of numerical examples involving various boundary value problems with complicated geometries and mixed boundary conditions is presented to validate the efficiency of the proposed method. We show that the IFMM preconditioner (with a nearly optimal ε of 10-2) clearly outperforms some common preconditioners for the BEM, achieving 1.2-10.8 times speed-up of the computations, in particular when the scale of the underlying scatterer is about five wavelengths or more. In addition, the IFMM preconditioner is capable of solving complicated problems (in a reasonable amount of time) that BD preconditioner can not.
Ma, Zhibo; Li, Mo; Roy, Sharmila; Liu, Kevin J; Romine, Matthew L; Lane, Derrick C; Patel, Sapna K; Cai, Haini N
2016-01-01
The three-dimensional (3D) organization of the eukaryotic genome is critical for its proper function. Evidence suggests that extensive chromatin loops form the building blocks of the genomic architecture, separating genes and gene clusters into distinct functional domains. These loops are anchored in part by a special type of DNA elements called chromatin boundary elements (CBEs). CBEs were originally found to insulate neighboring genes by blocking influences of transcriptional enhancers or the spread of silent chromatin. However, recent results show that chromatin loops can also play a positive role in gene regulation by looping out intervening DNA and “delivering” remote enhancers to gene promoters. In addition, studies from human and model organisms indicate that the configuration of chromatin loops, many of which are tethered by CBEs, is dynamically regulated during cell differentiation. In particular, a recent work by Li et al has shown that the SF1 boundary, located in the Drosophila Hox cluster, regulates local genes by tethering different subsets of chromatin loops: One subset enclose a neighboring gene ftz, limiting its access by the surrounding Scr enhancers and restrict the spread of repressive histones during early embryogenesis; and the other loops subdivide the Scr regulatory region into independent domains of enhancer accessibility. The enhancer-blocking activity of these CBE elements varies greatly in strength and tissue distribution. Further, tandem pairing of SF1 and SF2 facilitate the bypass of distal enhancers in transgenic flies, providing a mechanism for endogenous enhancers to circumvent genomic interruptions resulting from chromosomal rearrangement. This study demonstrates how a network of chromatin boundaries, centrally organized by SF1, can remodel the 3D genome to facilitate gene regulation during development. PMID:27621770
Hussin, H.; Zaid, M.; Gaydecki, P.; El-Madaani, F.; Fernandes, B.
2006-03-06
This paper reports on recent modelling results obtained using finite-element analysis for penetrating a magnetic field through a 2 mm steel boundary. The object is to detect 16 mm steel bars placed under mild steel boundaries at different operating frequencies. To penetrate thicker steel boundaries and increase the depth penetration, a different configuration based on remote field eddy currents (RFEC) has been modelled.
Moon, Ji Young; Suh, Dae Chul; Lee, Yong Sang; Kim, Young Woo; Lee, Joon Sang
2014-02-01
Despite recent development of computational fluid dynamics (CFD) research, analysis of computational fluid dynamics of cerebral vessels has several limitations. Although blood is a non-Newtonian fluid, velocity and pressure fields were computed under the assumptions of incompressible, laminar, steady-state flows and Newtonian fluid dynamics. The pulsatile nature of blood flow is not properly applied in inlet and outlet boundaries. Therefore, we present these technical limitations and discuss the possible solution by comparing the theoretical and computational studies.
Moon, Ji Young; Lee, Yong Sang; Kim, Young Woo
2014-01-01
Despite recent development of computational fluid dynamics (CFD) research, analysis of computational fluid dynamics of cerebral vessels has several limitations. Although blood is a non-Newtonian fluid, velocity and pressure fields were computed under the assumptions of incompressible, laminar, steady-state flows and Newtonian fluid dynamics. The pulsatile nature of blood flow is not properly applied in inlet and outlet boundaries. Therefore, we present these technical limitations and discuss the possible solution by comparing the theoretical and computational studies. PMID:24642855
Nonlinear nonuniform torsional vibrations of bars by the boundary element method
NASA Astrophysics Data System (ADS)
Sapountzakis, E. J.; Tsipiras, V. J.
2010-05-01
In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross-section taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement-small strain theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post-buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an "average" axial displacement of the cross-section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the analog equation method, a BEM based method, leading to a system of nonlinear differential-algebraic equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental mode shape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the direct iteration technique (DIT), with a geometrically linear fundamental mode shape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand.
NASA Astrophysics Data System (ADS)
Faugeras, Blaise; Heumann, Holger
2017-08-01
Incorporating boundary conditions at infinity into simulations on bounded computational domains is a repeatedly occurring problem in scientific computing. The combination of finite element methods (FEM) and boundary element methods (BEM) is the obvious instrument, and we adapt here for the first time the two standard FEM-BEM coupling approaches to the free-boundary equilibrium problem: the Johnson-Nédélec coupling and the Bielak-MacCamy coupling. We recall also the classical approach for fusion applications, dubbed according to its first appearance von-Hagenow-Lackner coupling and present the less used alternative introduced by Albanese, Blum and de Barbieri in [2]. We show that the von-Hagenow-Lackner coupling suffers from undesirable non-optimal convergence properties, that suggest that other coupling schemes, in particular Johnson-Nédélec or Albanese-Blum-de Barbieri are more appropriate for non-linear equilibrium problems. Moreover, we show that any of such coupling methods requires Newton-like iteration schemes for solving the corresponding non-linear discrete algebraic systems.
NASA Technical Reports Server (NTRS)
Mclean, J. D.; Randall, J. L.
1979-01-01
A system of computer programs for calculating three dimensional transonic flow over wings, including details of the three dimensional viscous boundary layer flow, was developed. The flow is calculated in two overlapping regions: an outer potential flow region, and a boundary layer region in which the first order, three dimensional boundary layer equations are numerically solved. A consistent matching of the two solutions is achieved iteratively, thus taking into account viscous-inviscid interaction. For the inviscid outer flow calculations, the Jameson-Caughey transonic wing program FLO 27 is used, and the boundary layer calculations are performed by a finite difference boundary layer prediction program. Interface programs provide communication between the two basic flow analysis programs. Computed results are presented for the NASA F8 research wing, both with and without distributed surface suction.
Salt-water-freshwater transient upconing - An implicit boundary-element solution
Kemblowski, M.
1985-01-01
The boundary-element method is used to solve the set of partial differential equations describing the flow of salt water and fresh water separated by a sharp interface in the vertical plane. In order to improve the accuracy and stability of the numerical solution, a new implicit scheme was developed for calculating the motion of the interface. The performance of this scheme was tested by means of numerical simulation. The numerical results are compared to experimental results for a salt-water upconing under a drain problem. ?? 1985.
1981-03-01
with cubic elements on a uniform spacial mesh of width h and a uniform time step of duration At. We created this simple constant coefficient example...the boundary conditions are (4.6) b(0,t) = b(5,t) = 0, s (0,t) = 1. We solved this problem for 60/11 = 2 using cubic approximations, uniform time...7-7 MAR A1 S F DAVIS, J E FLAHERTY AFOSR-80-0192 UNCLASIFIEDm m om o mo El uuumuinouuun mhEmhshmhohEEI 11111!L132 12---5 HIl U .8 1111IL15N-- AFOSR
Study of light propagation in Asian and Caucasian skins by means of the Boundary Element Method
NASA Astrophysics Data System (ADS)
Ansari, M. A.; Massudi, R.
2009-09-01
Boundary Element Method (BEM) is explored to study transport of light in Asian and Caucasian skins. Precision of the method is compared with the Monte Carlo (MC) method and the Finite Difference Method (FDM) and it is observed that BEM offers more precise results and requires shorter running times. Reflection and penetration of different wavelengths from those skins are calculated. Maximum penetration depths are calculated using BEM and the results are compared with those obtained using MC and FDM. The method can simply be used to study transport of light in different types of tissues.
NASA Technical Reports Server (NTRS)
Williams, J. G.; Hierath, J. E.
1987-01-01
Tabulations are presented for the proper elements of 1227 higher accuracy orbits of faint minor planets encompassing earth and deep Mars crossers, Trojans, and Hildas. The distribution of the closest approach distance to Mars drops off sharply near zero, while that for Jupiter vanishes near 1.1 AU; it is suggested that Mars and Jupiter have caused these boundaries, so that the asteroid belt must have been larger early in the solar system's history. Some 3.5 percent of the sample, primarily shallow crossers, can impact Mars; the fortuitous alignments required for impact occur with near-simultaneity for these objects, so that they will episodically bombard Mars.
NASA Technical Reports Server (NTRS)
Williams, J. G.; Hierath, J. E.
1987-01-01
Tabulations are presented for the proper elements of 1227 higher accuracy orbits of faint minor planets encompassing earth and deep Mars crossers, Trojans, and Hildas. The distribution of the closest approach distance to Mars drops off sharply near zero, while that for Jupiter vanishes near 1.1 AU; it is suggested that Mars and Jupiter have caused these boundaries, so that the asteroid belt must have been larger early in the solar system's history. Some 3.5 percent of the sample, primarily shallow crossers, can impact Mars; the fortuitous alignments required for impact occur with near-simultaneity for these objects, so that they will episodically bombard Mars.
NASA Astrophysics Data System (ADS)
Heumann, Holger; Rapetti, Francesca
2017-04-01
Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.
The spectral-element method, Beowulf computing, and global seismology.
Komatitsch, Dimitri; Ritsema, Jeroen; Tromp, Jeroen
2002-11-29
The propagation of seismic waves through Earth can now be modeled accurately with the recently developed spectral-element method. This method takes into account heterogeneity in Earth models, such as three-dimensional variations of seismic wave velocity, density, and crustal thickness. The method is implemented on relatively inexpensive clusters of personal computers, so-called Beowulf machines. This combination of hardware and software enables us to simulate broadband seismograms without intrinsic restrictions on the level of heterogeneity or the frequency content.
Photodeposited diffractive optical elements of computer generated masks
NASA Astrophysics Data System (ADS)
Mirchin, N.; Peled, A.; Baal-Zedaka, I.; Margolin, R.; Zagon, M.; Lapsker, I.; Verdyan, A.; Azoulay, J.
2005-07-01
Diffractive optical elements (DOE) were synthesized on plastic substrates using the photodeposition (PD) technique by depositing amorphous selenium (a-Se) films with argon lasers and UV spectra light. The thin films were deposited typically onto polymethylmethacrylate (PMMA) substrates at room temperature. Scanned beam and contact mask modes were employed using computer-designed DOE lenses. Optical and electron micrographs characterize the surface details. The films were typically 200 nm thick.
A stochastic method for computing hadronic matrix elements
Alexandrou, Constantia; Constantinou, Martha; Dinter, Simon; ...
2014-01-24
In this study, we present a stochastic method for the calculation of baryon 3-point functions which is an alternative to the typically used sequential method offering more versatility. We analyze the scaling of the error of the stochastically evaluated 3-point function with the lattice volume and find a favorable signal to noise ratio suggesting that the stochastic method can be extended to large volumes providing an efficient approach to compute hadronic matrix elements and form factors.
Single Photon Holographic Qudit Elements for Linear Optical Quantum Computing
2011-05-01
in optical volume holography and designed and simulated practical single-photon, single-optical elements for qudit MUB-state quantum in- formation...Independent of the representation we use, the MUB states will ordinarily be modulated in both amplitude and phase. Recently a practical method has been...quantum computing with qudits (d ≥ 3) has been an efficient and practical quantum state sorter for photons whose complex fields are modulated in both
Transient Finite Element Computations on a Variable Transputer System
NASA Technical Reports Server (NTRS)
Smolinski, Patrick J.; Lapczyk, Ireneusz
1993-01-01
A parallel program to analyze transient finite element problems was written and implemented on a system of transputer processors. The program uses the explicit time integration algorithm which eliminates the need for equation solving, making it more suitable for parallel computations. An interprocessor communication scheme was developed for arbitrary two dimensional grid processor configurations. Several 3-D problems were analyzed on a system with a small number of processors.
Implicit extrapolation methods for multilevel finite element computations
Jung, M.; Ruede, U.
1994-12-31
The finite element package FEMGP has been developed to solve elliptic and parabolic problems arising in the computation of magnetic and thermomechanical fields. FEMGP implements various methods for the construction of hierarchical finite element meshes, a variety of efficient multilevel solvers, including multigrid and preconditioned conjugate gradient iterations, as well as pre- and post-processing software. Within FEMGP, multigrid {tau}-extrapolation can be employed to improve the finite element solution iteratively to higher order. This algorithm is based on an implicit extrapolation, so that the algorithm differs from a regular multigrid algorithm only by a slightly modified computation of the residuals on the finest mesh. Another advantage of this technique is, that in contrast to explicit extrapolation methods, it does not rely on the existence of global error expansions, and therefore neither requires uniform meshes nor global regularity assumptions. In the paper the authors will analyse the {tau}-extrapolation algorithm and present experimental results in the context of the FEMGP package. Furthermore, the {tau}-extrapolation results will be compared to higher order finite element solutions.
Computation of inviscid compressible flows about arbitrary geometries and moving boundaries
NASA Astrophysics Data System (ADS)
Bayyuk, Sami Alan
2008-10-01
The computational simulation of aerodynamic flows with moving boundaries has numerous scientific and practical motivations. In this work, a new technique for computation of inviscid, compressible flows about two-dimensional, arbitrarily-complex geometries that are allowed to undergo arbitrarily-complex motions or deformations is developed and studied. The computational technique is constructed from five main components: (i) an adaptive, Quadtree-based, Cartesian-Grid generation algorithm that divides the computational region into stationary square cells, with local refinement and coarsening to resolve the geometry of all internal boundaries, even as such boundaries move. The algorithm automatically clips cells that straddle boundaries to form arbitrary polygonal cells; (ii) a representation of internal boundaries as exact, infinitesimally-thin discontinuities separating two arbitrarily-different states. The exactness of this representation, and its preclusion of diffusive or dispersive effects while boundaries travel across the grid combines the advantages of Eulerian and Lagrangian methods and is the main distinguishing characteristic of the technique; (iii) a second-order-accurate Finite-Volume, Arbitrary Lagrangian-Eulerian, characteristic-based flow-solver. The discretization of the boundaries and their motion is matched with the discretization of the flux quadratures to ensure that the overall second-order-accurate discretization also satisfies The Geometric Conservation Laws; (iv) an algorithm for dynamic merging of the cells in the vicinity of internal boundaries to form composite cells that retain the same topologic configuration during individual boundary motion steps and can therefore be treated as deforming cells, eliminating the need to treat crossing of grid lines by moving boundaries. Cell merging is also used to circumvent the "small-cell problem" of non-boundary-conformal Cartesian Grids; and (v) a solution-adaptation algorithm for resolving flow
Computer simulation study of the structure of vacancies in grain boundaries
Brokman, A.; Bristowe, P.D.; Balluffi, R.W.
1981-01-01
The structure of vacancies in grain boundaries has been investigated by computer molecular statics employing pairwise potentials. In order to gain an impression of the vacancy structures which may occur generally, a number of variables was investigated including: metal type, boundary type, degree of lattice coincidence and choice of boundary site. In all cases the vacancies remained as distinguishable point defects in the relatively irregular boundary structures. However, it was found that the vacancy often induced relatively large atomic displacements in the core of the boundary. These displacements often occurred only in the direct vicinity of the vacancy, but in certain cases they were widely distributed in the boundary, sometimes at surprisingly large distances.
Computer simulation study of the structure of vacancies in grain boundaries
Brokman, A.; Bristowe, P.D.; Balluffi, R.W.
1981-10-01
The structure of vacancies in grain boundaries has been investigated by computer molecular statics employing pairwise potentials. In order to gain an impression of the vacancy structures which may occur generally, a number of variables was investigated, including metal type, boundary type, degree of lattice coincidence, and choice of boundary site. In all cases the vacancies remained as distinguishable point defects in the relatively irregular boundary structures. However, it was found that the vacancy often induced relatively large atomic displacements in the core of the boundary. These displacements often occurred only in the direct vicinity of the vacancy, but in certain cases they were widely distributed in the boundary, sometimes at surprisingly large distances. In certain cases the displacements included a large inward relaxation of one, or more, of the atoms neighboring the vacancy, and the initial vacant site became effectively ''split''.
An Improved Treatment of External Boundary for Three-Dimensional Flow Computations
NASA Technical Reports Server (NTRS)
Tsynkov, Semyon V.; Vatsa, Veer N.
1997-01-01
We present an innovative numerical approach for setting highly accurate nonlocal boundary conditions at the external computational boundaries when calculating three-dimensional compressible viscous flows over finite bodies. The approach is based on application of the difference potentials method by V. S. Ryaben'kii and extends our previous technique developed for the two-dimensional case. The new boundary conditions methodology has been successfully combined with the NASA-developed code TLNS3D and used for the analysis of wing-shaped configurations in subsonic and transonic flow regimes. As demonstrated by the computational experiments, the improved external boundary conditions allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution. Moreover, they may provide for a noticeable speedup of convergence of the multigrid iterations.
Nonreflecting Far-Field Boundary Conditions for Unsteady Transonic Flow Computation
NASA Technical Reports Server (NTRS)
Kwak, D.
1981-01-01
The approximate nonreflecting far-field boundary condition, as proposed by Engquisi and Majda, is implemented In the computer code LTRAN2. This code solves the Implicit finite-difference representation of the small-disturbance equations for unsteady transonic flows about airfoils. The nonreflecting boundary condition and the description of the algorithm for Implementing these conditions In LTRAN2 tire discussed. Various cases re computed and compared with results from the older, more conventional procedures. One concludes that the nonreflecting far-field boundary approximation allows the far-field boundary to be located closer to the airfoil; this permits a decrease in the computer lime required to obtain the solution through the use of fewer mesh points.
NASA Astrophysics Data System (ADS)
Dancette, S.; Browet, A.; Martin, G.; Willemet, M.; Delannay, L.
2016-06-01
A new procedure for microstructure-based finite element modeling of polycrystalline aggregates is presented. The proposed method relies (i) on an efficient graph-based community detection algorithm for crystallographic data segmentation and feature contour extraction and (ii) on the generation of selectively refined meshes conforming to grain boundaries. It constitutes a versatile and close to automatic environment for meshing complex microstructures. The procedure is illustrated with polycrystal microstructures characterized by orientation imaging microscopy. Hot deformation of a Duplex stainless steel is investigated based on ex-situ EBSD measurements performed on the same region of interest before and after deformation. A finite element mesh representing the initial microstructure is generated and then used in a crystal plasticity simulation of the plane strain compression. Simulation results and experiments are in relatively good agreement, confirming a large potential for such directly coupled experimental and modeling analyses, which is facilitated by the present image-based meshing procedure.
Ahmed, S.
1992-01-01
The physical processes involving leachate flow in a solid waste landfill are described by the unsaturated flow through the refuse to the saturated leachate mound at the bottom of a landfill. The moisture-flow in the unsaturated zone helps build up the saturated leachate mound at the bottom of a landfill. The moisture content in the unsaturated zone is obtained by solving the two-dimensional unsaturated moisture-flow equation using numerical techniques. A two-dimensional unsteady sate Flow Investigation for Landfill Leachate (FILL) model, based on the implicit finite-difference technique, has been developed to describe the leachate flow process in a landfill. To obtain accuracy and efficiency in numerical molding, it is important to investigate the numerical solution techniques suitable to solve the governing equations. Accuracy and efficiency of the boundary integral method over the finite-difference methods has been investigated. Two approaches, direct Green's function and perturbation Green's function formulations have been developed to solve the unsaturated flow problem. Direct Green's function and perturbation Green's function boundary integral solutions are found to be more accurate than both the Gauss-Seidel iteration and Gauss-Jordon elimination method of finite-difference solution. The efficiency of the boundary integral formulation for the computation of the moisture-flux is an advantage that is useful to estimate leachate of the moisture-flux is an advantage that is useful to estimate leachate accretion in a landfill. A close agreement of the internal fluxes with the exact solution shows the ability of the boundary integral methods to compute accurate recharge from the unsaturated zone to the saturated leachate mound.
Computer Simulations of Valveless Pumping using the Immersed Boundary Method
NASA Astrophysics Data System (ADS)
Jung, Eunok; Peskin, Charles
2000-03-01
Pumping blood in one direction is the main function of the heart, and the heart is equipped with valves that ensure unidirectional flow. Is it possible, though, to pump blood without valves? This report is intended to show by numerical simulation the possibility of a net flow which is generated by a valveless mechanism in a circulatory system. Simulations of valveless pumping are motivated by biomedical applications: cardiopulmonary resuscitation (CPR); and the human foetus before the development of the heart valves. The numerical method used in this work is immersed boundary method, which is applicable to problems involving an elastic structure interacting with a viscous incompressible fluid. This method has already been applied to blood flow in the heart, platelet aggregation during blood clotting, aquatic animal locomotion, and flow in collapsible tubes. The direction of flow inside a loop of tubing which consists of (almost) rigid and flexible parts is investigated when the boundary of one end of the flexible segment is forced periodically in time. Despite the absence of valves, net flow around the loop may appear in these simulations. Furthermore, we present the new, unexpected results that the direction of this flow is determined not only by the position of the periodic compression, but also by the frequency and amplitude of the driving force.
Acceleration of matrix element computations for precision measurements
Brandt, Oleg; Gutierrez, Gaston; Wang, M. H.L.S.; ...
2014-11-25
The matrix element technique provides a superior statistical sensitivity for precision measurements of important parameters at hadron colliders, such as the mass of the top quark or the cross-section for the production of Higgs bosons. The main practical limitation of the technique is its high computational demand. Using the example of the top quark mass, we present two approaches to reduce the computation time of the technique by a factor of 90. First, we utilize low-discrepancy sequences for numerical Monte Carlo integration in conjunction with a dedicated estimator of numerical uncertainty, a novelty in the context of the matrix elementmore » technique. We then utilize a new approach that factorizes the overall jet energy scale from the matrix element computation, a novelty in the context of top quark mass measurements. The utilization of low-discrepancy sequences is of particular general interest, as it is universally applicable to Monte Carlo integration, and independent of the computing environment.« less
Compute Element and Interface Box for the Hazard Detection System
NASA Technical Reports Server (NTRS)
Villalpando, Carlos Y.; Khanoyan, Garen; Stern, Ryan A.; Some, Raphael R.; Bailey, Erik S.; Carson, John M.; Vaughan, Geoffrey M.; Werner, Robert A.; Salomon, Phil M.; Martin, Keith E.; Spaulding, Matthew D.; Luna, Michael E.; Motaghedi, Shui H.; Trawny, Nikolas; Johnson, Andrew E.; Ivanov, Tonislav I.; Huertas, Andres; Whitaker, William D.; Goldberg, Steven B.
2013-01-01
The Autonomous Landing and Hazard Avoidance Technology (ALHAT) program is building a sensor that enables a spacecraft to evaluate autonomously a potential landing area to generate a list of hazardous and safe landing sites. It will also provide navigation inputs relative to those safe sites. The Hazard Detection System Compute Element (HDS-CE) box combines a field-programmable gate array (FPGA) board for sensor integration and timing, with a multicore computer board for processing. The FPGA does system-level timing and data aggregation, and acts as a go-between, removing the real-time requirements from the processor and labeling events with a high resolution time. The processor manages the behavior of the system, controls the instruments connected to the HDS-CE, and services the "heavy lifting" computational requirements for analyzing the potential landing spots.
NASA Astrophysics Data System (ADS)
Dandaroy, Indranil; Vondracek, Joseph; Hund, Ron; Hartley, Dayton
2005-09-01
The objective of this study was to develop a vibro-acoustic computational model of the Raytheon King Air 350 turboprop aircraft with an intent to reduce propfan noise in the cabin. To develop the baseline analysis, an acoustic cavity model of the aircraft interior and a structural dynamics model of the aircraft fuselage were created. The acoustic model was an indirect boundary element method representation using SYSNOISE, while the structural model was a finite-element method normal modes representation in NASTRAN and subsequently imported to SYSNOISE. In the acoustic model, the fan excitation sources were represented employing the Ffowcs Williams-Hawkings equation. The acoustic and the structural models were fully coupled in SYSNOISE and solved to yield the baseline response of acoustic pressure in the aircraft interior and vibration on the aircraft structure due to fan noise. Various vibration absorbers, tuned to fundamental blade passage tone (100 Hz) and its first harmonic (200 Hz), were applied to the structural model to study their effect on cabin noise reduction. Parametric studies were performed to optimize the number and location of these passive devices. Effects of synchrophasing and absorptive noise treatments applied to the aircraft interior were also investigated for noise reduction.
Katz, B F
2001-11-01
Following previous work by the author involving the calculation of an individual head-related transfer function (HRTF) using a Boundary Element Method (BEM) approach, impedance conditions are now included to take account of the acoustic properties of human hair. In addition, comparisons are made here between calculations and measured values for the HRTF of a specific individual. Numerous works have been published regarding the measurement of HRTFs, but rarely are several methods compared for the same individual. The results presented in the work compare two different measurement techniques and a computational BEM for acquiring an individual HRTF. Impedance effects have been incorporated in the BEM model for hair based on measured data, providing a final set for comparison. Measurement results show significant variations for the same individual. Computational results show good agreement within the range of experimental variations. Definite trends are observed for many directions, while the limitations of the methods are also highlighted for others. The effects of incorporating hair impedance are shown to provide an improvement in the correlation of computational results, indicating an affect of hair impedance on the HRTF.
Tailoring wind properties by various passive roughness elements in a boundary-layer wind tunnel
NASA Astrophysics Data System (ADS)
Varshney, Kapil
2012-08-01
Boundary-layer wind tunnel provides a unique platform to reproduce urban, suburban and rural atmospheric boundary layer (ABL) by using roughness devices such as vortex generators, floor roughness, barrier walls, and slots in the extended test-section floor in the contraction cone. Each passive device impacts wind properties in a certain way. In this study, influence of various passive devices on wind properties has been investigated. Experiments using eighteen different configurations of the passive devices have been carried out to simulate urban, sub-urban, and rural climate conditions in a boundary-layer wind tunnel. The effect of each configuration on the wind characteristics is presented. It was found that higher barrier height and more number of roughness elements on the floor, generated higher turbulence and therefore higher model scale factors were obtained. However, increased slot width in the extended test-section floor in the contraction cone of the wind tunnel seemed to have a little effect on wind characteristics.
NASA Astrophysics Data System (ADS)
Johnson, Kyle; Thurow, Brian; Kim, Taehoon; Blois, Gianluca; Christensen, Kenneth
2016-11-01
Three-dimensional, three-component (3D-3C) measurements were made using a plenoptic camera on the flow around a roughness element immersed in a turbulent boundary layer. A refractive index matched approach allowed whole-field optical access from a single camera to a measurement volume that includes transparent solid geometries. In particular, this experiment measures the flow over a single hemispherical roughness element made of acrylic and immersed in a working fluid consisting of Sodium Iodide solution. Our results demonstrate that plenoptic particle image velocimetry (PIV) is a viable technique to obtaining statistically-significant volumetric velocity measurements even in a complex separated flow. The boundary layer to roughness height-ratio of the flow was 4.97 and the Reynolds number (based on roughness height) was 4.57×103. Our measurements reveal key flow features such as spiraling legs of the shear layer, a recirculation region, and shed arch vortices. Proper orthogonal decomposition (POD) analysis was applied to the instantaneous velocity and vorticity data to extract these features. Supported by the National Science Foundation Grant No. 1235726.
NASA Astrophysics Data System (ADS)
Simmons, Daniel; Cools, Kristof; Sewell, Phillip
2016-11-01
Time domain electromagnetic simulation tools have the ability to model transient, wide-band applications, and non-linear problems. The Boundary Element Method (BEM) and the Transmission Line Modeling (TLM) method are both well established numerical techniques for simulating time-varying electromagnetic fields. The former surface based method can accurately describe outwardly radiating fields from piecewise uniform objects and efficiently deals with large domains filled with homogeneous media. The latter volume based method can describe inhomogeneous and non-linear media and has been proven to be unconditionally stable. Furthermore, the Unstructured TLM (UTLM) enables modelling of geometrically complex objects by using triangular meshes which removes staircasing and unnecessary extensions of the simulation domain. The hybridization of BEM and UTLM which is described in this paper is named the Boundary Element Unstructured Transmission-line (BEUT) method. It incorporates the advantages of both methods. The theory and derivation of the 2D BEUT method is described in this paper, along with any relevant implementation details. The method is corroborated by studying its correctness and efficiency compared to the traditional UTLM method when applied to complex problems such as the transmission through a system of Luneburg lenses and the modelling of antenna radomes for use in wireless communications.
A boundary element approach to estimate the free surface in stratified two-phase flow
NASA Astrophysics Data System (ADS)
Ren, Shangjie; Dong, Feng; Tan, Chao; Xu, Yaoyuan
2012-10-01
Two-phase flows widely exist in many industries. Measuring the phase distribution in two-phase flow is important for the optimization and control of some industrial processes. Electrical resistance tomography (ERT) is a promising non-intrusive visualization technique for monitoring the two-phase flow. However, due to its nonlinear and ill-posed character, high-quality image reconstruction is difficult and some iterative approach is time consuming. In this paper, a boundary element approach is presented for directly estimating the free-surface in two-phase flow using ERT. The unknown free surface is parameterized by a Bézier curve. Coefficients of its control points are estimated by minimizing a residual function using the iterative Levenberg-Marquardt method. To speed up the estimation process, the physical model of ERT is formulated using a boundary element method. Based on this formulation, the forward problem is fast solved through a small size system matrix and the Jacobian matrix is efficiently calculated using an analytic method. After several numerical experiments, this approach is proved fast and precise and several factors influencing the estimation quality are analyzed based on these simulations.
Simmons, Daniel Cools, Kristof; Sewell, Phillip
2016-11-01
Time domain electromagnetic simulation tools have the ability to model transient, wide-band applications, and non-linear problems. The Boundary Element Method (BEM) and the Transmission Line Modeling (TLM) method are both well established numerical techniques for simulating time-varying electromagnetic fields. The former surface based method can accurately describe outwardly radiating fields from piecewise uniform objects and efficiently deals with large domains filled with homogeneous media. The latter volume based method can describe inhomogeneous and non-linear media and has been proven to be unconditionally stable. Furthermore, the Unstructured TLM (UTLM) enables modelling of geometrically complex objects by using triangular meshes which removes staircasing and unnecessary extensions of the simulation domain. The hybridization of BEM and UTLM which is described in this paper is named the Boundary Element Unstructured Transmission-line (BEUT) method. It incorporates the advantages of both methods. The theory and derivation of the 2D BEUT method is described in this paper, along with any relevant implementation details. The method is corroborated by studying its correctness and efficiency compared to the traditional UTLM method when applied to complex problems such as the transmission through a system of Luneburg lenses and the modelling of antenna radomes for use in wireless communications. - Graphical abstract:.
Multi-Region Boundary Element Analysis for Coupled Thermal-Fracturing Processes in Geomaterials
NASA Astrophysics Data System (ADS)
Shen, Baotang; Kim, Hyung-Mok; Park, Eui-Seob; Kim, Taek-Kon; Wuttke, Manfred W.; Rinne, Mikael; Backers, Tobias; Stephansson, Ove
2013-01-01
This paper describes a boundary element code development on coupled thermal-mechanical processes of rock fracture propagation. The code development was based on the fracture mechanics code FRACOD that has previously been developed by Shen and Stephansson (Int J Eng Fracture Mech 47:177-189, 1993) and FRACOM (A fracture propagation code—FRACOD, User's manual. FRACOM Ltd. 2002) and simulates complex fracture propagation in rocks governed by both tensile and shear mechanisms. For the coupled thermal-fracturing analysis, an indirect boundary element method, namely the fictitious heat source method, was implemented in FRACOD to simulate the temperature change and thermal stresses in rocks. This indirect method is particularly suitable for the thermal-fracturing coupling in FRACOD where the displacement discontinuity method is used for mechanical simulation. The coupled code was also extended to simulate multiple region problems in which rock mass, concrete linings and insulation layers with different thermal and mechanical properties were present. Both verification and application cases were presented where a point heat source in a 2D infinite medium and a pilot LNG underground cavern were solved and studied using the coupled code. Good agreement was observed between the simulation results, analytical solutions and in situ measurements which validates an applicability of the developed coupled code.
NASA Astrophysics Data System (ADS)
Hazer, D.; Schmidt, E.; Unterhinninghofen, R.; Richter, G. M.; Dillmann, R.
2009-08-01
Abnormal hemodynamics and biomechanics of blood flow and vessel wall conditions in the arteries may result in severe cardiovascular diseases. Cardiovascular diseases result from complex flow pattern and fatigue of the vessel wall and are prevalent causes leading to high mortality each year. Computational Fluid Dynamics (CFD), Computational Structure Mechanics (CSM) and Fluid Structure Interaction (FSI) have become efficient tools in modeling the individual hemodynamics and biomechanics as well as their interaction in the human arteries. The computations allow non-invasively simulating patient-specific physical parameters of the blood flow and the vessel wall needed for an efficient minimally invasive treatment. The numerical simulations are based on the Finite Element Method (FEM) and require exact and individual mesh models to be provided. In the present study, we developed a numerical tool to automatically generate complex patient-specific Finite Element (FE) mesh models from image-based geometries of healthy and diseased vessels. The mesh generation is optimized based on the integration of mesh control functions for curvature, boundary layers and mesh distribution inside the computational domain. The needed mesh parameters are acquired from a computational grid analysis which ensures mesh-independent and stable simulations. Further, the generated models include appropriate FE sets necessary for the definition of individual boundary conditions, required to solve the system of nonlinear partial differential equations governed by the fluid and solid domains. Based on the results, we have performed computational blood flow and vessel wall simulations in patient-specific aortic models providing a physical insight into the pathological vessel parameters. Automatic mesh generation with individual awareness in terms of geometry and conditions is a prerequisite for performing fast, accurate and realistic FEM-based computations of hemodynamics and biomechanics in the
Ren, Shangjie; Dong, Feng
2016-06-28
Electrical capacitance tomography (ECT) is a non-destructive detection technique for imaging the permittivity distributions inside an observed domain from the capacitances measurements on its boundary. Owing to its advantages of non-contact, non-radiation, high speed and low cost, ECT is promising in the measurements of many industrial or biological processes. However, in the practical industrial or biological systems, a deposit is normally seen in the inner wall of its pipe or vessel. As the actual region of interest (ROI) of ECT is surrounded by the deposit layer, the capacitance measurements become weakly sensitive to the permittivity perturbation occurring at the ROI. When there is a major permittivity difference between the deposit and the ROI, this kind of shielding effect is significant, and the permittivity reconstruction becomes challenging. To deal with the issue, an interface and permittivity simultaneous reconstruction approach is proposed. Both the permittivity at the ROI and the geometry of the deposit layer are recovered using the block coordinate descent method. The boundary and finite-elements coupling method is employed to improve the computational efficiency. The performance of the proposed method is evaluated with the simulation tests. This article is part of the themed issue 'Supersensing through industrial process tomography'.
Ren, Shangjie; Dong, Feng
2016-01-01
Electrical capacitance tomography (ECT) is a non-destructive detection technique for imaging the permittivity distributions inside an observed domain from the capacitances measurements on its boundary. Owing to its advantages of non-contact, non-radiation, high speed and low cost, ECT is promising in the measurements of many industrial or biological processes. However, in the practical industrial or biological systems, a deposit is normally seen in the inner wall of its pipe or vessel. As the actual region of interest (ROI) of ECT is surrounded by the deposit layer, the capacitance measurements become weakly sensitive to the permittivity perturbation occurring at the ROI. When there is a major permittivity difference between the deposit and the ROI, this kind of shielding effect is significant, and the permittivity reconstruction becomes challenging. To deal with the issue, an interface and permittivity simultaneous reconstruction approach is proposed. Both the permittivity at the ROI and the geometry of the deposit layer are recovered using the block coordinate descent method. The boundary and finite-elements coupling method is employed to improve the computational efficiency. The performance of the proposed method is evaluated with the simulation tests. This article is part of the themed issue ‘Supersensing through industrial process tomography’. PMID:27185960
On buffer layers as non-reflecting computational boundaries
NASA Technical Reports Server (NTRS)
Hayder, M. Ehtesham; Turkel, Eli L.
1996-01-01
We examine an absorbing buffer layer technique for use as a non-reflecting boundary condition in the numerical simulation of flows. One such formulation was by Ta'asan and Nark for the linearized Euler equations. They modified the flow inside the buffer zone to artificially make it supersonic in the layer. We examine how this approach can be extended to the nonlinear Euler equations. We consider both a conservative and a non-conservative form modifying the governing equations in the buffer layer. We compare this with the case that the governing equations in the layer are the same as in the interior domain. We test the effectiveness of these buffer layers by a simulation of an excited axisymmetric jet based on a nonlinear compressible Navier-Stokes equations.
On buffer layers as non-reflecting computational boundaries
NASA Technical Reports Server (NTRS)
Hayder, M. Ehtesham; Turkel, Eli L.
1996-01-01
We examine an absorbing buffer layer technique for use as a non-reflecting boundary condition in the numerical simulation of flows. One such formulation was by Ta'asan and Nark for the linearized Euler equations. They modified the flow inside the buffer zone to artificially make it supersonic in the layer. We examine how this approach can be extended to the nonlinear Euler equations. We consider both a conservative and a non-conservative form modifying the governing equations in the buffer layer. We compare this with the case that the governing equations in the layer are the same as in the interior domain. We test the effectiveness of these buffer layers by a simulation of an excited axisymmetric jet based on a nonlinear compressible Navier-Stokes equations.
Quantifying trace element and isotope fluxes at the ocean–sediment boundary: a review
Berelson, William M.; Severmann, Silke
2016-01-01
Quantifying fluxes of trace elements and their isotopes (TEIs) at the ocean's sediment–water boundary is a pre-eminent challenge to understand their role in the present, past and future ocean. There are multiple processes that drive the uptake and release of TEIs, and properties that determine their rates are unevenly distributed (e.g. sediment composition, redox conditions and (bio)physical dynamics). These factors complicate our efforts to find, measure and extrapolate TEI fluxes across ocean basins. GEOTRACES observations are unveiling the oceanic distributions of many TEIs for the first time. These data evidence the influence of the sediment–water boundary on many TEI cycles, and underline the fact that our knowledge of the source–sink fluxes that sustain oceanic distributions is largely missing. Present flux measurements provide low spatial coverage and only part of the empirical basis needed to predict TEI flux variations. Many of the advances and present challenges facing TEI flux measurements are linked to process studies that collect sediment cores, pore waters, sinking material or seawater in close contact with sediments. However, such sampling has not routinely been viable on GEOTRACES expeditions. In this article, we recommend approaches to address these issues: firstly, with an interrogation of emergent data using isotopic mass-balance and inverse modelling techniques; and secondly, by innovating pursuits of direct TEI flux measurements. We exemplify the value of GEOTRACES data with a new inverse model estimate of benthic Al flux in the North Atlantic Ocean. Furthermore, we review viable flux measurement techniques tailored to the sediment–water boundary. We propose that such activities are aimed at regions that intersect the GEOTRACES Science Plan on the basis of seven criteria that may influence TEI fluxes: sediment provenance, composition, organic carbon supply, redox conditions, sedimentation rate, bathymetry and the benthic nepheloid
Quantifying trace element and isotope fluxes at the ocean-sediment boundary: a review
NASA Astrophysics Data System (ADS)
Homoky, William B.; Weber, Thomas; Berelson, William M.; Conway, Tim M.; Henderson, Gideon M.; van Hulten, Marco; Jeandel, Catherine; Severmann, Silke; Tagliabue, Alessandro
2016-11-01
Quantifying fluxes of trace elements and their isotopes (TEIs) at the ocean's sediment-water boundary is a pre-eminent challenge to understand their role in the present, past and future ocean. There are multiple processes that drive the uptake and release of TEIs, and properties that determine their rates are unevenly distributed (e.g. sediment composition, redox conditions and (bio)physical dynamics). These factors complicate our efforts to find, measure and extrapolate TEI fluxes across ocean basins. GEOTRACES observations are unveiling the oceanic distributions of many TEIs for the first time. These data evidence the influence of the sediment-water boundary on many TEI cycles, and underline the fact that our knowledge of the source-sink fluxes that sustain oceanic distributions is largely missing. Present flux measurements provide low spatial coverage and only part of the empirical basis needed to predict TEI flux variations. Many of the advances and present challenges facing TEI flux measurements are linked to process studies that collect sediment cores, pore waters, sinking material or seawater in close contact with sediments. However, such sampling has not routinely been viable on GEOTRACES expeditions. In this article, we recommend approaches to address these issues: firstly, with an interrogation of emergent data using isotopic mass-balance and inverse modelling techniques; and secondly, by innovating pursuits of direct TEI flux measurements. We exemplify the value of GEOTRACES data with a new inverse model estimate of benthic Al flux in the North Atlantic Ocean. Furthermore, we review viable flux measurement techniques tailored to the sediment-water boundary. We propose that such activities are aimed at regions that intersect the GEOTRACES Science Plan on the basis of seven criteria that may influence TEI fluxes: sediment provenance, composition, organic carbon supply, redox conditions, sedimentation rate, bathymetry and the benthic nepheloid inventory
NASA Astrophysics Data System (ADS)
Foote, Kenneth G.; Francis, David T. I.
2003-04-01
The boundary-element method has been applied to backscattering and extinction of sound by swimbladdered fish at the lowest, breathing-mode resonance. Corresponding cross sections have been computed for specimens of two representative kinds of swimbladder-bearing fish, namely physostomes and physoclists, which, respectively, possess and lack an external duct. The respective fishes are herring (Clupea harengus) and pollack (Pollachius pollachius), for which swimbladder morphometric data are available. The depth dependences of the cross sections are computed over the range 0-500 m. Comparisons are made with measurements and other modeled results for a number of species. [Work supported by ONR.
The effect of boundary constraints on finite element modelling of the human pelvis.
Watson, Peter J; Dostanpor, Ali; Fagan, Michael J; Dobson, Catherine A
2017-05-01
The use of finite element analysis (FEA) to investigate the biomechanics of anatomical systems critically relies on the specification of physiologically representative boundary conditions. The biomechanics of the pelvis has been the specific focus of a number of FEA studies previously, but it is also a key aspect in other investigations of, for example, the hip joint or new design of hip prostheses. In those studies, the pelvis has been modelled in a number of ways with a variety of boundary conditions, ranging from a model of the whole pelvic girdle including soft tissue attachments to a model of an isolated hemi-pelvis. The current study constructed a series of FEA models of the same human pelvis to investigate the sensitivity of the predicted stress distributions to the type of boundary conditions applied, in particular to represent the sacro-iliac joint and pubic symphysis. Varying the method of modelling the sacro-iliac joint did not produce significant variations in the stress distribution, however changes to the modelling of the pubic symphysis were observed to have a greater effect on the results. Over-constraint of the symphysis prevented the bending of the pelvis about the greater sciatic notch, and underestimated high stresses within the ilium. However, permitting medio-lateral translation to mimic widening of the pelvis addressed this problem. These findings underline the importance of applying the appropriate boundary conditions to FEA models, and provide guidance on suitable methods of constraining the pelvis when, for example, scan data has not captured the full pelvic girdle. The results also suggest a valid method for performing hemi-pelvic modelling of cadaveric or archaeological remains which are either damaged or incomplete.
NASA Astrophysics Data System (ADS)
Meng, Weijuan; Fu, Li-Yun
2017-08-01
The finite element method is a very important tool for modeling seismic wave propagation in complex media, but it usually consumes a large amount of memory which significantly decreases computational efficiency when solving large-scale seismic problems. Here, a modified finite element method (MFEM) is proposed to improve efficiency. Triangular elements are employed to mesh the topography and the discontinuous interface more flexibly. In the two-dimensional case, the Jacobian matrix is obtained by using three controlling points instead of all nodes in each element with MFEM, which separates the Jacobian matrix from the stiffness matrix. The kernel matrices of the stiffness matrix rather than the global matrix are stored, and memory requirements are thus reduced significantly. Meanwhile, the element-by-element scheme is adopted to spare large sparse matrices and make the program easily parallelized. A second-order perfectly matched layer (PML) is also implemented to eliminate artificial reflections. Finally, the accuracy and efficiency of our algorithm are validated by numerical tests.
HYDRA, A finite element computational fluid dynamics code: User manual
Christon, M.A.
1995-06-01
HYDRA is a finite element code which has been developed specifically to attack the class of transient, incompressible, viscous, computational fluid dynamics problems which are predominant in the world which surrounds us. The goal for HYDRA has been to achieve high performance across a spectrum of supercomputer architectures without sacrificing any of the aspects of the finite element method which make it so flexible and permit application to a broad class of problems. As supercomputer algorithms evolve, the continuing development of HYDRA will strive to achieve optimal mappings of the most advanced flow solution algorithms onto supercomputer architectures. HYDRA has drawn upon the many years of finite element expertise constituted by DYNA3D and NIKE3D Certain key architectural ideas from both DYNA3D and NIKE3D have been adopted and further improved to fit the advanced dynamic memory management and data structures implemented in HYDRA. The philosophy for HYDRA is to focus on mapping flow algorithms to computer architectures to try and achieve a high level of performance, rather than just performing a port.
Increasing Computational Efficiency of Cochlear Models Using Boundary Layers
Alkhairy, Samiya A.; Shera, Christopher A.
2016-01-01
Our goal is to develop methods to improve the efficiency of computational models of the cochlea for applications that require the solution accurately only within a basal region of interest, specifically by decreasing the number of spatial sections needed for simulation of the problem with good accuracy. We design algebraic spatial and parametric transformations to computational models of the cochlea. These transformations are applied after the basal region of interest and allow for spatial preservation, driven by the natural characteristics of approximate spatial causality of cochlear models. The project is of foundational nature and hence the goal is to design, characterize and develop an understanding and framework rather than optimization and globalization. Our scope is as follows: designing the transformations; understanding the mechanisms by which computational load is decreased for each transformation; development of performance criteria; characterization of the results of applying each transformation to a specific physical model and discretization and solution schemes. In this manuscript, we introduce one of the proposed methods (complex spatial transformation) for a case study physical model that is a linear, passive, transmission line model in which the various abstraction layers (electric parameters, filter parameters, wave parameters) are clearer than other models. This is conducted in the frequency domain for multiple frequencies using a second order finite difference scheme for discretization and direct elimination for solving the discrete system of equations. The performance is evaluated using two developed simulative criteria for each of the transformations. In conclusion, the developed methods serve to increase efficiency of a computational traveling wave cochlear model when spatial preservation can hold, while maintaining good correspondence with the solution of interest and good accuracy, for applications in which the interest is in the solution
Increasing computational efficiency of cochlear models using boundary layers
NASA Astrophysics Data System (ADS)
Alkhairy, Samiya A.; Shera, Christopher A.
2015-12-01
Our goal is to develop methods to improve the efficiency of computational models of the cochlea for applications that require the solution accurately only within a basal region of interest, specifically by decreasing the number of spatial sections needed for simulation of the problem with good accuracy. We design algebraic spatial and parametric transformations to computational models of the cochlea. These transformations are applied after the basal region of interest and allow for spatial preservation, driven by the natural characteristics of approximate spatial causality of cochlear models. The project is of foundational nature and hence the goal is to design, characterize and develop an understanding and framework rather than optimization and globalization. Our scope is as follows: designing the transformations; understanding the mechanisms by which computational load is decreased for each transformation; development of performance criteria; characterization of the results of applying each transformation to a specific physical model and discretization and solution schemes. In this manuscript, we introduce one of the proposed methods (complex spatial transformation) for a case study physical model that is a linear, passive, transmission line model in which the various abstraction layers (electric parameters, filter parameters, wave parameters) are clearer than other models. This is conducted in the frequency domain for multiple frequencies using a second order finite difference scheme for discretization and direct elimination for solving the discrete system of equations. The performance is evaluated using two developed simulative criteria for each of the transformations. In conclusion, the developed methods serve to increase efficiency of a computational traveling wave cochlear model when spatial preservation can hold, while maintaining good correspondence with the solution of interest and good accuracy, for applications in which the interest is in the solution
NASA Technical Reports Server (NTRS)
Choudhari, Meelan; Li, Fei; Bynum, Michael; Kegerise, Michael; King, Rudolph
2015-01-01
Computations are performed to study laminar-turbulent transition due to isolated roughness elements in boundary layers at Mach 3.5 and 5.95, with an emphasis on flow configurations for which experimental measurements from low disturbance wind tunnels are available. The Mach 3.5 case corresponds to a roughness element with right-triangle planform with hypotenuse that is inclined at 45 degrees with respect to the oncoming stream, presenting an obstacle with spanwise asymmetry. The Mach 5.95 case corresponds to a circular roughness element along the nozzle wall of the Purdue BAMQT wind tunnel facility. In both cases, the mean flow distortion due to the roughness element is characterized by long-lived streamwise streaks in the roughness wake, which can support instability modes that did not exist in the absence of the roughness element. The linear amplification characteristics of the wake flow are examined towards the eventual goal of developing linear growth correlations for the onset of transition.
Computation of turbulent boundary layers on curved surfaces, 1 June 1975 - 31 January 1976
NASA Technical Reports Server (NTRS)
Wilcox, D. C.; Chambers, T. L.
1976-01-01
An accurate method was developed for predicting effects of streamline curvature and coordinate system rotation on turbulent boundary layers. A new two-equation model of turbulence was developed which serves as the basis of the study. In developing the new model, physical reasoning is combined with singular perturbation methods to develop a rational, physically-based set of equations which are, on the one hand, as accurate as mixing-length theory for equilibrium boundary layers and, on the other hand, suitable for computing effects of curvature and rotation. The equations are solved numerically for several boundary layer flows over plane and curved surfaces. For incompressible boundary layers, results of the computations are generally within 10% of corresponding experimental data. Somewhat larger discrepancies are noted for compressible applications.
Computational modeling of unsteady loads in tidal boundary layers
NASA Astrophysics Data System (ADS)
Alexander, Spencer R.
As ocean current turbines move from the design stage into production and installation, a better understanding of oceanic turbulent flows and localized loading is required to more accurately predict turbine performance and durability. In the present study, large eddy simulations (LES) are used to measure the unsteady loads and bending moments that would be experienced by an ocean current turbine placed in a tidal channel. The LES model captures currents due to winds, waves, thermal convection, and tides, thereby providing a high degree of physical realism. Probability density functions, means, and variances of unsteady loads are calculated, and further statistical measures of the turbulent environment are also examined, including vertical profiles of Reynolds stresses, two-point correlations, and velocity structure functions. The simulations show that waves and tidal velocity had the largest impact on the strength of off-axis turbine loads. By contrast, boundary layer stability and wind speeds were shown to have minimal impact on the strength of off- axis turbine loads. It is shown both analytically and using simulation results that either transverse velocity structure functions or two-point transverse velocity spatial correlations are good predictors of unsteady loading in tidal channels.
Kreuzer, Wolfgang; Majdak, Piotr; Chen, Zhengsheng
2010-01-01
Head-related transfer functions (HRTFs) play an important role in spatial sound localization. The boundary element method (BEM) can be applied to calculate HRTFs from non-contact visual scans. Because of high computational complexity, HRTF simulations with BEM for the whole head and pinnae have only been performed for frequencies below 10 kHz. In this study, the fast multipole method (FMM) is coupled with BEM to simulate HRTFs for a wide frequency range. The basic approach of the FMM and its implementation are described. A mesh with over 70 000 elements was used to calculate HRTFs for one subject. With this mesh, the method allowed to calculate HRTFs for frequencies up to 35 kHz. Comparison to acoustically-measured HRTFs has been performed for frequencies up to 16 kHz, showing a good congruence below 7 kHz. Simulations with an additional shoulder mesh improved the congruence in the vertical direction. Reduction in the mesh size by 5% resulted in a substantially-worse representation of spectral cues. The effects of temperature and mesh perturbation were negligible. The FMM appears to be a promising approach for HRTF simulations. Further limitations and potential advantages of the FMM-coupled BEM are discussed. PMID:19739742
Computer-aided boundary delineation of agricultural lands
NASA Technical Reports Server (NTRS)
Cheng, Thomas D.; Angelici, Gary L.; Slye, Robert E.; Ma, Matt
1989-01-01
The National Agricultural Statistics Service of the United States Department of Agriculture (USDA) presently uses labor-intensive aerial photographic interpretation techniques to divide large geographical areas into manageable-sized units for estimating domestic crop and livestock production. Prototype software, the computer-aided stratification (CAS) system, was developed to automate the procedure, and currently runs on a Sun-based image processing system. With a background display of LANDSAT Thematic Mapper and United States Geological Survey Digital Line Graph data, the operator uses a cursor to delineate agricultural areas, called sampling units, which are assigned to strata of land-use and land-cover types. The resultant stratified sampling units are used as input into subsequent USDA sampling procedures. As a test, three counties in Missouri were chosen for application of the CAS procedures. Subsequent analysis indicates that CAS was five times faster in creating sampling units than the manual techniques were.
NASA Astrophysics Data System (ADS)
Kawai, Toshiyuki; Rinoie, Kenichi
Aircraft conceptual design method currently used for the university design education mainly utilises empirical values based on the statistical database to determine the main design parameters. Therefore, it is often difficult for students to understand the effects of aerodynamic parameters such as a wing aspect ratio and a taper ratio during the design process. In this paper, a conceptual design method that incorporates a boundary element method is discussed so that aerodynamic characteristic estimations are possible and that the students can easily comprehend the effects of aerodynamic parameters while designing the airplane. A single engine light airplane has been designed by the present conceptual design method. The results obtained by the present method and those by the conventional method are compared and discussed.
NASA Astrophysics Data System (ADS)
Mitharwal, Rajendra; Andriulli, Francesco P.
2015-11-01
This work presents a Boundary Element Method (BEM) formulation for contactless electromagnetic field assessments. The new scheme is based on a regularised BEM approach that requires the use of electric measurements only. The regularisation is obtained by leveraging on an extension of Calderón techniques to rectangular systems leading to well-conditioned problems independent of the discretisation density. This enables the use of highly discretized Huygens surfaces that can be consequently placed very near to the radiating source. In addition, the new regularised scheme is hybridised with both surfacic homogeneous and volumetric inhomogeneous forward BEM solvers accelerated with fast matrix-vector multiplication schemes. This allows for rapid and effective dosimetric assessments and permits the use of inhomogeneous and realistic head phantoms. Numerical results corroborate the theory and confirms the practical effectiveness of all newly proposed formulations.
Noise simulation of aircraft engine fans by the boundary element method
NASA Astrophysics Data System (ADS)
Pyatunin, K. R.; Arkharova, N. V.; Remizov, A. E.
2016-07-01
Numerical simulation results of the civil aircraft engine fan stage noise in the far field are presented. Non-steady-state rotor-stator interaction is calculated the commercial software that solves the Navier-Stokes equations using differentturbulence models. Noise propagation to the far acoustic field is calculated by the boundary element method using acoustic Lighthill analogies without taking into account the mean current in the air inlet duct. The calculated sound pressure levels at points 50 m from the engine are presented, and the directional patterns of the acoustic radiation are shown. The use of the eddy resolving turbulence model to calculate rotor-stator interaction increases the accuracy in predicting fan stage noise.
Katz, B F
2001-11-01
Human spatial perception of sound is a complex phenomenon. The Head-Related Transfer Function (HRTF) is a vital component to spatial sound perception. In order improve the understanding of the correlation between the HRTF and specific geometry of the head and pinna, a Boundary Element Method (BEM) has been used to calculate a portion of the HRTF of an individual based on precise geometrical data. Advantages of this approach include the ability to alter the geometry of the individual through the model in ways which are not possible with real subjects. Several models are used in the study, including a head with no pinna and several sized spheres. Calculations are performed for various source locations around the head. Results are presented for rigid model cases. Effects of variations on impedance and comparisons to measured data will be presented in the subsequent paper.
Evaluation of boundary element methods for the EEG forward problem: Effect of linear interpolation
Schlitt, H.A.; Heller, L.; Best, E.; Ranken, D.M. ); Aaron, R. )
1995-01-01
We implement the approach for solving the boundary integral equation for the electroencephalography (EEG) forward problem proposed by de Munck, in which the electric potential varies linearly across each plane triangle of the mesh. Previous solutions have assumed the potential is constant across an element. We calculate the electric potential and systematically investigate the effect of different mesh choices and dipole locations by using a three concentric sphere head model for which there is an analytic solution. Implementing the linear interpolation approximation results in errors that are approximately half those of the same mesh when the potential is assumed to be constant, and provides a reliable method for solving the problem. 12 refs., 8 figs.
Automatic Recognition of Element Classes and Boundaries in the Birdsong with Variable Sequences.
Koumura, Takuya; Okanoya, Kazuo
2016-01-01
Researches on sequential vocalization often require analysis of vocalizations in long continuous sounds. In such studies as developmental ones or studies across generations in which days or months of vocalizations must be analyzed, methods for automatic recognition would be strongly desired. Although methods for automatic speech recognition for application purposes have been intensively studied, blindly applying them for biological purposes may not be an optimal solution. This is because, unlike human speech recognition, analysis of sequential vocalizations often requires accurate extraction of timing information. In the present study we propose automated systems suitable for recognizing birdsong, one of the most intensively investigated sequential vocalizations, focusing on the three properties of the birdsong. First, a song is a sequence of vocal elements, called notes, which can be grouped into categories. Second, temporal structure of birdsong is precisely controlled, meaning that temporal information is important in song analysis. Finally, notes are produced according to certain probabilistic rules, which may facilitate the accurate song recognition. We divided the procedure of song recognition into three sub-steps: local classification, boundary detection, and global sequencing, each of which corresponds to each of the three properties of birdsong. We compared the performances of several different ways to arrange these three steps. As results, we demonstrated a hybrid model of a deep convolutional neural network and a hidden Markov model was effective. We propose suitable arrangements of methods according to whether accurate boundary detection is needed. Also we designed the new measure to jointly evaluate the accuracy of note classification and boundary detection. Our methods should be applicable, with small modification and tuning, to the songs in other species that hold the three properties of the sequential vocalization.
Automatic Recognition of Element Classes and Boundaries in the Birdsong with Variable Sequences
Okanoya, Kazuo
2016-01-01
Researches on sequential vocalization often require analysis of vocalizations in long continuous sounds. In such studies as developmental ones or studies across generations in which days or months of vocalizations must be analyzed, methods for automatic recognition would be strongly desired. Although methods for automatic speech recognition for application purposes have been intensively studied, blindly applying them for biological purposes may not be an optimal solution. This is because, unlike human speech recognition, analysis of sequential vocalizations often requires accurate extraction of timing information. In the present study we propose automated systems suitable for recognizing birdsong, one of the most intensively investigated sequential vocalizations, focusing on the three properties of the birdsong. First, a song is a sequence of vocal elements, called notes, which can be grouped into categories. Second, temporal structure of birdsong is precisely controlled, meaning that temporal information is important in song analysis. Finally, notes are produced according to certain probabilistic rules, which may facilitate the accurate song recognition. We divided the procedure of song recognition into three sub-steps: local classification, boundary detection, and global sequencing, each of which corresponds to each of the three properties of birdsong. We compared the performances of several different ways to arrange these three steps. As results, we demonstrated a hybrid model of a deep convolutional neural network and a hidden Markov model was effective. We propose suitable arrangements of methods according to whether accurate boundary detection is needed. Also we designed the new measure to jointly evaluate the accuracy of note classification and boundary detection. Our methods should be applicable, with small modification and tuning, to the songs in other species that hold the three properties of the sequential vocalization. PMID:27442240
NASA Astrophysics Data System (ADS)
Örley, Felix; Pasquariello, Vito; Hickel, Stefan; Adams, Nikolaus A.
2015-02-01
The conservative immersed interface method for representing complex immersed solid boundaries or phase interfaces on Cartesian grids is improved and extended to allow for the simulation of weakly compressible fluid flows through moving geometries. We demonstrate that an approximation of moving interfaces by a level-set field results in unphysical oscillations in the vicinity of sharp corners when dealing with weakly compressible fluids such as water. By introducing an exact reconstruction of the cut-cell properties directly based on a surface triangulation of the immersed boundary, we are able to recover the correct flow evolution free of numerical artifacts. The new method is based on cut-elements. It provides sub-cell resolution of the geometry and handles flows through narrow closing or opening gaps in a straightforward manner. We validate our method with canonical flows around oscillating cylinders. We demonstrate that the method allows for an accurate prediction of flows around moving obstacles in weakly compressible liquid flows with cavitation effects. In particular, we show that the cavitating flow through a closing fuel injector control valve, which is an example for a complex application with interaction of stationary and moving parts, can be predicted by the method.
Krylov subspace iterative methods for boundary element method based near-field acoustic holography.
Valdivia, Nicolas; Williams, Earl G
2005-02-01
The reconstruction of the acoustic field for general surfaces is obtained from the solution of a matrix system that results from a boundary integral equation discretized using boundary element methods. The solution to the resultant matrix system is obtained using iterative regularization methods that counteract the effect of noise on the measurements. These methods will not require the calculation of the singular value decomposition, which can be expensive when the matrix system is considerably large. Krylov subspace methods are iterative methods that have the phenomena known as "semi-convergence," i.e., the optimal regularization solution is obtained after a few iterations. If the iteration is not stopped, the method converges to a solution that generally is totally corrupted by errors on the measurements. For these methods the number of iterations play the role of the regularization parameter. We will focus our attention to the study of the regularizing properties from the Krylov subspace methods like conjugate gradients, least squares QR and the recently proposed Hybrid method. A discussion and comparison of the available stopping rules will be included. A vibrating plate is considered as an example to validate our results.
Analysis of periodic 3D viscous flows using a quadratic discrete Galerkin boundary element method
NASA Astrophysics Data System (ADS)
Chan, Chiu Y.; Beris, Antony N.; Advani, Suresh G.
1994-05-01
A discrete Galerkin boundary element technique with a quadratic approximation of the variables was developed to simulate the three-dimensional (3D) viscous flow established in periodic assemblages of particles in suspensions and within a periodic porous medium. The Batchelor's unit-cell approach is used. The Galerkin formulation effectively handles the discontinuity in the traction arising in flow boundaries with edges or corners, such as the unit cell in this case. For an ellipsoidal dilute suspension over the range of aspect ratio studied (1 to 54), the numerical solutions of the rotational velocity of the particles and the viscosity correction were found to agree with the analytic values within 0.2% and 2% respectively, even with coarse meshes. In a suspension of cylindrical particles the calculated period of rotation agreed with the experimental data. However, Burgers' predictions for the correction to the suspension viscosity were found to be 30% too low and therefore the concept of the equivalent ellipsoidal ratio is judged to be inadequate. For pressure-driven flow through a fixed bed of fibers, the prediction on the permeability was shown to deviate by as much as 10% from the value calculated based on approximate permeability additivity rules using the corresponding values for planar flow past a periodic array of parallel cylinders. These applications show the versatility of the technique for studying viscous flows in complicated 3D geometries.
NASA Astrophysics Data System (ADS)
Williams, M. K.; Johnson, K. M.
2015-12-01
Recent literature investigating active folding indicates that crustal-scale anticlines grow primarily through slip on underlying faults. Such studies use the geometry and uplift rates of active fault-related folds to infer fault slip rate based upon an assumed kinematic relationship between fault slip and particle motion in the surrounding crust. Our method uses a boundary element model of flexural slip folding called BEAFS (Boundary Element Analysis of Flexural Slip), allowing us to focus on the mechanics of deformation.In many cases, the shallow geometry (<5km) of natural folds are well constrained by subsurface data. However, the geometry of the causative blind thrust faults are often not well imaged. By comparing our numerical simulations with published subsurface and surface data on naturally occurring active folds, we can determine fault geometry and the extent to which various mechanisms are controlling fold evolution. For this work, we present our model results for the underlying faults at Kettleman Hills South Dome, Kettleman Hills North Dome, and Coalinga Anticline in the San Joaquin Valley of Central California. The rupturing of blind thrust faults associated with actively growing anticlines such as these pose a significant global seismic hazard. Our study area is of particular interest as it is the site of two such recent earthquakes—a Mw=6.5 earthquake in 1983 at Coalinga and a Mw=6.1 in 1985 at Kettleman Hills North Dome. Thus, we can compare the published earthquake data from these events to the parameters predicted by our model results from BEAFS.
The boundary element method for light scattering by ice crystals and its implementation in BEM++
NASA Astrophysics Data System (ADS)
Groth, S. P.; Baran, A. J.; Betcke, T.; Havemann, S.; Śmigaj, W.
2015-12-01
A number of methods exist for solving the problem of electromagnetic scattering by atmospheric ice crystals. Amongst these methods, only a few are used to generate "benchmark" results in the atmospheric science community. Most notably, the T-matrix method, Discrete Dipole Approximation, and the Finite-Difference Time-Domain method. The Boundary Element Method (BEM), however, has received considerably less attention in this community despite its extensive use and development in other areas of applied mathematics and engineering. Recently the group of Betcke et al. (2015 [1]) at University College London has released a high performance open source boundary element library called BEM++. In this paper, we employ BEM++ to calculate the scattering properties of hexagonal ice columns of fixed orientation, as well as more complicated particles such as hollow columns and bullet-rosettes. The results for hexagonal columns are compared to those obtained using a highly accurate and well-established T-matrix method (Baran et al., 2001 [2]) for a range of different wavelengths and size parameters. It is shown that the results are in excellent agreement and that BEM++ is a fast alternative to the T-matrix method and others for generating benchmark results. However, the large memory requirements of BEM++ cause it to be limited to size parameters ~15 on a standard desktop PC if an accuracy of roughly 1% is required. The main advantages of BEM++ over many other methods are its flexibility to be applied to homogeneous dielectric particles of arbitrarily complex shape, and its open availability. This flexibility is illustrated by the application of BEM++ to scattering by hollow columns with different cavity types, as well as bullet-rosettes with 2-6 branches.
Standardization of computational experiments in unsteady turbulent boundary-layer flow
NASA Technical Reports Server (NTRS)
Carr, L. W.
1977-01-01
Numerical experiments are proposed as standard cases to be computed by all who plan to analyze unsteady turbulent boundary layer behavior. In this way, differences between the results obtained by various methods can be compared in a completely defined environment. The test cases range in difficulty from time relaxation study of the steady flow on a flat plate to the analysis of unsteady reversed flow. Initial and boundary conditions are fully defined for each case and representative outputs are presented. It is recommended that tabulated samples of computations of these test cases be published in a compendium of results.
Fast Computation of Global Sensitivity Kernel Database Based on Spectral-Element Simulations
NASA Astrophysics Data System (ADS)
Sales de Andrade, Elliott; Liu, Qinya
2017-07-01
Finite-frequency sensitivity kernels, a theoretical improvement from simple infinitely thin ray paths, have been used extensively in recent global and regional tomographic inversions. These sensitivity kernels provide more consistent and accurate interpretation of a growing number of broadband measurements, and are critical in mapping 3D heterogeneous structures of the mantle. Based on Born approximation, the calculation of sensitivity kernels requires the interaction of the forward wavefield and an adjoint wavefield generated by placing adjoint sources at stations. Both fields can be obtained accurately through numerical simulations of seismic wave propagation, particularly important for kernels of phases that cannot be sufficiently described by ray theory (such as core-diffracted waves). However, the total number of forward and adjoint numerical simulations required to build kernels for individual source-receiver pairs and to form the design matrix for classical tomography is computationally unaffordable. In this paper, we take advantage of the symmetry of 1D reference models, perform moment tensor forward and point force adjoint spectral-element simulations, and save six-component strain fields only on the equatorial plane based on the open-source spectral-element simulation package, SPECFEM3D_GLOBE. Sensitivity kernels for seismic phases at any epicentral distance can be efficiently computed by combining forward and adjoint strain wavefields from the saved strain field database, which significantly reduces both the number of simulations and the amount of storage required for global tomographic problems. Based on this technique, we compute traveltime, amplitude and/or boundary kernels of isotropic and radially anisotropic elastic parameters for various (P, S, P_{diff}, S_{diff}, depth, surface-reflected, surface wave, S 660 S boundary, etc.) phases for 1D ak135 model, in preparation for future global tomographic inversions.
Mazzotti, M.; Bartoli, I.; Marzani, A.; Viola, E.
2013-09-01
Highlights: •Dispersive properties of viscoelastic waveguides and cavities are computed using a regularized 2.5D BEM. •Linear viscoelasticity is introduced at the constitutive level by means of frequency dependent complex moduli. •A contour integral algorithm is used to solve the nonlinear eigenvalue problem. •The Sommerfeld radiation condition is used to select the permissible Riemann sheets. •Attenuation of surface waves in cavities approaches the attenuation of Rayleigh waves. -- Abstract: A regularized 2.5D boundary element method (BEM) is proposed to predict the dispersion properties of damped stress guided waves in waveguides and cavities of arbitrary cross-section. The wave attenuation, induced by material damping, is introduced using linear viscoelastic constitutive relations and described in a spatial manner by the imaginary component of the axial wavenumber. The discretized dispersive wave equation results in a nonlinear eigenvalue problem, which is solved obtaining complex axial wavenumbers for a fixed frequency using a contour integral algorithm. Due to the singular characteristics and the multivalued feature of the wave equation, the requirement of holomorphicity inside the contour region over the complex wavenumber plane is fulfilled by the introduction of the Sommerfeld branch cuts and by the choice of the permissible Riemann sheets. A post processing analysis is developed for the extraction of the energy velocity of propagative guided waves. The reliability of the method is demonstrated by comparing the results obtained for a rail and a bar with square cross-section with those obtained from a 2.5D Finite Element formulation also known in literature as Semi Analytical Finite Element (SAFE) method. Next, to show the potential of the proposed numerical framework, dispersion properties are predicted for surface waves propagating along cylindrical cavities of arbitrary cross-section. It is demonstrated that the attenuation of surface waves
Validity of a moving boundary finite element model for salt intrusion in a branching estuary
NASA Astrophysics Data System (ADS)
Das, D. B.; Nassehi, V.
A previously developed scheme for modelling of salt intrusion in estuaries with significant flow channel boundary variations during tidal cycles has been applied to a narrow branching estuary. It is shown that realistic simulations for complex tidal water systems can be obtained with this scheme provided that a suitable modification to the solution algorithm is implemented. The required modification is explained in detail and the model is applied to simulate salt intrusion in the Upper Milford Haven estuary in Wales, UK. Essentially, this moving boundary scheme introduces a distinct procedure for transient mass balance to ensure logical division of flow at an estuary junction and tracking of fluid particle trajectories along various branches of the estuary. Computational results and available field survey data for depth-averaged salinities are compared to determine the accuracy of the developed model. It is shown that the numerical results converge closer to field values than those previously reported. The method promises to provide new insights for environmental assessment, such as the determination of more accurate effluent discharge policies for estuaries.
FLASH: A finite element computer code for variably saturated flow
Baca, R.G.; Magnuson, S.O.
1992-05-01
A numerical model was developed for use in performance assessment studies at the INEL. The numerical model, referred to as the FLASH computer code, is designed to simulate two-dimensional fluid flow in fractured-porous media. The code is specifically designed to model variably saturated flow in an arid site vadose zone and saturated flow in an unconfined aquifer. In addition, the code also has the capability to simulate heat conduction in the vadose zone. This report presents the following: description of the conceptual frame-work and mathematical theory; derivations of the finite element techniques and algorithms; computational examples that illustrate the capability of the code; and input instructions for the general use of the code. The FLASH computer code is aimed at providing environmental scientists at the INEL with a predictive tool for the subsurface water pathway. This numerical model is expected to be widely used in performance assessments for: (1) the Remedial Investigation/Feasibility Study process and (2) compliance studies required by the US Department of Energy Order 5820.2A.
Isakson, Marcia J; Chotiros, Nicholas P
2011-03-01
A finite element model for the reverberation and propagation in a shallow water waveguide with a sandy bottom was calculated for five different environments at a center frequency of 250 Hz. The various environments included a rough water/sediment interface, a rough air/water interface, roughness at both interfaces and downward and upward refracting sound speed profiles with roughness at both interfaces. When compared to other models of reverberation such as ray theory, coupled modes, and parabolic equations, finite elements predicted higher levels of reverberation. At early times, this is due to the "fathometer" return, energy that is normally incident on the boundaries at zero range. At later times, the increased reverberation was due to high angle scattering paths between the two interfaces. Differences in reverberation levels among the environments indicated that scattered energy from the air/water interface is transmitted into the bottom at steep angles. This led to a large decrease in reverberation for a rough air/water interface relative to a rough water/sediment interface. Sound speed profile effects on reverberation were minimal at this frequency range. Calculations of the scintillation index of the different environments indicated that most of the reverberation was relatively Rayleigh-like with heavier tailed distributions at longer ranges. © 2011 Acoustical Society of America
De Corato, M.; Slot, J.J.M.; Hütter, M.; D'Avino, G.; Maffettone, P.L.; Hulsen, M.A.
2016-07-01
In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.
Roncal, Julissa; Guyot, Romain; Hamon, Perla; Crouzillat, Dominique; Rigoreau, Michel; Konan, Olivier N'Guessan; Rakotomalala, Jean-Jacques; Nowak, Michael D; Davis, Aaron P; de Kochko, Alexandre
2016-02-01
The completion of the genome assembly for the economically important coffee plant Coffea canephora (Rubiaceae) has allowed the use of bioinformatic tools to identify and characterize a diverse array of transposable elements (TEs), which can be used in evolutionary studies of the genus. An overview of the copy number and location within the C. canephora genome of four TEs is presented. These are tested for their use as molecular markers to unravel the evolutionary history of the Millotii Complex, a group of six wild coffee (Coffea) species native to Madagascar. Two TEs from the Gypsy superfamily successfully recovered some species boundaries and geographic structure among samples, whereas a TE from the Copia superfamily did not. Notably, species occurring in evergreen moist forests of eastern and southeastern Madagascar were divergent with respect to species in other habitats and regions. Our results suggest that the peak of transpositional activity of the Gypsy and Copia TEs occurred, respectively, before and after the speciation events of the tested Madagascan species. We conclude that the utilization of active TEs has considerable potential to unravel the evolutionary history and delimitation of closely related Coffea species. However, the selection of TE needs to be experimentally tested, since each element has its own evolutionary history. Different TEs with similar copy number in a given species can render different dendrograms; thus copy number is not a good selection criterion to attain phylogenetic resolution.
Gartling, D.K.
1996-05-01
The theoretical and numerical background for the finite element computer program, TORO II, is presented in detail. TORO II is designed for the multi-dimensional analysis of nonlinear, electromagnetic field problems described by the quasi-static form of Maxwell`s equations. A general description of the boundary value problems treated by the program is presented. The finite element formulation and the associated numerical methods used in TORO II are also outlined. Instructions for the use of the code are documented in SAND96-0903; examples of problems analyzed with the code are also provided in the user`s manual. 24 refs., 8 figs.
Computations for group sequential boundaries using the Lan-DeMets spending function method.
Reboussin, D M; DeMets, D L; Kim, K M; Lan, K K
2000-06-01
We describe an interactive Fortran program which performs computations related to the design and analysis of group sequential clinical trials using Lan-DeMets spending functions. Many clinical trials include interim analyses of accumulating data and rely on group sequential methods to avoid consequent inflation of the type I error rate. The computations are appropriate for interim test statistics whose distribution or limiting distribution is multivariate normal with independent increments. Recent theoretical results indicate that virtually any design likely to be used in a clinical trial will fall into this category. Interim analyses need not be equally spaced, and their number need not be specified in advance. In addition to determining sequential boundaries using an alpha spending function, the program can perform power computations, compute probabilities associated with a given set of boundaries, and generate confidence intervals.
NASA Technical Reports Server (NTRS)
Collins, J. D.; Volakis, John L.
1992-01-01
A method that combines the finite element and boundary integral techniques for the numerical solution of electromagnetic scattering problems is presented. The finite element method is well known for requiring a low order storage and for its capability to model inhomogeneous structures. Of particular emphasis in this work is the reduction of the storage requirement by terminating the finite element mesh on a boundary in a fashion which renders the boundary integrals in convolutional form. The fast Fourier transform is then used to evaluate these integrals in a conjugate gradient solver, without a need to generate the actual matrix. This method has a marked advantage over traditional integral equation approaches with respect to the storage requirement of highly inhomogeneous structures. Rectangular, circular, and ogival mesh termination boundaries are examined for two-dimensional scattering. In the case of axially symmetric structures, the boundary integral matrix storage is reduced by exploiting matrix symmetries and solving the resulting system via the conjugate gradient method. In each case several results are presented for various scatterers aimed at validating the method and providing an assessment of its capabilities. Important in methods incorporating boundary integral equations is the issue of internal resonance. A method is implemented for their removal, and is shown to be effective in the two-dimensional and three-dimensional applications.
SYMBMAT: Symbolic computation of quantum transition matrix elements
NASA Astrophysics Data System (ADS)
Ciappina, M. F.; Kirchner, T.
2012-08-01
We have developed a set of Mathematica notebooks to compute symbolically quantum transition matrices relevant for atomic ionization processes. The utilization of a symbolic language allows us to obtain analytical expressions for the transition matrix elements required in charged-particle and laser induced ionization of atoms. Additionally, by using a few simple commands, it is possible to export these symbolic expressions to standard programming languages, such as Fortran or C, for the subsequent computation of differential cross sections or other observables. One of the main drawbacks in the calculation of transition matrices is the tedious algebraic work required when initial states other than the simple hydrogenic 1s state need to be considered. Using these notebooks the work is dramatically reduced and it is possible to generate exact expressions for a large set of bound states. We present explicit examples of atomic collisions (in First Born Approximation and Distorted Wave Theory) and laser-matter interactions (within the Dipole and Strong Field Approximations and different gauges) using both hydrogenic wavefunctions and Slater-Type Orbitals with arbitrary nlm quantum numbers as initial states. Catalogue identifier: AEMI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMI_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 71 628 No. of bytes in distributed program, including test data, etc.: 444 195 Distribution format: tar.gz Programming language: Mathematica Computer: Single machines using Linux or Windows (with cores with any clock speed, cache memory and bits in a word) Operating system: Any OS that supports Mathematica. The notebooks have been tested under Windows and Linux and with versions 6.x, 7.x and 8.x Classification: 2.6 Nature of problem
Computer graphic visualization of orbiter lower surface boundary-layer transition
NASA Technical Reports Server (NTRS)
Throckmorton, D. A.; Hartung, L. C.
1984-01-01
Computer graphic techniques are applied to the processing of Shuttle Orbiter flight data in order to create a visual presentation of the extent and movement of the boundary-layer transition front over the orbiter lower surface during entry. Flight-measured surface temperature-time histories define the onset and completion of the boundary-layer transition process at any measurement location. The locus of points which define the spatial position of the boundary-layer transition front on the orbiter planform is plotted at each discrete time for which flight data are available. Displaying these images sequentially in real-time results in an animated simulation of the in-flight boundary-layer transition process.
Computer graphic visualization of orbiter lower surface boundary-layer transition
NASA Technical Reports Server (NTRS)
Throckmorton, D. A.; Hartung, L. C.
1984-01-01
Computer graphic techniques are applied to the processing of Shuttle Orbiter flight data in order to create a visual presentation of the extent and movement of the boundary-layer transition front over the orbiter lower surface during entry. Flight-measured surface temperature-time histories define the onset and completion of the boundary-layer transition process at any measurement location. The locus of points which define the spatial position of the boundary-layer transition front on the orbiter planform is plotted at each discrete time for which flight data are available. Displaying these images sequentially in real-time results in an animated simulation of the in-flight boundary-layer transition process.
Numerical computation of transonic flows by finite-element and finite-difference methods
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.
1978-01-01
Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.
External Boundary Conditions for Three-Dimensional Problems of Computational Aerodynamics
NASA Technical Reports Server (NTRS)
Tsynkov, Semyon V.
1997-01-01
We consider an unbounded steady-state flow of viscous fluid over a three-dimensional finite body or configuration of bodies. For the purpose of solving this flow problem numerically, we discretize the governing equations (Navier-Stokes) on a finite-difference grid. The grid obviously cannot stretch from the body up to infinity, because the number of the discrete variables in that case would not be finite. Therefore, prior to the discretization we truncate the original unbounded flow domain by introducing some artificial computational boundary at a finite distance of the body. Typically, the artificial boundary is introduced in a natural way as the external boundary of the domain covered by the grid. The flow problem formulated only on the finite computational domain rather than on the original infinite domain is clearly subdefinite unless some artificial boundary conditions (ABC's) are specified at the external computational boundary. Similarly, the discretized flow problem is subdefinite (i.e., lacks equations with respect to unknowns) unless a special closing procedure is implemented at this artificial boundary. The closing procedure in the discrete case is called the ABC's as well. In this paper, we present an innovative approach to constructing highly accurate ABC's for three-dimensional flow computations. The approach extends our previous technique developed for the two-dimensional case; it employs the finite-difference counterparts to Calderon's pseudodifferential boundary projections calculated in the framework of the difference potentials method (DPM) by Ryaben'kii. The resulting ABC's appear spatially nonlocal but particularly easy to implement along with the existing solvers. The new boundary conditions have been successfully combined with the NASA-developed production code TLNS3D and used for the analysis of wing-shaped configurations in subsonic (including incompressible limit) and transonic flow regimes. As demonstrated by the computational experiments
NASA Astrophysics Data System (ADS)
Schirmer, M.; Strauch, G.; Reinstorf, F.; Schirmer, K.
2007-10-01
The present work presents an alternative time-marching technique for boundary element formulations based on static fundamental solutions. The domain boundary element method (D-BEM) is adopted and the time-domain Green’s matrices of the elastodynamic problem are considered in order to generate a recursive relationship to evaluate displacements and velocities at each time-step. Taking into account the Newmark method, the Green’s matrices of the problem are numerically and implicitly evaluated, establishing the Green Newmark method. At the end of the work, numerical examples are presented, verifying the accuracy and potentialities of the new methodology.
NASA Astrophysics Data System (ADS)
Ringwelski, S.; Gabbert, U.
2010-10-01
A recently developed approach for the simulation and design of a fluid-loaded lightweight structure with surface-mounted piezoelectric actuators and sensors capable of actively reducing the sound radiation and the vibration is presented. The objective of this paper is to describe the theoretical background of the approach in which the FEM is applied to model the actively controlled shell structure. The FEM is also employed to model finite fluid domains around the shell structure as well as fluid domains that are partially or totally bounded by the structure. Boundary elements are used to characterize the unbounded acoustic pressure fields. The approach presented is based on the coupling of piezoelectric and acoustic finite elements with boundary elements. A coupled finite element-boundary element model is derived by introducing coupling conditions at the fluid-fluid and fluid-structure interfaces. Because of the possibility of using piezoelectric patches as actuators and sensors, feedback control algorithms can be implemented directly into the multi-coupled structural-acoustic approach to provide a closed-loop model for the design of active noise and vibration control. In order to demonstrate the applicability of the approach developed, a number of test simulations are carried out and the results are compared with experimental data. As a test case, a box-shaped shell structure with surface-mounted piezoelectric actuators and four sensors and an open rearward end is considered. A comparison between the measured values and those predicted by the coupled finite element-boundary element model shows a good agreement.
Determination of vacancy mechanism for grain boundary self-diffusion by computer simulation
Balluffi, R.W.; Kwok, T.; Bristowe, P.D.; Brokman, A.; Ho, P.S.; Yip, S.
1981-08-01
This note reports efforts to establish the GB self-diffusion mechanism in a bcc iron /SIGMA/.5 (36.9/degree/) (001) (310) tilt boundary using the combined methods of computer molecular statics and molecular dynamics simulation to provide quantitative microscopic evidence in favor of the vacancy mechanism. 16 refs.
Computational study of protein secondary structure elements: Ramachandran plots revisited.
Carrascoza, Francisco; Zaric, Snezana; Silaghi-Dumitrescu, Radu
2014-05-01
Potential energy surface (PES) were built for nineteen amino acids using density functional theory (PW91 and DFT M062X/6-311**). Examining the energy as a function of the φ/ψ dihedral angles in the allowed regions of the Ramachandran plot, amino acid groups that share common patterns on their PES plots and global minima were identified. These patterns show partial correlation with their structural and pharmacophoric features. Differences between these computational results and the experimentally noted permitted conformations of each amino acid are rationalized on the basis of attractive intra- and inter-molecular non-covalent interactions. The present data are focused on the intrinsic properties of an amino acid - an element which to our knowledge is typically ignored, as larger models are always used for the sake of similarity to real biological polypeptides.
1984-04-01
BOUNDARY ELEIENT METHOD AS FOR THE TEST PROBLEM 6. FINAL REMARKS 9 REFERENCES FIGURE APPENDIX: Convergence of Gauss- Seidel Method for Positive...6 7 cx2p a17 c y, cr S2’f 3’ a 4 cy2 Uv 3 cF 2 FIG. 1 DISCRETIZATION OF A REGION f, AND ITS BOUNDARY r APPENDIX Convergence of Gauss- Seidel Method for...Positive Definite Hermitian Matrices To make the memo self-contained, a proof of convergence for the Gauss- Seidel method as applied to a positive
NASA Technical Reports Server (NTRS)
Fulton, Robert E.
1985-01-01
Research performed over the past 10 years in engineering data base management and parallel computing is discussed, and certain opportunities for research toward the next generation of structural analysis capability are proposed. Particular attention is given to data base management associated with the IPAD project and parallel processing associated with the Finite Element Machine project, both sponsored by NASA, and a near term strategy for a distributed structural analysis capability based on relational data base management software and parallel computers for a future structural analysis system.
NASA Technical Reports Server (NTRS)
Fulton, Robert E.
1985-01-01
Research performed over the past 10 years in engineering data base management and parallel computing is discussed, and certain opportunities for research toward the next generation of structural analysis capability are proposed. Particular attention is given to data base management associated with the IPAD project and parallel processing associated with the Finite Element Machine project, both sponsored by NASA, and a near term strategy for a distributed structural analysis capability based on relational data base management software and parallel computers for a future structural analysis system.
Improved lattice computation of proton decay matrix elements
NASA Astrophysics Data System (ADS)
Aoki, Yasumichi; Izubuchi, Taku; Shintani, Eigo; Soni, Amarjit
2017-07-01
We present an improved result for the lattice computation of the proton decay matrix elements in Nf=2 +1 QCD. In this study, by adopting the error reduction technique of all-mode-averaging, a significant improvement of the statistical accuracy is achieved for the relevant form factor of proton (and also neutron) decay on the gauge ensemble of Nf=2 +1 domain-wall fermions with mπ=0.34 - 0.69 GeV on a 2.7 fm3 lattice, as used in our previous work [1]. We improve the total accuracy of matrix elements to 10-15% from 30-40% for p →π e+ or from 20-40% for p →K ν ¯. The accuracy of the low-energy constants α and β in the leading-order baryon chiral perturbation theory (BChPT) of proton decay are also improved. The relevant form factors of p →π estimated through the "direct" lattice calculation from the three-point function appear to be 1.4 times smaller than those from the "indirect" method using BChPT with α and β . It turns out that the utilization of our result will provide a factor 2-3 larger proton partial lifetime than that obtained using BChPT. We also discuss the use of these parameters in a dark matter model.
Over, D J; Conaway, C A; Katz, D J; Goodfellow, W D; Gregoire, D C
1997-08-01
The Frasnian-Famennian boundary is recognized as the culmination of a global mass extinction in the Late Devonian. In western New York State the boundary is a distinct horizon within a pyritic black shale bed of the upper Hanover Shale defined by the first occurrence of Palmatolepis triangularis in the absence of Frasnian conodonts. The boundary is characterized by a minor disconformity marked by a lag concentration of conodonts. Iridium at the boundary is 0.11-0.24 ng/g, two to five times background levels of <0.05 ng/g; other Ir enrichments of 0.38 ng/g and 0.49 ng/g occur within 50 cm of the conodont-constrained boundary. Numerous Ir enrichments in the boundary interval suggest extraterrestrial accretion and platinum group element (PGE) concentration at disconformities, or mobilization and concentration in organic-rich/pyritic-rich laminations from cosmic or terrestrial sources. PGE ratios of Pt/Pd and Ku/Ir at the boundary horizon approximate chondritic ratios and are suggestive of an unaltered extraterrestrial source. These values do not conclusively establish a single extraterrestrial impact as the ultimate cause of the Frasnian-Famennian mass extinction, especially given the presence of similar Ir enrichments elsewhere in the section and the absence at the boundary of microtektites and shocked mineral grains.
NASA Technical Reports Server (NTRS)
Margolis, S. V.; Doehne, E. F.
1988-01-01
Trace element and stable isotope analyses were performed on a series of sediment samples crossing the Cretaceous-Tertiary (K-T) boundary from critical sections at Aumaya and Sopelano, Spain. The aim is to possibly distinguish extraterrestrial vs. volcanic or authigenic concentration of platinum group and other elements in K-T boundary transitional sediments. These sediments also have been shown to contain evidence for step-wise extinction of several groups of marine invertebrates, associated with negative oxygen and carbon isotope excursions occurring during the last million years of the Cretaceous. These isotope excursions have been interpreted to indicate major changes in ocean thermal regime, circulation, and ecosystems that may be related to multiple events during latest Cretaceous time. Results to date on the petrographic and geochemical analyses of the Late Cretaceous and Early Paleocene sediments indicate that diagenesis has obviously affected the trace element geochemistry and stable isotope compositions at Zumaya. Mineralogical and geochemical analysis of K-T boundary sediments at Zumaya suggest that a substantial fraction of anomalous trace elements in the boundary marl are present in specific mineral phases. Platinum and nickel grains perhaps represent the first direct evidence of siderophile-rich minerals at the boundary. The presence of spinels and Ni-rich particles as inclusions in aluminosilicate spherules from Zumaya suggests an original, non-diagenetic origin for the spherules. Similar spherules from southern Spain (Caravaca), show a strong marine authigenic overprint. This research represents a new approach in trying to directly identify the sedimentary mineral components that are responsible for the trace element concentrations associated with the K-T boundary.
Matrix element method for high performance computing platforms
NASA Astrophysics Data System (ADS)
Grasseau, G.; Chamont, D.; Beaudette, F.; Bianchini, L.; Davignon, O.; Mastrolorenzo, L.; Ochando, C.; Paganini, P.; Strebler, T.
2015-12-01
Lot of efforts have been devoted by ATLAS and CMS teams to improve the quality of LHC events analysis with the Matrix Element Method (MEM). Up to now, very few implementations try to face up the huge computing resources required by this method. We propose here a highly parallel version, combining MPI and OpenCL, which makes the MEM exploitation reachable for the whole CMS datasets with a moderate cost. In the article, we describe the status of two software projects under development, one focused on physics and one focused on computing. We also showcase their preliminary performance obtained with classical multi-core processors, CUDA accelerators and MIC co-processors. This let us extrapolate that with the help of 6 high-end accelerators, we should be able to reprocess the whole LHC run 1 within 10 days, and that we have a satisfying metric for the upcoming run 2. The future work will consist in finalizing a single merged system including all the physics and all the parallelism infrastructure, thus optimizing implementation for best hardware platforms.
Finite element modeling of crustal deformation in the North America-Caribbean Plate Boundary Zone
NASA Astrophysics Data System (ADS)
Lundgren, P. R.; Russo, R. M.
1996-05-01
We have developed two-dimensional spherical shell finite element models of elastic displacements in the North America-Caribbean (NA-Ca) plate boundary zone (PBZ) in order to quantify crust and fault motions in the PBZ. The models we derive are dependent on both the internal fault constraints and the NA-Ca Euler pole we used. Since the location and magnitude of the NA-Ca euler pole are still matters of much debate, we consider three Euler poles [DeMets et al., 1990; Calais and Mercier de Lépinay, 1993; and Deng and Sykes, 1995]. We compare the resulting finite element model displacements to recent seismicity and to geological and geophysical field observations. The model of DeMets et al. [1990], NUVEL-1, features an NA-Ca relative velocity across the PBZ which is less than the observed Cayman spreading axis rate, and thus, the finite element model based on it produces fault motions which are inconsistent with observation. The Calais and Mercier de Lépinay [1993] (C&M), and Deng and Sykes [1995] (D&S) models both yield far-field rates across the PBZ at the point of the Cayman spreading center of approximately 20 mm/yr, a value greater than the observed rate. The greatest differences in the latter two models lie in the motion calculated for the area around Puerto Rico. Both models feature a counterclockwise rotation of the PBZ around Puerto Rico with opening of the Anegada Passage and compression at the Muertos Trough south of eastern Hispaniola. The C&M-based model produces normal opening of the Anegada Passage fault system, while the D&S-based model produces left-lateral transtension across the Anegada Passage fault system, the result of continuum crustal motions which are nearly orthogonal between the two models in the area NE of Puerto Rico. We conclude that the C&M-based model better matches geological observations of PBZ fault motions and deformation primarily on the basis of the Anegada Passage results. Because of this rotation of the PBZ from Hispaniola to
An immersed boundary computational model for acoustic scattering problems with complex geometries.
Sun, Xiaofeng; Jiang, Yongsong; Liang, An; Jing, Xiaodong
2012-11-01
An immersed boundary computational model is presented in order to deal with the acoustic scattering problem by complex geometries, in which the wall boundary condition is treated as a direct body force determined by satisfying the non-penetrating boundary condition. Two distinct discretized grids are used to discrete the fluid domain and immersed boundary, respectively. The immersed boundaries are represented by Lagrangian points and the direct body force determined on these points is applied on the neighboring Eulerian points. The coupling between the Lagrangian points and Euler points is linked by a discrete delta function. The linearized Euler equations are spatially discretized with a fourth-order dispersion-relation-preserving scheme and temporal integrated with a low-dissipation and low-dispersion Runge-Kutta scheme. A perfectly matched layer technique is applied to absorb out-going waves and in-going waves in the immersed bodies. Several benchmark problems for computational aeroacoustic solvers are performed to validate the present method.
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Fang, Jun; Kurbatskii, Konstantin A.
1996-01-01
A set of nonhomogeneous radiation and outflow conditions which automatically generate prescribed incoming acoustic or vorticity waves and, at the same time, are transparent to outgoing sound waves produced internally in a finite computation domain is proposed. This type of boundary condition is needed for the numerical solution of many exterior aeroacoustics problems. In computational aeroacoustics, the computation scheme must be as nondispersive ans nondissipative as possible. It must also support waves with wave speeds which are nearly the same as those of the original linearized Euler equations. To meet these requirements, a high-order/large-stencil scheme is necessary The proposed nonhomogeneous radiation and outflow boundary conditions are designed primarily for use in conjunction with such high-order/large-stencil finite difference schemes.
Gao, Hao; Wang, Huiming; Berry, Colin; Luo, Xiaoyu; Griffith, Boyce E
2014-01-01
Finite stress and strain analyses of the heart provide insight into the biomechanics of myocardial function and dysfunction. Herein, we describe progress toward dynamic patient-specific models of the left ventricle using an immersed boundary (IB) method with a finite element (FE) structural mechanics model. We use a structure-based hyperelastic strain-energy function to describe the passive mechanics of the ventricular myocardium, a realistic anatomical geometry reconstructed from clinical magnetic resonance images of a healthy human heart, and a rule-based fiber architecture. Numerical predictions of this IB/FE model are compared with results obtained by a commercial FE solver. We demonstrate that the IB/FE model yields results that are in good agreement with those of the conventional FE model under diastolic loading conditions, and the predictions of the LV model using either numerical method are shown to be consistent with previous computational and experimental data. These results are among the first to analyze the stress and strain predictions of IB models of ventricular mechanics, and they serve both to verify the IB/FE simulation framework and to validate the IB/FE model. Moreover, this work represents an important step toward using such models for fully dynamic fluid–structure interaction simulations of the heart. © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons, Ltd. PMID:24799090
Gao, Hao; Wang, Huiming; Berry, Colin; Luo, Xiaoyu; Griffith, Boyce E
2014-11-01
Finite stress and strain analyses of the heart provide insight into the biomechanics of myocardial function and dysfunction. Herein, we describe progress toward dynamic patient-specific models of the left ventricle using an immersed boundary (IB) method with a finite element (FE) structural mechanics model. We use a structure-based hyperelastic strain-energy function to describe the passive mechanics of the ventricular myocardium, a realistic anatomical geometry reconstructed from clinical magnetic resonance images of a healthy human heart, and a rule-based fiber architecture. Numerical predictions of this IB/FE model are compared with results obtained by a commercial FE solver. We demonstrate that the IB/FE model yields results that are in good agreement with those of the conventional FE model under diastolic loading conditions, and the predictions of the LV model using either numerical method are shown to be consistent with previous computational and experimental data. These results are among the first to analyze the stress and strain predictions of IB models of ventricular mechanics, and they serve both to verify the IB/FE simulation framework and to validate the IB/FE model. Moreover, this work represents an important step toward using such models for fully dynamic fluid-structure interaction simulations of the heart. © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons, Ltd.
GYC: A program to compute the turbulent boundary layer on a rotating cone
NASA Technical Reports Server (NTRS)
Sullivan, R. D.
1976-01-01
A computer program, GYC, which is capable of computing the properties of a compressible turbulent boundary layer on a rotating axisymmetric cone-cylinder body, according to the principles of invariant modeling was studied. The program is extended to include the calculation of the turbulence scale by a differential equation. GYC is in operation on the CDC-7600 computer and has undergone several corrections and improvements as a result of the experience gained. The theoretical basis for the program and the method of implementation, as well as information on its operation are given.
Cost Considerations in Nonlinear Finite-Element Computing
NASA Technical Reports Server (NTRS)
Utku, S.; Melosh, R. J.; Islam, M.; Salama, M.
1985-01-01
Conference paper discusses computational requirements for finiteelement analysis using quasi-linear approach to nonlinear problems. Paper evaluates computational efficiency of different computer architecturtural types in terms of relative cost and computing time.
Experimental and Computational Boundary-Layer Studies In a Supersonic Two-Dimensional Nozzle
NASA Technical Reports Server (NTRS)
Demetriades, Anthony; Brogan, Torence P.; King, Lyndell S.; Reda, Daniel C.; Davis, Sanford (Technical Monitor)
1998-01-01
Experiments and computations were carried out on the adiabatic laminar boundary layer developing along the surfaces of a two-dimensional supersonic nozzle, consisting of upper and lower contoured nozzle blocks and flat sidewalls. Two- and three-dimensional Navier-Stokes codes, as well as two-dimensional boundary-layer codes were employed. These codes were adapted to the characteristics of a specific wind tunnel nozzle, so that their numerical results could be directly compared with experimental data obtained in the same nozzle. Such comparisons were made for the boundary-layer growth on the nozzle contoured surfaces, and for the boundary-layer growth, surface streamlines and surface shear on the sidewalls. The three-dimensional Navier-Stokes code was found to be the only one to correctly predict the mean laminar boundary-layer flow on both the sidewalls and the contoured surfaces. Theory and experiment both indicated that the sidewall flow is highly three-dimensional, with non-uniform shear, corner vortices and a boundary layer strongly distorted by cross flows induced by lateral pressure gradients.
Towards an effective non-reflective boundary condition for computational aeroacoustics
NASA Astrophysics Data System (ADS)
Gill, James; Fattah, Ryu; Zhang, Xin
2017-03-01
A generic, non-reflective zonal transverse characteristic boundary condition is described for computational aeroacoustics, which shows superior performance to existing non-reflective boundary conditions for two-dimensional linearized Euler simulations. The new condition is based on a characteristic non-reflective method, and also contains optimised use of transverse characteristic terms and a zonal forcing region. The performance of the new method and several existing non-reflective acoustic boundary conditions is quantitatively compared using a plane wave test case. The performance of buffer zone, perfectly matched layer, far-field, and characteristic non-reflective methods is compared, following an optimisation of the tuneable parameters in each method to give best performance. The study uses a high-order linearised Euler equation solver to assess non-reflective boundary conditions with a variety of cases. The performance is compared for downstream travelling acoustic waves with varying frequency and incident angle, and at various Mach numbers. The current study includes a more comprehensive evaluation than previous studies which used constant values of tuneable parameters or qualitative assessment methods. The new zonal transverse characteristic boundary condition is shown to give improved performance in comparison to the other tested outflow boundary conditions for two-dimensional linearized Euler simulations, and is also shown to give good performance when used as an inflow condition.
NASA Astrophysics Data System (ADS)
Uğurlu, B.
2015-03-01
A boundary element solution method is proposed for linear vibration analysis of fluid-coupled thin plates. The method is based on replacing the associated biharmonic operator with two successive harmonic operators, leading to a coupled system of boundary integral equations with simpler properties: the fundamental solution has an elementary form, and complicated singularity removal techniques can be avoided. The fluid flow due to the plate motion is taken as a potential field, and its effect on the plate dynamics is incorporated into the analysis by invoking another boundary integral solution, described over the fluid-plate interface. The body terms in the plate boundary integral equations are considered by the dual reciprocity boundary element formulation. Three different radial basis functions are employed as interpolation functions, alone and augmented with polynomial and sine expansions, to represent the body terms. The performance of the method is investigated from several perspectives by adopting plates with different shapes and/or boundary conditions; excellent approximations are obtained in general: the convergence behavior is consistent, both dry and wet frequency parameters are predicted accurately, and the mode shapes are captured even with rough models. In some of the studied problems, however, deviated results are obtained for specific modes. Furthermore, it is observed that the performance of the method depends on the implemented DRM functions, and combining radial basis functions with global expansions does not yield noticeable improvements.
El-Awady, J.; Biner, S.; Ghoniem, N.
2007-11-07
We present a self-consistent formulation of 3-D parametric dislocation dynamics (PDD) with the boundary element method (BEM) to describe dislocation motion, and hence microscopic plastic flow in finite volumes. We develop quantitative measures of the accuracy and convergence of the method by considering a comparison with known analytical solutions. It is shown that the method displays absolute convergence with increasing the number of quadrature points on the dislocation loop and the surface mesh density. The error in the image force on a screw dislocation approaching a free surface is shown to increase as the dislocation approaches the surface, but is nevertheless controllable. For example, at a distance of one lattice parameter from the surface, the relative error is less than 5% for a surface mesh with an element size of 1000 x 2000 (in units of lattice parameter), and 64 quadrature points. The Eshelby twist angle in a finite-length cylinder containing a coaxial screw dislocation is also used to benchmark the method. Finally, large scale 3-D simulation results of single slip behavior in cylindrical microcrystals are presented. Plastic flow characteristics and the stress-strain behavior of cylindrical microcrystals under compression are shown to be in agreement with experimental observations. It is shown that the mean length of dislocations trapped at the surface is the dominant factor in determining the size effects on hardening of single crystals. The influence of surface image fields on the flow stress is finally explored. It is shown that the flow stress is reduced by as much as 20% for small single crystals of size less than 0.15 {micro}m.
Adaptation of a program for nonlinear finite element analysis to the CDC STAR 100 computer
NASA Technical Reports Server (NTRS)
Pifko, A. B.; Ogilvie, P. L.
1978-01-01
The conversion of a nonlinear finite element program to the CDC STAR 100 pipeline computer is discussed. The program called DYCAST was developed for the crash simulation of structures. Initial results with the STAR 100 computer indicated that significant gains in computation time are possible for operations on gloval arrays. However, for element level computations that do not lend themselves easily to long vector processing, the STAR 100 was slower than comparable scalar computers. On this basis it is concluded that in order for pipeline computers to impact the economic feasibility of large nonlinear analyses it is absolutely essential that algorithms be devised to improve the efficiency of element level computations.
The condensation of ampholytes in steady state moving boundaries - Analysis by computer simulation
NASA Technical Reports Server (NTRS)
Mosher, Richard A.; Thormann, Wolfgang
1986-01-01
A digital simulation of the behavior of amphoteric sample components in moving steady state boundaries is presented. Complete computer simulation data, including profiles of concentration, conductivity and pH as functions of time, are given for both cationic and anionic electrolyte configurations which incorporate one amphoteric sample constituent. The condensation of ampholytes in steady state moving boundaries is shown to proceed via an isotachophoretic mechanism and not by isoelectric focusing. Mobility (velocity) relationships necessary for sample components to form steady state zones are discussed.
The condensation of ampholytes in steady state moving boundaries - Analysis by computer simulation
NASA Technical Reports Server (NTRS)
Mosher, Richard A.; Thormann, Wolfgang
1986-01-01
A digital simulation of the behavior of amphoteric sample components in moving steady state boundaries is presented. Complete computer simulation data, including profiles of concentration, conductivity and pH as functions of time, are given for both cationic and anionic electrolyte configurations which incorporate one amphoteric sample constituent. The condensation of ampholytes in steady state moving boundaries is shown to proceed via an isotachophoretic mechanism and not by isoelectric focusing. Mobility (velocity) relationships necessary for sample components to form steady state zones are discussed.
NASA Astrophysics Data System (ADS)
Ji, Zhen-Lin; Wang, Xue-Ren
2008-06-01
In marine engine exhaust silencing systems, the presence of exhaust gas flow influences the sound propagation inside the systems and the acoustic attenuation performance of silencers. In order to investigate the effects of three-dimensional gas flow and acoustic damping on the acoustic attenuation characteristics of marine engine exhaust silencers, a dual reciprocity boundary element method (DRBEM) was developed. The acoustic governing equation in three-dimensional potential flow was derived first, and then the DRBEM numerical procedure is given. Compared to the conventional boundary element method (CBEM), the DRBEM considers the second order terms of flow Mach number in the acoustic governing equation, so it is suitable for the cases with higher Mach number subsonic flow. For complex exhaust silencers, it is difficult to apply the single-domain boundary element method, so a substructure approach based on the dual reciprocity boundary element method is presented. The experiments for measuring transmission loss of silencers are conducted, and the experimental setup and measurements are explained. The transmission loss of a single expansion chamber silencer with extended inlet and outlet were predicted by DRBEM and compared with the measurements. The good agreements between predictions and measurements are observed, which demonstrated that the derived acoustic governing equation and the DRBEM numerical procedure in the present study are correct.
NASA Astrophysics Data System (ADS)
Kirilovskiy, S. V.; Poplavskaya, T. V.
2016-11-01
The work presents the results of numerical modeling of a supersonic flow around a blunted cone with an isolated cylindrical roughness on the forebody surface in the three-dimensional formulation. The roughness element is shown to distort the mean flow and to give rise to small-amplitude disturbances with distinguished spectral peaks in the boundary layer.
The Koshak section: Evidence for element fractionation and an oxidation event at the K/T boundary
NASA Technical Reports Server (NTRS)
Nazarov, M. A.; Badjukov, D. D.; Barsukova, L. D.; Kolesov, G. M.; Naidin, D. P.
1993-01-01
The Koshak site is a new K/T section located about 125 km EEN of the Fort Shevchenko city, Mangyshlak, Kazakhstan. In this paper, we report results of geochemical and mineralogical studies of this section which indicate a deep element fractionation and an oxidation event at the K/T boundary.
Computation of turbulent boundary layers employing the defect wall-function method. M.S. Thesis
NASA Technical Reports Server (NTRS)
Brown, Douglas L.
1994-01-01
In order to decrease overall computational time requirements of spatially-marching parabolized Navier-Stokes finite-difference computer code when applied to turbulent fluid flow, a wall-function methodology, originally proposed by R. Barnwell, was implemented. This numerical effort increases computational speed and calculates reasonably accurate wall shear stress spatial distributions and boundary-layer profiles. Since the wall shear stress is analytically determined from the wall-function model, the computational grid near the wall is not required to spatially resolve the laminar-viscous sublayer. Consequently, a substantially increased computational integration step size is achieved resulting in a considerable decrease in net computational time. This wall-function technique is demonstrated for adiabatic flat plate test cases from Mach 2 to Mach 8. These test cases are analytically verified employing: (1) Eckert reference method solutions, (2) experimental turbulent boundary-layer data of Mabey, and (3) finite-difference computational code solutions with fully resolved laminar-viscous sublayers. Additionally, results have been obtained for two pressure-gradient cases: (1) an adiabatic expansion corner and (2) an adiabatic compression corner.
Computational study of flow noise from small gaps in turbulent boundary layers
NASA Astrophysics Data System (ADS)
Hao, Jin; Ji, Minsuk; Wang, Meng
2011-11-01
The noise induced by small gaps underneath low-Mach-number turbulent boundary layers is studied using large-eddy simulation and Lighthill's equation. The latter is solved by employing an acoustically compact Green's function for the gap and by a boundary-element method. The gap leading-edge height is 13 % of the boundary-layer thickness, and the gap width and trailing-edge height are varied to investigate their effect on sound generation. The radiated acoustic field is dominated by the forward-facing step in the gap and resembles forward-step noise for wide gaps and/or asymmetric gaps with the trailing edge higher than the leading edge. For narrow and symmetric gaps, destructive interference of the sound from leading and trailing edges causes a significant decline in the low-frequency spectral content and thereby creates a broad spectral peak in the mid-frequency range. The effect of acoustic noncompactness of gaps is investigated by comparing solutions based on a compact Green's function and those from a boundary-element calculation. Excellent agreement is observed at low frequencies and away from the wall-normal direction. At higher frequencies, the sound field deviates from that of a compact streamwise dipole. The elevated level of surface pressure fluctuations induced by gaps and their recovery to equilibrium conditions are also examined. Supported by ONR Grant N00014-09-1-0602.
An efficient quadrature for 2.5D boundary element calculations
NASA Astrophysics Data System (ADS)
Kasess, Christian H.; Kreuzer, Wolfgang; Waubke, Holger
2016-11-01
In recent years, the boundary element method has become a widely used tool for calculating the mitigation effects of noise barriers. However, since for large structures calculations in 3D become very inefficient, most of the standard implementations are only in 2D. This means that the noise source is implicitly assumed to be given by a coherent line source, which is not realistic in most cases. By using a Fourier transform with respect to a spatial coordinate along the length of the structure it is possible to reduce the 3D problem to several 2D problems with distinct wavenumbers which allows the simulation of more realistic noise sources and which is typically referred to as 2.5D BEM. To that end, it is necessary to numerically calculate a Fourier-like integral over all the 2D solutions. In this work, an efficient way to calculate this integral is given building on existing approaches using Clenshaw-Curtis-Filon quadrature and demodulation combined with an adaptive order-selection scheme. As BEM calculations are costly, the main focus of the method introduced lies on avoiding too many of these calculations. The efficiency of the method is illustrated using two different examples: a reflecting cylinder and an L-shaped noise barrier.
Image guided near-infrared spectroscopy of breast tissue in vivo using boundary element method
NASA Astrophysics Data System (ADS)
Srinivasan, Subhadra; Carpenter, Colin M.; Ghadyani, Hamid R.; Taka, Senate J.; Kaufman, Peter A.; Diflorio-Alexander, Roberta M.; Wells, Wendy A.; Pogue, Brian W.; Paulsen, Keith D.
2010-11-01
We demonstrate quantitative functional imaging using image-guided near-infrared spectroscopy (IG-NIRS) implemented with the boundary element method (BEM) for reconstructing 3-D optical property estimates in breast tissue in vivo. A multimodality MRI-NIR system was used to collect measurements of light reflectance from breast tissue. The BEM was used to model light propagation in 3-D based only on surface discretization in order to reconstruct quantitative values of total hemoglobin (HbT), oxygen saturation, water, and scatter. The technique was validated in experimental measurements from heterogeneous breast-shaped phantoms with known values and applied to a total of seven subjects comprising six healthy individuals and one participant with cancer imaged at two time points during neoadjuvant chemotherapy. Using experimental measurements from a heterogeneous breast phantom, BEM for IG-NIRS produced accurate values for HbT in the inclusion with a <3% error. Healthy breast tissues showed higher HbT and water in fibroglandular tissue than in adipose tissue. In a subject with cancer, the tumor showed higher HbT compared to the background. HbT in the tumor was reduced by 9 μM during treatment. We conclude that 3-D MRI-NIRS with BEM provides quantitative and functional characterization of breast tissue in vivo through measurement of hemoglobin content. The method provides potentially complementary information to DCE-MRI for tumor characterization.
Soerensen, Anne L; Skov, Henrik; Jacob, Daniel J; Soerensen, Britt T; Johnson, Matthew S
2010-10-01
Gaseous elemental mercury (GEM) and reactive gaseous mercury (RGM) were measured during an eight month circumnavigation to obtain knowledge of their worldwide distributions in the marine boundary layer (MBL). Background GEM concentrations were found to be 1.32 ± 0.2 ng/m(3) (summer) and 2.62 ± 0.4 ng/m(3) (spring) in the northern hemisphere and 1.27 ± 0.2 ng/m(3) (spring and summer) in the southern hemisphere. Radiation and relative humidity are shown to control diurnal cycles of RGM. During the cruise the ship passed areas of clean MBL air, air influenced by biomass burning (South Atlantic) and air with high concentrations of GEM and RGM of unknown origin (Antarctic). High GEM concentrations above the Atlantic indicate that emission from the ocean can be an important GEM source. Our data combined with data from earlier cruises provides adequate information to establish a seasonal cycle for the Atlantic. Results show a cycle similar to that found at Mace Head, Ireland but with larger amplitude. We have improved the basic knowledge of mean GEM and RGM concentrations in the MBL worldwide and shown how natural sources and reemissions can affect GEM concentrations in the MBL.
Finite element modeling of stress in the Nazca plate - Driving forces and plate boundary earthquakes
NASA Technical Reports Server (NTRS)
Richardson, R. M.
1978-01-01
The state of stress within the Nazca plate due to plate driving forces and large plate boundary earthquakes has been analyzed by applying a finite element method using the wave front solution technique to models of the intraplate stress field in a single plate using a refined grid. Although only static elastic models have been explicitly calculated, certain limiting cases of an elastic plate over a viscous asthenosphere were also treated. A state of nearly east-west compression inferred from the source mechanism of thrust earthquakes in the interior of the plate requires ridge pushing forces. The net pulling force on the oceanic plate by the subducted slab has a maximum value comparable to pushing forces. The estimated horizontal deviatoric stress in intraplate regions, based on potential forces associated with the ridge, is on the order of a few hundred bars. The intraplate stress field in the region of the 1960 earthquake may change by a few tens of bars at most once the asthenosphere has relaxed, with changes on the order of one bar occurring at greater distances into the plate. The changes in the intraplate stress field are probably not noticeable unless the lithosphere is near failure.
Image guided near-infrared spectroscopy of breast tissue in vivo using boundary element method.
Srinivasan, Subhadra; Carpenter, Colin M; Ghadyani, Hamid R; Taka, Senate J; Kaufman, Peter A; Diflorio-Alexander, Roberta M; Wells, Wendy A; Pogue, Brian W; Paulsen, Keith D
2010-01-01
We demonstrate quantitative functional imaging using image-guided near-infrared spectroscopy (IG-NIRS) implemented with the boundary element method (BEM) for reconstructing 3-D optical property estimates in breast tissue in vivo. A multimodality MRI-NIR system was used to collect measurements of light reflectance from breast tissue. The BEM was used to model light propagation in 3-D based only on surface discretization in order to reconstruct quantitative values of total hemoglobin (HbT), oxygen saturation, water, and scatter. The technique was validated in experimental measurements from heterogeneous breast-shaped phantoms with known values and applied to a total of seven subjects comprising six healthy individuals and one participant with cancer imaged at two time points during neoadjuvant chemotherapy. Using experimental measurements from a heterogeneous breast phantom, BEM for IG-NIRS produced accurate values for HbT in the inclusion with a <3% error. Healthy breast tissues showed higher HbT and water in fibroglandular tissue than in adipose tissue. In a subject with cancer, the tumor showed higher HbT compared to the background. HbT in the tumor was reduced by 9 μM during treatment. We conclude that 3-D MRI-NIRS with BEM provides quantitative and functional characterization of breast tissue in vivo through measurement of hemoglobin content. The method provides potentially complementary information to DCE-MRI for tumor characterization.
NASA Astrophysics Data System (ADS)
Elliott, David; Johnston, Peter R.
2007-06-01
In the two-dimensional boundary element method, one often needs to evaluate numerically integrals of the form where j2 is a quadratic, g is a polynomial and f is a rational, logarithmic or algebraic function with a singularity at zero. The constants a and b are such that -1[less-than-or-equals, slant]a[less-than-or-equals, slant]1 and 0
Finite element modeling of stress in the Nazca plate - Driving forces and plate boundary earthquakes
NASA Technical Reports Server (NTRS)
Richardson, R. M.
1978-01-01
The state of stress within the Nazca plate due to plate driving forces and large plate boundary earthquakes has been analyzed by applying a finite element method using the wave front solution technique to models of the intraplate stress field in a single plate using a refined grid. Although only static elastic models have been explicitly calculated, certain limiting cases of an elastic plate over a viscous asthenosphere were also treated. A state of nearly east-west compression inferred from the source mechanism of thrust earthquakes in the interior of the plate requires ridge pushing forces. The net pulling force on the oceanic plate by the subducted slab has a maximum value comparable to pushing forces. The estimated horizontal deviatoric stress in intraplate regions, based on potential forces associated with the ridge, is on the order of a few hundred bars. The intraplate stress field in the region of the 1960 earthquake may change by a few tens of bars at most once the asthenosphere has relaxed, with changes on the order of one bar occurring at greater distances into the plate. The changes in the intraplate stress field are probably not noticeable unless the lithosphere is near failure.
Boundary element method for optical force calibration in microfluidic dual-beam optical trap
NASA Astrophysics Data System (ADS)
Solmaz, Mehmet E.; Çetin, Barbaros; Baranoǧlu, Besim; Serhathoǧlu, Murat; Biyikli, Necmi
2015-08-01
The potential use of optical forces in microfluidic environment enables highly selective bio-particle manipulation. Manipulation could be accomplished via trapping or pushing a particle due to optical field. Empirical determination of optical force is often needed to ensure efficient operation of manipulation. The external force applied to a trapped particle in a microfluidic channel is a combination of optical and drag forces. The optical force can be found by measuring the particle velocity for a certain laser power level and a multiplicative correction factor is applied for the proximity of the particle to the channel surface. This method is not accurate especially for small microfluidic geometries where the particle size is in Mie regime and is comparable to channel cross section. In this work, we propose to use Boundary Element Method (BEM) to simulate fluid flow within the micro-channel with the presence of the particle to predict drag force. Pushing experiments were performed in a dual-beam optical trap and particle's position information was extracted. The drag force acting on the particle was then obtained using BEM and other analytical expressions, and was compared to the calculated optical force. BEM was able to predict the behavior of the optical force due to the inclusion of all the channel walls.
Guo, Xiasheng; Cai, Chenliang; Xu, Guangyao; Yang, Yanye; Tu, Juan; Huang, PinTong; Zhang, Dong
2017-11-01
Sonoporation has been widely accepted as a significant tool for gene delivery as well as some bio-effects like hemolysis, bringing in high demands of looking into its underlying mechanism. A two-dimensional (2D) boundary element method (BEM) model was developed to investigate microbubble-cell interaction, especially the morphological and mechanical characteristics around the close-to-bubble point (CP) on cell membrane. Based on time evolution analysis of sonoporation, detailed information was extracted from the model for analysis, including volume expansion ratio of the bubble, areal expansion ratio of the cell, jet velocity and CP displacement. Parametric studies were carried out, revealing the influence of different ultrasound parameters (i.e., driving frequency and acoustic pressure) and geometrical configurations (i.e., bubble-cell distance and initial bubble radius). This model could become a powerful tool not only for understanding bubble-cell interactions, but also for optimizing the strategy of sonoporation, such that it could be safer and of higher efficiency for biological and medical studies especially in clinics. Copyright © 2017 Elsevier B.V. All rights reserved.
NASA Astrophysics Data System (ADS)
Kim, So Gu
2013-12-01
On March 26, 2010 an underwater explosion (UWE) led to the sinking of the ROKS Cheonan. The official Multinational Civilian-Military Joint Investigation Group (MCMJIG) report concluded that the cause of the underwater explosion was a 250 kg net explosive weight (NEW) detonation at a depth of 6-9 m from a DPRK "CHT-02D" torpedo. Kim and Gitterman (2012a) determined the NEW and seismic magnitude as 136 kg at a depth of approximately 8m and 2.04, respectively using basic hydrodynamics based on theoretical and experimental methods as well as spectral analysis and seismic methods. The purpose of this study was to clarify the cause of the UWE via more detailed methods using bubble dynamics and simulation of propellers as well as forensic seismology. Regarding the observed bubble pulse period of 0.990 s, 0.976 s and 1.030 s were found in case of a 136 NEW at a detonation depth of 8 m using the boundary element method (BEM) and 3D bubble shape simulations derived for a 136 kg NEW detonation at a depth of 8 m approximately 5 m portside from the hull centerline. Here we show through analytical equations, models and 3D bubble shape simulations that the most probable cause of this underwater explosion was a 136 kg NEW detonation at a depth of 8m attributable to a ROK littoral "land control" mine (LCM).
Silencing near tRNA genes is nucleosome-mediated and distinct from boundary element function
Good, Paul D.; Kendall, Ann; Ignatz-Hoover, James; Miller, Erin L.; Pai, Dave A.; Rivera, Sara R.; Carrick, Brian; Engelke, David R.
2013-01-01
Transfer RNA (tRNA) genes and other RNA polymerase III transcription units are dispersed in high copy throughout nuclear genomes, and can antagonize RNA polymerase II transcription in their immediate chromosomal locus. Previous work in Saccharomyces cerevisiae found that this local silencing required subnuclear clustering of the tRNA genes near the nucleolus. Here we show that the silencing also requires nucleosome participation, though the nature of the nucleosome interaction appears distinct from other forms of transcriptional silencing. Analysis of an extensive library of histone amino acid substitutions finds a large number of residues that affect the silencing, both in the histone N-terminal tails and on the nucleosome disk surface. The residues on the disk surfaces involved are largely distinct from those affecting other regulatory phenomena. Consistent with the large number of histone residues affecting tgm silencing, survey of chromatin modification mutations shows that several enzymes known to affect nucleosome modification and positioning are also required. The enzymes include an Rpd3 deacetylase complex, Hos1 deacetylase, Glc7 phosphatase, and the RSC nucleosome remodeling activity, but not multiple other activities required for other silencing forms or boundary element function at tRNA gene loci. Models for communication between the tRNA gene transcription complexes and local chromatin are discussed. PMID:23707796
Silencing near tRNA genes is nucleosome-mediated and distinct from boundary element function.
Good, Paul D; Kendall, Ann; Ignatz-Hoover, James; Miller, Erin L; Pai, Dave A; Rivera, Sara R; Carrick, Brian; Engelke, David R
2013-08-15
Transfer RNA (tRNA) genes and other RNA polymerase III transcription units are dispersed in high copy throughout nuclear genomes, and can antagonize RNA polymerase II transcription in their immediate chromosomal locus. Previous work in Saccharomyces cerevisiae found that this local silencing required subnuclear clustering of the tRNA genes near the nucleolus. Here we show that the silencing also requires nucleosome participation, though the nature of the nucleosome interaction appears distinct from other forms of transcriptional silencing. Analysis of an extensive library of histone amino acid substitutions finds a large number of residues that affect the silencing, both in the histone N-terminal tails and on the nucleosome disk surface. The residues on the disk surfaces involved are largely distinct from those affecting other regulatory phenomena. Consistent with the large number of histone residues affecting tgm silencing, survey of chromatin modification mutations shows that several enzymes known to affect nucleosome modification and positioning are also required. The enzymes include an Rpd3 deacetylase complex, Hos1 deacetylase, Glc7 phosphatase, and the RSC nucleosome remodeling activity, but not multiple other activities required for other silencing forms or boundary element function at tRNA gene loci. Models for communication between the tRNA gene transcription complexes and local chromatin are discussed. Copyright © 2013 Elsevier B.V. All rights reserved.
High-speed laminar-turbulent boundary layer transition induced by a discrete roughness element
NASA Astrophysics Data System (ADS)
Iyer, Prahladh; Mahesh, Krishnan
2013-11-01
Direct numerical simulation (DNS) is used to study laminar to turbulent transition induced by a discrete hemispherical roughness element in a high-speed laminar boundary layer. The simulations are performed under conditions matching the experiments of Danehy et al. (AIAA Paper 2009-394, 2009) for free-stream Mach numbers of 3.37, 5.26 and 8.23. It is observed that the Mach 8.23 flow remains laminar downstream of the roughness, while the lower Mach numbers undergo transition. The Mach 3.37 flow undergoes transition closer to the bump when compared with Mach 5.26, in agreement with experimental observations. Transition is accompanied by an increase in Cf and Ch (Stanton number). Even for the case that did not undergo transition (Mach 8.23), streamwise vortices induced by the roughness cause a significant rise in Cf until 20 D downstream. The mean van Driest transformed velocity and Reynolds stress for Mach 3.37 and 5.26 show good agreement with available data. A local Reynolds number based on the wall properties is seen to correlate with the onset of transition for the cases considered. Partially supported by NASA.
A finite element method for the computation of transonic flow past airfoils
NASA Technical Reports Server (NTRS)
Eberle, A.
1980-01-01
A finite element method for the computation of the transonic flow with shocks past airfoils is presented using the artificial viscosity concept for the local supersonic regime. Generally, the classic element types do not meet the accuracy requirements of advanced numerical aerodynamics requiring special attention to the choice of an appropriate element. A series of computed pressure distributions exhibits the usefulness of the method.
MPSalsa a finite element computer program for reacting flow problems. Part 2 - user`s guide
Salinger, A.; Devine, K.; Hennigan, G.; Moffat, H.
1996-09-01
This manual describes the use of MPSalsa, an unstructured finite element (FE) code for solving chemically reacting flow problems on massively parallel computers. MPSalsa has been written to enable the rigorous modeling of the complex geometry and physics found in engineering systems that exhibit coupled fluid flow, heat transfer, mass transfer, and detailed reactions. In addition, considerable effort has been made to ensure that the code makes efficient use of the computational resources of massively parallel (MP), distributed memory architectures in a way that is nearly transparent to the user. The result is the ability to simultaneously model both three-dimensional geometries and flow as well as detailed reaction chemistry in a timely manner on MT computers, an ability we believe to be unique. MPSalsa has been designed to allow the experienced researcher considerable flexibility in modeling a system. Any combination of the momentum equations, energy balance, and an arbitrary number of species mass balances can be solved. The physical and transport properties can be specified as constants, as functions, or taken from the Chemkin library and associated database. Any of the standard set of boundary conditions and source terms can be adapted by writing user functions, for which templates and examples exist.
Evaluation of several non-reflecting computational boundary conditions for duct acoustics
NASA Technical Reports Server (NTRS)
Watson, Willie R.; Zorumski, William E.; Hodge, Steve L.
1994-01-01
Several non-reflecting computational boundary conditions that meet certain criteria and have potential applications to duct acoustics are evaluated for their effectiveness. The same interior solution scheme, grid, and order of approximation are used to evaluate each condition. Sparse matrix solution techniques are applied to solve the matrix equation resulting from the discretization. Modal series solutions for the sound attenuation in an infinite duct are used to evaluate the accuracy of each non-reflecting boundary conditions. The evaluations are performed for sound propagation in a softwall duct, for several sources, sound frequencies, and duct lengths. It is shown that a recently developed nonlocal boundary condition leads to sound attenuation predictions considerably more accurate for short ducts. This leads to a substantial reduction in the number of grid points when compared to other non-reflecting conditions.
A numerical method for computing unsteady 2-D boundary layer flows
NASA Technical Reports Server (NTRS)
Krainer, Andreas
1988-01-01
A numerical method for computing unsteady two-dimensional boundary layers in incompressible laminar and turbulent flows is described and applied to a single airfoil changing its incidence angle in time. The solution procedure adopts a first order panel method with a simple wake model to solve for the inviscid part of the flow, and an implicit finite difference method for the viscous part of the flow. Both procedures integrate in time in a step-by-step fashion, in the course of which each step involves the solution of the elliptic Laplace equation and the solution of the parabolic boundary layer equations. The Reynolds shear stress term of the boundary layer equations is modeled by an algebraic eddy viscosity closure. The location of transition is predicted by an empirical data correlation originating from Michel. Since transition and turbulence modeling are key factors in the prediction of viscous flows, their accuracy will be of dominant influence to the overall results.
NASA Technical Reports Server (NTRS)
Erb, R. B. (Principal Investigator)
1973-01-01
The author has identified the following significant results. An objective technique was developed to measure the surface area of water bodies. Nineteen water bodies in the Houston and Galveston, Texas area were selected as a basis for the technique development. The actual surface area of each body was determined from rectified and enlarged NASA aircraft photography. A clustering algorithm was used to produce classification maps of the region from ERTS-1 data. Certain classes were identified as being 100% water. Other classes were identified as being mixtures of water with land or vegetation. The number of picture elements falling on each water body and its boundary were counted. A linear regression analysis was performed to relate the total number of picture elements and boundary elements counted to the actual surface area. The standard error of the estimate was 6.7 acres. The absolute error was not a function of the actual surface area of the water body.
Adaptive finite element simulation of flow and transport applications on parallel computers
NASA Astrophysics Data System (ADS)
Kirk, Benjamin Shelton
design and to demonstrate the capability for resolving complex multiscale processes efficiently and reliably. The first application considered is the simulation of chemotactic biological systems such as colonies of Escherichia coli. This work appears to be the first application of AMR to chemotactic processes. These systems exhibit transient, highly localized features and are important in many biological processes, which make them ideal for simulation with adaptive techniques. A nonlinear reaction-diffusion model for such systems is described and a finite element formulation is developed. The solution methodology is described in detail. Several phenomenological studies are conducted to study chemotactic processes and resulting biological patterns which use the parallel adaptive refinement capability developed in this work. The other application study is much more extensive and deals with fine scale interactions for important hypersonic flows arising in aerospace applications. These flows are characterized by highly nonlinear, convection-dominated flowfields with very localized features such as shock waves and boundary layers. These localized features are well-suited to simulation with adaptive techniques. A novel treatment of the inviscid flux terms arising in a streamline-upwind Petrov-Galerkin finite element formulation of the compressible Navier-Stokes equations is also presented and is found to be superior to the traditional approach. The parallel adaptive finite element formulation is then applied to several complex flow studies, culminating in fully three-dimensional viscous flows about complex geometries such as the Space Shuttle Orbiter. Physical phenomena such as viscous/inviscid interaction, shock wave/boundary layer interaction, shock/shock interaction, and unsteady acoustic-driven flowfield response are considered in detail. A computational investigation of a 25°/55° double cone configuration details the complex multiscale flow features and investigates a
Computer simulation of diffractive optical element (DOE) performance
NASA Astrophysics Data System (ADS)
Delacour, Jacques F.; Venturino, Jean-Claude; Gouedard, Yannick
2004-02-01
Diffractive optical elements (DOE), also known as computer generated holograms (CGH), can transform an illuminating laser beam into a specified intensity distribution by diffraction rather than refraction or reflection. These are widely used in coherent light systems with beam shaping purposes, as an alignment tool or as a structured light generator. The diffractive surface is split into an array of sub-wavelength depth cells. Each of these locally transforms the beam by phase adaptation. Based on the work of the LSP lab from the University of Strasbourg, France, we have developed a unique industry-oriented tool. It allows the user first to optimize a DOE using the Gerchberg-Saxton algorithm. This part can manage sources from the simple plane wave to high order Gaussian modes or complex maps defined beams and objective patterns based on BMP images. A simulation part permits then to test the performance of the DOE with regard to system parameters, dealing with the beam, the DOE itself and the system organization. This will meet the needs of people concerned by tolerancing issues. Focusing on the industrial problem of beam shaping, we will present the whole DOE design sequence, starting from the generation of a DOE up to the study of the sensitivity of its performance according to the variation of several parameters of the system. For example, we will show the influence of the position of the beam on diffraction efficiency. This unique feature formerly neglected in industrial design process will lead the way to production quality improvement.
Valero, C.; Javierre, E.; García-Aznar, J. M.; Gómez-Benito, M. J.
2015-01-01
SUMMARY Wound healing is a process driven by biochemical and mechanical variables in which new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Due to the regularity of this morphology, we approximate the evolution of the wound through its cross-section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem while maintaining allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the non-linear problem we use the Finite Element Method and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds. PMID:24443355
Valero, C; Javierre, E; García-Aznar, J M; Gómez-Benito, M J
2014-06-01
Wound healing is a process driven by biochemical and mechanical variables in which a new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work, we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Because of the regularity of this morphology, we approximate the evolution of the wound through its cross section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem; while allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction, we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the nonlinear problem, we use the finite element method (FEM) and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds. Copyright © 2014 John Wiley & Sons, Ltd.
NASA Astrophysics Data System (ADS)
Franzoni, Linda P.; Duvall, Tracy A.
2005-09-01
In the high-frequency limit, vibrating panels subject to spatially random, temporally broadband forcing are shown to have broadband power and directivity properties than can be characterized by a limited set of parameters, based on numerical simulations. The radiated pressure field is parametrized in terms of direction, wave speed ratio, panel damping, and dimensionless frequency. A source directivity equation dependent on these variables is presented. The radiation properties of this equation are incorporated to simulate vibrating wall panels in an energy/intensity-based boundary-element method (BEM) developed for the prediction of steady-state, broadband, reverberant sound fields in enclosures having either diffusely or specularly reflecting boundaries. The BEM method uses uncorrelated broadband directional intensity sources to construct the source and reflection sound fields and predict mean-square pressure distributions in enclosures. Because uncorrelated broadband directional intensity sources are used, the system does not require a frequency-by-frequency-based solution, thereby reducing computational expense. Simulations are compared to exact solutions obtained by computationally expensive frequency-by-frequency modal methods. When fully developed, the directed application of this method is aircraft interior noise caused by exterior boundary layer excitation on fuselage panels.
Global Artificial Boundary Conditions for Computation of External Flow Problems with Propulsive Jets
NASA Technical Reports Server (NTRS)
Tsynkov, Semyon; Abarbanel, Saul; Nordstrom, Jan; Ryabenkii, Viktor; Vatsa, Veer
1998-01-01
We propose new global artificial boundary conditions (ABC's) for computation of flows with propulsive jets. The algorithm is based on application of the difference potentials method (DPM). Previously, similar boundary conditions have been implemented for calculation of external compressible viscous flows around finite bodies. The proposed modification substantially extends the applicability range of the DPM-based algorithm. In the paper, we present the general formulation of the problem, describe our numerical methodology, and discuss the corresponding computational results. The particular configuration that we analyze is a slender three-dimensional body with boat-tail geometry and supersonic jet exhaust in a subsonic external flow under zero angle of attack. Similarly to the results obtained earlier for the flows around airfoils and wings, current results for the jet flow case corroborate the superiority of the DPM-based ABC's over standard local methodologies from the standpoints of accuracy, overall numerical performance, and robustness.
NASA Astrophysics Data System (ADS)
Licata, Nicholas A.; Fuller, Nathaniel J.
Understanding the physical mechanisms by which an individual cell interacts with its environment often requires detailed information about the fluid in which the cell is immersed. Mass transport between the interior of the cell and the external environment is influenced by the flow of the extracellular fluid and the molecular diffusivity. Analytical calculations of the flow field are challenging in simple geometries, and not generally available in more realistic cases with irregular domain boundaries. Motivated by these problems, we discuss the numerical solution of Stokes equation by implementing a Gauss-Seidel algorithm on a staggered computational grid. The computed velocity profile is used as input to numerically solve the advection-diffusion equation for mass transport. Special attention is paid to the case of two-dimensional flows at large Péclet number. The numerical results are compared with a perturbative analytical treatment of the concentration boundary layer.
NASA Astrophysics Data System (ADS)
Ren, Zhengyong; Kalscheuer, Thomas; Greenhalgh, Stewart; Maurer, Hansruedi
2013-02-01
We have developed a generalized and stable surface integral formula for 3-D uniform inducing field and plane wave electromagnetic induction problems, which works reliably over a wide frequency range. Vector surface electric currents and magnetic currents, scalar surface electric charges and magnetic charges are treated as the variables. This surface integral formula is successfully applied to compute the electromagnetic responses of 3-D topography to low frequency magnetotelluric and high frequency radio-magnetotelluric fields. The standard boundary element method which is used to solve this surface integral formula quickly exceeds the memory capacity of modern computers for problems involving hundreds of thousands of unknowns. To make the surface integral formulation applicable and capable of dealing with large-scale 3-D geo-electromagnetic problems, we have developed a matrix-free adaptive multilevel fast multipole boundary element solver. By means of the fast multipole approach, the time-complexity of solving the final system of linear equations is reduced to O(m log m) and the memory cost is reduced to O(m), where m is the number of unknowns. The analytical solutions for a half-space model were used to verify our numerical solutions over the frequency range 0.001-300 kHz. In addition, our numerical solution shows excellent agreement with a published numerical solution for an edge-based finite-element method on a trapezoidal hill model at a frequency of 2 Hz. Then, a high frequency simulation for a similar trapezoidal hill model was used to study the effects of displacement currents in the radio-magnetotelluric frequency range. Finally, the newly developed algorithm was applied to study the effect of moderate topography and to evaluate the applicability of a 2-D RMT inversion code that assumes a flat air-Earth interface, on RMT field data collected at Smørgrav, southern Norway. This paper constitutes the first part of a hybrid boundary element-finite element
NASA Astrophysics Data System (ADS)
Alam Khan, Najeeb; Razzaq, Oyoon Abdul
2016-03-01
In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.
Computational Fluid Dynamics of the Boundary Layer Characteristics of a Pacific Bluefin Tuna
2015-09-18
subtracted from the cube using a Boolean operation. The same meshing procedure was employed on the surface of the cube and the meshed interface between the...advanced propulsion mechanism (or both). The issue of whether the boundary layer on a tuna swimming at typical speeds (1 to 2 body lengths/sec) is laminar...compute the approximate lateral location at which transition to turbulence occurs on the tuna for various swimming speeds, and to determine the maximum
Boundary condition computational procedures for inviscid, supersonic steady flow field calculations
NASA Technical Reports Server (NTRS)
Abbett, M. J.
1971-01-01
Results are given of a comparative study of numerical procedures for computing solid wall boundary points in supersonic inviscid flow calculatons. Twenty five different calculation procedures were tested on two sample problems: a simple expansion wave and a simple compression (two-dimensional steady flow). A simple calculation procedure was developed. The merits and shortcomings of the various procedures are discussed, along with complications for three-dimensional and time-dependent flows.
REM (relative element magnitude): program explanation and computer program listing
VanTrump, George; Alminas, Henry V.
1978-01-01
The REM (relative element magnitude) program is designed as an aid in the characterization of geochemical anomalies. The program ranks the magnitudes of anomalies of individual elements within a multielement geochemical anomaly.
Barrett, Richard Frederick; Heroux, Michael Allen; Vaughan, Courtenay Thomas
2012-04-01
A broad range of scientific computation involves the use of difference stencils. In a parallel computing environment, this computation is typically implemented by decomposing the spacial domain, inducing a 'halo exchange' of process-owned boundary data. This approach adheres to the Bulk Synchronous Parallel (BSP) model. Because commonly available architectures provide strong inter-node bandwidth relative to latency costs, many codes 'bulk up' these messages by aggregating data into a message as a means of reducing the number of messages. A renewed focus on non-traditional architectures and architecture features provides new opportunities for exploring alternatives to this programming approach. In this report we describe miniGhost, a 'miniapp' designed for exploration of the capabilities of current as well as emerging and future architectures within the context of these sorts of applications. MiniGhost joins the suite of miniapps developed as part of the Mantevo project.
Shen, Yongxing; Lee, Minhwan; Lee, Wonyoung; Barnett, David M; Pinsky, Peter M; Prinz, Friedrich B
2008-01-23
Electrostatic force microscopy (EFM) is a special design of non-contact atomic force microscopy used for detecting electrostatic interactions between the probe tip and the sample. Its resolution is limited by the finite probe size and the long-range characteristics of electrostatic forces. Therefore, quantitative analysis is crucial to understanding the relationship between the actual local surface potential distribution and the quantities obtained from EFM measurements. To study EFM measurements on bimetallic samples with surface potential inhomogeneities as a special case, we have simulated such measurements using the boundary element method and calculated the force component and force gradient component that would be measured by amplitude modulation (AM) EFM and frequency modulation (FM) EFM, respectively. Such analyses have been performed for inhomogeneities of various shapes and sizes, for different tip-sample separations and tip geometries, for different applied voltages, and for different media (e.g., vacuum or water) in which the experiment is performed. For a sample with a surface potential discontinuity, the FM-EFM resolution expression agrees with the literature; however, the simulation for AM-EFM suggests the existence of an optimal tip radius of curvature in terms of resolution. On the other hand, for samples with strip- and disk-shaped surface potential inhomogeneities, we have obtained quantitative expressions for the detectability size requirements as a function of experimental conditions for both AM- and FM-EFMs, which suggest that a larger tip radius of curvature is moderately favored for detecting the presence of such inhomogeneities.
NASA Astrophysics Data System (ADS)
Hoppe, R. H. W.; Linsenmann, C.
2012-05-01
The immersed boundary method (IB) is known as a powerful technique for the numerical solution of fluid-structure interaction problems as, for instance, the motion and deformation of viscoelastic bodies immersed in an external flow. It is based on the treatment of the flow equations within an Eulerian framework and of the equations of motion of the immersed bodies with respect to a Lagrangian coordinate system including interaction equations providing the transfer between both frames. The classical IB uses finite differences, but the IBM can be set up within a finite element approach in the spatial variables as well (FE-IB). The discretization in time usually relies on the Backward Euler (BE) method for the semidiscretized flow equations and the Forward Euler (FE) method for the equations of motion of the immersed bodies. The BE/FE FE-IB is subject to a CFL-type condition, whereas the fully implicit BE/BE FE-IB is unconditionally stable. The latter one can be solved numerically by Newton-type methods whose convergence properties are dictated by an appropriate choice of the time step size, in particular, if one is faced with sudden changes in the total energy of the system. In this paper, taking advantage of the well developed affine covariant convergence theory for Newton-type methods, we study a predictor-corrector continuation strategy in time with an adaptive choice of the continuation steplength. The feasibility of the approach and its superiority to BE/FE FE-IB is illustrated by two representative numerical examples.
NASA Astrophysics Data System (ADS)
Liu, X.
2013-12-01
In many natural and human-impacted rivers, the porous sediment beds are either fully or partially covered by large roughness elements, such as gravels and boulders. The existence of these large roughness elements, which are in direct contact with the turbulent river flow, changes the dynamics of mass and momentum transfer across the river bed. It also impacts the overall hydraulics in the river channel and over time, indirectly influences the geomorphological evolution of the system. Ideally, one should resolve each of these large roughness elements in a computational fluid model. This approach is apparently not feasible due to the prohibitive computational cost. Considering a typical river bed with armoring, the distribution of sediment sizes usually shows significant vertical variations. Computationally, it poses great challenge to resolve all the size scales. Similar multiscale problem exists in the much broader porous media flow field. To cope with this, we propose a hybrid computational approach where the large surface roughness elements are resolved using immersed boundary method and sediment layers below (usually finer) are modeled by adding extra drag terms in momentum equations. Large roughness elements are digitized using a 3D laser scanner. They are put into the computational domain using the collision detection and rigid body dynamics algorithms which guarantees realistic and physically-correct spatial arrangement of the surface elements. Simulation examples have shown the effectiveness of the hybrid approach which captures the effect of the surface roughness on the turbulent flow as well as the hyporheic flow pattern in and out of the bed.
NASA Astrophysics Data System (ADS)
Ovcharova, Nina
2017-01-01
In this paper, we couple regularization techniques of nondifferentiable optimization with the h-version of the boundary element method (h-BEM) to solve nonsmooth variational problems arising in contact mechanics. As a model example we consider the delamination problem. The variational formulation of this problem leads to a hemivariational inequality (HVI)with a nonsmooth functional defined on the contact boundary. This problem is first regularized and then discretized by a h-BEM. We prove convergence of the h-BEM Galerkin solution of the regularized problem in the energy norm, provide an a-priori error estimate and give a numerical example.
Computation of sharp-fin-induced shockwave/turbulent boundary layer interactions
NASA Technical Reports Server (NTRS)
Horstman, C. C.
1986-01-01
Solutions of the Reynolds-averaged Navier-Stokes equations are presented and are compared with a family of experimental results for the three-dimensional interaction of a sharp-fin-induced shock wave with a turbulent boundary layer. The solutions predict most of the essential features of the flow fields for various shock-wave strengths. However, some features of the measured flow fields, such as secondary separation and size of the largest separated zones were not accurately computed. The computed flow fields, aided by particle tracing techniques, display a prominent vortical structure which can be correlated with the observed surface phenomena.
Pseudo-organ boundary conditions applied to a computational fluid dynamics model of the human aorta.
Yull Park, Joong; Young Park, Chan; Mo Hwang, Chang; Sun, Kyung; Goo Min, Byoung
2007-08-01
In three-dimensional numerical studies of the aorta, it is difficult to apply proper boundary conditions at the end of each major aortic branch because of interactions between blood and organs. Organs and body parts were assumed to be likened to cylindrically shaped porous media, so-called pseudo-organs, and treated in the computational domain as forms of hemodynamic resistance. Permeability functions were determined from two-dimensional axisymmetric computations of each aortic branch and these functions were then used in an unsteady three-dimensional simulation of the complete aorta. Substantially accurate cardiac output (5.91 L/min) and blood distributions to the major branches were predicted.
NASA Technical Reports Server (NTRS)
Cebeci, T.; Carr, L. W.
1978-01-01
A computer program is described which provides solutions of two dimensional equations appropriate to laminar and turbulent boundary layers for boundary conditions with an external flow which fluctuates in magnitude. The program is based on the numerical solution of the governing boundary layer equations by an efficient two point finite difference method. An eddy viscosity formulation was used to model the Reynolds shear stress term. The main features of the method are briefly described and instructions for the computer program with a listing are provided. Sample calculations to demonstrate its usage and capabilities for laminar and turbulent unsteady boundary layers with an external flow which fluctuated in magnitude are presented.
Glass, Micheal W.; Hogan, Roy E., Jr.; Gartling, David K.
2010-03-01
The need for the engineering analysis of systems in which the transport of thermal energy occurs primarily through a conduction process is a common situation. For all but the simplest geometries and boundary conditions, analytic solutions to heat conduction problems are unavailable, thus forcing the analyst to call upon some type of approximate numerical procedure. A wide variety of numerical packages currently exist for such applications, ranging in sophistication from the large, general purpose, commercial codes, such as COMSOL, COSMOSWorks, ABAQUS and TSS to codes written by individuals for specific problem applications. The original purpose for developing the finite element code described here, COYOTE, was to bridge the gap between the complex commercial codes and the more simplistic, individual application programs. COYOTE was designed to treat most of the standard conduction problems of interest with a user-oriented input structure and format that was easily learned and remembered. Because of its architecture, the code has also proved useful for research in numerical algorithms and development of thermal analysis capabilities. This general philosophy has been retained in the current version of the program, COYOTE, Version 5.0, though the capabilities of the code have been significantly expanded. A major change in the code is its availability on parallel computer architectures and the increase in problem complexity and size that this implies. The present document describes the theoretical and numerical background for the COYOTE program. This volume is intended as a background document for the user's manual. Potential users of COYOTE are encouraged to become familiar with the present report and the simple example analyses reported in before using the program. The theoretical and numerical background for the finite element computer program, COYOTE, is presented in detail. COYOTE is designed for the multi-dimensional analysis of nonlinear heat conduction problems
Solution of elastic-plastic shallow shell problems by the boundary element method
NASA Astrophysics Data System (ADS)
Xiaolin, Peng
1987-02-01
The boundary integral equations for elasto-plastic problems of shallow shells are established by using the fundamental solutions of shallow shells derived previously. The strains and stress-resultants in the plastic region are used as unknown variables. The simultaneous nonlinear equations of these variables and unknown boundary values are established and solved by direct iteration method.
Cooper, Christopher D; Bardhan, Jaydeep P; Barba, L A
2014-03-01
The continuum theory applied to biomolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known apbs finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2% in solvation energy, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the apbs solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe code is in the order of 1-2% error, when running on one gpu card (nvidia Tesla C2075), compared with apbs running on six Intel Xeon cpu cores. PyGBe achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using gpus via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license.
Computation of incompressible viscous flows through artificial heart devices with moving boundaries
NASA Technical Reports Server (NTRS)
Kiris, Cetin; Rogers, Stuart; Kwak, Dochan; Chang, I.-DEE
1991-01-01
The extension of computational fluid dynamics techniques to artificial heart flow simulations is illustrated. Unsteady incompressible Navier-Stokes equations written in 3-D generalized curvilinear coordinates are solved iteratively at each physical time step until the incompressibility condition is satisfied. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. The efficiency and robustness of the time accurate formulation of the algorithm are tested by computing the flow through model geometries. A channel flow with a moving indentation is computed and validated with experimental measurements and other numerical solutions. In order to handle the geometric complexity and the moving boundary problems, a zonal method and an overlapping grid embedding scheme are used, respectively. Steady state solutions for the flow through a tilting disk heart valve was compared against experimental measurements. Good agreement was obtained. The flow computation during the valve opening and closing is carried out to illustrate the moving boundary capability.
NASA Technical Reports Server (NTRS)
Jin, Jian-Ming; Volakis, John L.
1990-01-01
A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is employed to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.
NASA Astrophysics Data System (ADS)
Kalatehjari, R.; Liou, T. S.
2016-12-01
Carrying out numerical simulations of fluid flow and solute transport in an interconnected discrete fracture network (DFN) is computationally demanding. However, the efficiency of simulation can be greatly enhanced if DFN can be properly converted into equivalent continuous porous medium (ECPM). In this study, a new upscaling algorithm using boundary element method (BEM) and volume averaging method is developed and used in steady-state flow field to convert DFN into ECPM. Considering a grid of favorable size in a low-permeable fractured rock, fractures are meshed by triangular elements. Initial head and velocity at boundary nodes of each fracture are achieved by applying boundary conditions. Assuming steady-state flow, a system of linear equations is then developed based on BEM to obtain head distribution in fracture planes by iterative calculation. The calculated head values at mesh nodes are then employed to find the velocity field. Finally, volume-averaged Darcy velocity and head gradient of the grid are applied to develop a system of linear equations for upscaling calculation. The minimum number of sufficient flow simulations to solve the over-determined system of linear equations is defined by evaluating the mass balance error. The solution is expressed in terms of heterogeneous and anisotropic block permeability tensors. A computer code was developed by Matlab to satisfy the calculation and visualization purposes. Benchmark examples were successfully verified to demonstrate the robustness of this method. In addition, a stochastic DFN model was analyzed to validate the functionality of the method in real case. To verify the results of this case, FracMan V7.5 was used to generate stochastic DFN model and flow simulations within the grid were solved by its internal MAFIC tool. A comparison of the results in terms of mass conservation and velocity field successfully verified the application of the proposed upscaling algorithm for low-permeability fractured rock.
NASA Technical Reports Server (NTRS)
Cebeci, T.; Kaups, K.; Ramsey, J. A.
1977-01-01
A computer program for calculating three dimensional compressible laminar and turbulent boundary layers on arbitrary wings is described and presented. The computer program consists of three separate programs, namely, a geometry program to represent the wing analytically, a velocity program to compute the external velocity components from a given experimental pressure distribution and a finite difference boundary layer method to solve the governing equations for compressible flows. To illustrate the usage of the computer program, three different test cases are presented and the preparation of the input data as well as the computed output data is discussed in some detail.
Bennett, J.P.; Wetmore, C.M.
1999-01-01
Four species of lichen (Cladina rangiferina, Evernia mesomorpha, Hypogymnia physodes, and Parmelia sulcata) were sampled at six locations in the Boundary Waters Canoe Area Wilderness three times over a span of 11 years and analyzed for concentrations of 16 chemical elements to test the hypotheses that corticolous species would accumulate higher amounts of chemical elements than terricolous species, and that 11 years were sufficient to detect spatial patterns and temporal trends in element contents. Multivariate analyses of over 2770 data points revealed two principal components that accounted for 68% of the total variance in the data. These two components, the first highly loaded with Al, B, Cr, Fe, Ni and S, and the second loaded with Ca, Cd, Mg and Mn, were inversely related to each other over time and space. The first component was interpreted as consisting of an anthropogenic and a dust component, while the second, primarily a nutritional component. Cu, K, Na, P, Pb and Zn were not highly loaded on either component. Component 1 decreased significantly over the 11 years and from west to east, while component 2 increased. The corticolous species were more enriched in heavy metals than the terricolous species. All four elements in component 2 in H. physodes were above enrichment thresholds for this species. Species differences on the two components were greater than the effects of time and space, suggesting that biomonitoring with lichens is strongly species dependent. Some localities in the Boundary Waters Canoe Area Wilderness appear enriched in some anthropogenic elements for no obvious reasons.
Assessment of Turbulent Shock-Boundary Layer Interaction Computations Using the OVERFLOW Code
NASA Technical Reports Server (NTRS)
Oliver, A. B.; Lillard, R. P.; Schwing, A. M.; Blaisdell, G> A.; Lyrintzis, A. S.
2007-01-01
The performance of two popular turbulence models, the Spalart-Allmaras model and Menter s SST model, and one relatively new model, Olsen & Coakley s Lag model, are evaluated using the OVERFLOWcode. Turbulent shock-boundary layer interaction predictions are evaluated with three different experimental datasets: a series of 2D compression ramps at Mach 2.87, a series of 2D compression ramps at Mach 2.94, and an axisymmetric coneflare at Mach 11. The experimental datasets include flows with no separation, moderate separation, and significant separation, and use several different experimental measurement techniques (including laser doppler velocimetry (LDV), pitot-probe measurement, inclined hot-wire probe measurement, preston tube skin friction measurement, and surface pressure measurement). Additionally, the OVERFLOW solutions are compared to the solutions of a second CFD code, DPLR. The predictions for weak shock-boundary layer interactions are in reasonable agreement with the experimental data. For strong shock-boundary layer interactions, all of the turbulence models overpredict the separation size and fail to predict the correct skin friction recovery distribution. In most cases, surface pressure predictions show too much upstream influence, however including the tunnel side-wall boundary layers in the computation improves the separation predictions.
Smith, Emily M.; Lajoie, Bryan R.; Jain, Gaurav; Dekker, Job
2016-01-01
Three-dimensional genome structure plays an important role in gene regulation. Globally, chromosomes are organized into active and inactive compartments while, at the gene level, looping interactions connect promoters to regulatory elements. Topologically associating domains (TADs), typically several hundred kilobases in size, form an intermediate level of organization. Major questions include how TADs are formed and how they are related to looping interactions between genes and regulatory elements. Here we performed a focused 5C analysis of a 2.8 Mb chromosome 7 region surrounding CFTR in a panel of cell types. We find that the same TAD boundaries are present in all cell types, indicating that TADs represent a universal chromosome architecture. Furthermore, we find that these TAD boundaries are present irrespective of the expression and looping of genes located between them. In contrast, looping interactions between promoters and regulatory elements are cell-type specific and occur mostly within TADs. This is exemplified by the CFTR promoter that in different cell types interacts with distinct sets of distal cell-type-specific regulatory elements that are all located within the same TAD. Finally, we find that long-range associations between loci located in different TADs are also detected, but these display much lower interaction frequencies than looping interactions within TADs. Interestingly, interactions between TADs are also highly cell-type-specific and often involve loci clustered around TAD boundaries. These data point to key roles of invariant TAD boundaries in constraining as well as mediating cell-type-specific long-range interactions and gene regulation. PMID:26748519
NASA Astrophysics Data System (ADS)
Barucq, H.; Bendali, A.; Fares, M.; Mattesi, V.; Tordeux, S.
2017-02-01
A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly its outstanding ability to reduce the instabilities known as the "pollution effect" in the literature on numerical simulations of long-range wave propagation.
Grouped element-by-element iteration schemes for incompressible flow computations
NASA Astrophysics Data System (ADS)
Tezduyar, T. E.; Liou, J.
1989-05-01
Grouped element-by-element (GEBE) iteration schemes for incompressible flows are presented in the context of vorticity- stream function formulation. The GEBE procedure is a variation of the EBE procedure and is based on arrangement of the elements into groups with no inter-element coupling within each group. With the GEBE approach, vectorization and parallel implementation of the EBE method becomes more clear. The savings in storage and CPU time are demonstrated with two unsteady flow problems.