Parallel computation using boundary elements in solid mechanics
NASA Technical Reports Server (NTRS)
Chien, L. S.; Sun, C. T.
1990-01-01
The inherent parallelism of the boundary element method is shown. The boundary element is formulated by assuming the linear variation of displacements and tractions within a line element. Moreover, MACSYMA symbolic program is employed to obtain the analytical results for influence coefficients. Three computational components are parallelized in this method to show the speedup and efficiency in computation. The global coefficient matrix is first formed concurrently. Then, the parallel Gaussian elimination solution scheme is applied to solve the resulting system of equations. Finally, and more importantly, the domain solutions of a given boundary value problem are calculated simultaneously. The linear speedups and high efficiencies are shown for solving a demonstrated problem on Sequent Symmetry S81 parallel computing system.
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.
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 consistent boundary quantities in finite element thermal-fluid solutions
NASA Technical Reports Server (NTRS)
Thornton, E. A.
1982-01-01
The consistent boundary quantity method for computing derived quantities from finite element nodal variable solutions is investigated. The method calculates consistent, continuous boundary surface quantities such as heat fluxes, flow velocities, and surface tractions from nodal variables such as temperatures, velocity potentials, and displacements. Consistent and lumped coefficient matrix solutions for such problems are compared. The consistent approach may produce more accurate boundary quantities, but spurious oscillations may be produced in the vicinity of discontinuities. The uncoupled computations of the lumped approach provide greater flexibility in dealing with discontinuities and provide increased computational efficiency. The consistent boundary quantity approach can be applied to solution boundaries other than those with Dirichlet boundary conditions, and provides more accurate results than the customary method of differentiation of interpolation polynomials.
An accurate quadrature technique for the contact boundary in 3D finite element computations
NASA Astrophysics Data System (ADS)
Duong, Thang X.; Sauer, Roger A.
2015-01-01
This paper presents a new numerical integration technique for 3D contact finite element implementations, focusing on a remedy for the inaccurate integration due to discontinuities at the boundary of contact surfaces. The method is based on the adaptive refinement of the integration domain along the boundary of the contact surface, and is accordingly denoted RBQ for refined boundary quadrature. It can be used for common element types of any order, e.g. Lagrange, NURBS, or T-Spline elements. In terms of both computational speed and accuracy, RBQ exhibits great advantages over a naive increase of the number of quadrature points. Also, the RBQ method is shown to remain accurate for large deformations. Furthermore, since the sharp boundary of the contact surface is determined, it can be used for various purposes like the accurate post-processing of the contact pressure. Several examples are presented to illustrate the new technique.
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.
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
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. PMID:19275294
Computation of the transient flow in zoned anisotropic porous media by the boundary element method
NASA Astrophysics Data System (ADS)
Bruch, E.; Grilli, S.
Results on the application of the BEM to transient two-dimensional flows in zoned anisotropic porous media are presented, including the iterative calculation of the free surface seepage position. The classical BEM equations are discretized by linear, quadratic, or cubic elements, employing special singular numerical quadrature rules. The method is improved by the incorporation of a subregion division. The present technique is shown to be very accurate and to avoid previously encountered oscillation problems.
Computing texture boundaries from images.
Voorhees, H; Poggio, T
1988-05-26
Recent computational and psychological theories of human texture vision assert that texture discrimination is based on first-order differences in geometric and luminance attributes of texture elements, called 'textons'. Significant differences in the density, orientation, size, or contrast of line segments or other small features in an image have been shown to cause immediate perception of texture boundaries. However, the psychological theories, which are based on the perception of synthetic images composed of lines and symbols, neglect two important issues. First, how can textons be computed from grey-level images of natural scenes? And second, how, exactly, can texture boundaries be found? Our analysis of these two issues has led to an algorithm that is fully implemented and which successfully detects boundaries in natural images. We propose that blobs computed by a centre-surround operator are useful as texture elements, and that a simple non-parametric statistic can be used to compare local distributions of blob attributes to locate texture boundaries. Although designed for natural images, our computation agrees with some psychophysical findings, in particular, those of Adelson and Bergen (described in the preceding article), which cast doubt on the hypothesis that line segment crossings or termination points are textons. PMID:3374570
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…
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 element and finite element coupling for aeroacoustics simulations
NASA Astrophysics Data System (ADS)
Balin, Nolwenn; Casenave, Fabien; Dubois, François; Duceau, Eric; Duprey, Stefan; Terrasse, Isabelle
2015-08-01
We consider the scattering of acoustic perturbations in the presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert transformation to recover the Helmholtz equation. The well-known setting of boundary element method for the Helmholtz equation is available. In the second zone, the flow quantities are space dependent, we have to consider a local resolution, namely the finite element method. Herein, we carry out the coupling of these two methods and present various applications and validation test cases. The source term is given through the decomposition of an incident acoustic field on a section of the computational domain's boundary. Validations against analytic, another numerical method and measurements on different test cases are 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.
NASA Astrophysics Data System (ADS)
Friedrich, J.
1999-08-01
As lecturers, our main concern and goal is to develop more attractive and efficient ways of communicating up-to-date scientific knowledge to our students and facilitate an in-depth understanding of physical phenomena. Computer-based instruction is very promising to help both teachers and learners in their difficult task, which involves complex cognitive psychological processes. This complexity is reflected in high demands on the design and implementation methods used to create computer-assisted learning (CAL) programs. Due to their concepts, flexibility, maintainability and extended library resources, object-oriented modeling techniques are very suitable to produce this type of pedagogical tool. Computational fluid dynamics (CFD) enjoys not only a growing importance in today's research, but is also very powerful for teaching and learning fluid dynamics. For this purpose, an educational PC program for university level called 'CFDLab 1.1' for Windows™ was developed with an interactive graphical user interface (GUI) for multitasking and point-and-click operations. It uses the dual reciprocity boundary element method as a versatile numerical scheme, allowing to handle a variety of relevant governing equations in two dimensions on personal computers due to its simple pre- and postprocessing including 2D Laplace, Poisson, diffusion, transient convection-diffusion.
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.
Symmetric Galerkin boundary formulations employing curved elements
NASA Technical Reports Server (NTRS)
Kane, J. H.; Balakrishna, C.
1993-01-01
Accounts of the symmetric Galerkin approach to boundary element analysis (BEA) have recently been published. This paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency. A new symmetric Galerkin theoretical formulation for both the (harmonic) heat conduction and the (biharmonic) elasticity problem that employs regularized singular and hypersingular boundary integral equations (BIEs) is presented. The novel use of regularized BIEs in the Galerkin context is shown to allow straightforward incorporation of curved, isoparametric elements. A symmetric reusable intrinsic sample point (RISP) numerical integration algorithm is shown to produce a Galerkin (i.e., double) integration strategy that is competitive with its counterpart (i.e., singular) integration procedure in the collocation BEA approach when the time saved in the symmetric equation solution phase is also taken into account. This new formulation is shown to be capable of employing hypersingular BIEs while obviating the requirement of C 1 continuity, a fact that allows the employment of the popular continuous element technology. The behavior of the symmetric Galerkin BEA method with regard to both direct and iterative equation solution operations is also addressed. A series of example problems are presented to quantify the performance of this symmetric approach, relative to the more conventional unsymmetric BEA, in terms of both accuracy and efficiency. It is concluded that appropriate implementations of the symmetric Galerkin approach to BEA indeed have the potential to be competitive with, if not superior to, collocation-based BEA, for large-scale problems.
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.
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.
Computation of grain boundary stiffness and mobility from boundary fluctuations.
Hoyt, Jeffrey John; Foiles, Stephen Martin
2005-06-01
Grain boundary stiffness and mobility determine the kinetics of curvature-driven grain growth. Here the stiffness and mobility are computed using an analysis of fluctuations in the grain boundary position during molecular dynamics simulations. This work represents the first determination of grain boundary stiffness for a realistic three-dimensional system. The results indicate that the boundary stiffness for a given boundary plane has a strong dependence on the direction of the boundary distortion. The mobility deduced is comparable with that determined in previous computer simulation studies. The advantages and limitations of the fluctuation approach are discussed.
Finite element solution theory for three-dimensional boundary flows
NASA Technical Reports Server (NTRS)
Baker, A. J.
1974-01-01
A finite element algorithm is derived for the numerical solution of a three-dimensional flow field described by a system of initial-valued, elliptic boundary value partial differential equations. The familiar three-dimensional boundary layer equations belong to this description when diffusional processes in only one coordinate direction are important. The finite element algorithm transforms the original description into large order systems of ordinary differential equations written for the dependent variables discretized at node points of an arbitrarily irregular computational lattice. The generalized elliptic boundary conditions is piecewise valid for each dependent variable on boundaries that need not explicitly coincide with coordinate surfaces. Solutions for sample problems in laminar and turbulent boundary flows illustrate favorable solution accuracy, convergence, and versatility.
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., II; 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.
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.
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.
Gravity field determination using boundary element methods
NASA Astrophysics Data System (ADS)
Klees, Roland
1993-09-01
The Boundary Element Method (BEM), a numerical technique for solving boundary integral equations, is introduced to determine the earth's gravity field. After a short survey on its main principles, we apply this method to the fixed gravimetric boundary value problem (BVP), i.e. the determination of the earth's gravitational potential from measurements of the intensity of the gravity field in points on the earth's surface. We show how to linearize this nonlinear BVP using an implicit function theorem and how to transform the linearized BVP into a boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation into a linear system of equations. We discuss the major problems of this approach for setting up and solving the linear system. The BVP is numerically solved for a bounded part of the earth's surface using a high resolution reference gravity model, measured gravity values of high density, and a 50 ṡ 50 m2 digital terrain model to describe the earth's surface. We obtain a gravity field resolution of 1 ṡ 1 km2 with an accuracy of the order 10-3 to 10-4 in about 1 CPU-hour on a Siemens/Fujitsu SIMD vector pipeline machine using highly sophisticated numerical integration techniques and fast equation solvers. We conclude that BEM is a powerful numerical tool for solving boundary value problems and may be an alternative to classical geodetic techniques.
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.
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.
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.
NASA Technical Reports Server (NTRS)
Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.
1991-01-01
The present FEM technique addresses both linear and nonlinear boundary value problems encountered in computational physics by handling general three-dimensional regions, boundary conditions, and material properties. The box finite elements used are defined by a Cartesian grid independent of the boundary definition, and local refinements proceed by dividing a given box element into eight subelements. Discretization employs trilinear approximations on the box elements; special element stiffness matrices are included for boxes cut by any boundary surface. Illustrative results are presented for representative aerodynamics problems involving up to 400,000 elements.
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.
The scs' boundary element: characterization of boundary element-associated factors.
Hart, C M; Zhao, K; Laemmli, U K
1997-02-01
Boundary elements are thought to define the peripheries of chromatin domains and to restrict enhancer-promoter interactions to their target genes within their domains. We previously characterized a cDNA encoding the BEAF-32A protein (32A), which binds with high affinity to the scs' boundary element from the Drosophila melanogaster 87A7 hsp70 locus. Here, we report a second protein, BEAF-32B, that differs from 32A only in its amino terminus. Unlike 32A, it has the same DNA binding specificity as the complete BEAF activity affinity purified from Drosophila. We characterize three domains in these proteins. Heterocomplex formation is mediated by their identical carboxy-terminal domains, and DNA binding is mediated by their unique amino-terminal domains. The identical middle domains of 32A and 32B are dispensable for the functions described here, although they may be important for boundary element function. 32A and 32B apparently form trimers, and the ratio of 32A to 32B varies at different loci on polytene chromosomes as judged by immunofluorescence. The scs' element contains a high- and low-affinity binding site for BEAF. We observed that interaction with the low-affinity site is facilitated by binding to the high-affinity site some 200 bp distant. PMID:9001253
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.
Computer Aids Delineation Of Boundaries In Farmlands
NASA Technical Reports Server (NTRS)
Slyle, R.; Cheng, T.; Ma, M.; Angelici, G.
1992-01-01
Computer-aided stratification (CAS) procedure developmental procedure of image-processing computer equipment and programs partly automating delineation of boundaries between areas. These areas, "primary sampling units", are images of primarily agricultural lands composed by melding digital Landsat Thematic Mapper data and Digital Line Graph data from United States Geological Survey. CAS output data used as inputs for subsequent sampling procedures from which statistics on uses of agricultural lands developed.
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.
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.
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.
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
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.
NASA Technical Reports Server (NTRS)
Pates, Carl S., III
1991-01-01
A boundary element formulation, along with detailed solution procedure for determining the acoustic field inside a three-dimensional, rectangular duct is presented in this paper. The results of classical and boundary element solutions are compared for a typical rectangular duct by restricting the input frequency in such a way that only plane wave propagation is possible. The effect of changing the type and number of discrete boundary elements on the computed sound pressure levels inside the duct is also presented.
A Curved, Elastostatic Boundary Element for Plane Anisotropic Structures
NASA Technical Reports Server (NTRS)
Smeltzer, Stanley S.; Klang, Eric C.
2001-01-01
The plane-stress equations of linear elasticity are used in conjunction with those of the boundary element method to develop a novel curved, quadratic boundary element applicable to structures composed of anisotropic materials in a state of plane stress or plane strain. The curved boundary element is developed to solve two-dimensional, elastostatic problems of arbitrary shape, connectivity, and material type. As a result of the anisotropy, complex variables are employed in the fundamental solution derivations for a concentrated unit-magnitude force in an infinite elastic anisotropic medium. Once known, the fundamental solutions are evaluated numerically by using the known displacement and traction boundary values in an integral formulation with Gaussian quadrature. All the integral equations of the boundary element method are evaluated using one of two methods: either regular Gaussian quadrature or a combination of regular and logarithmic Gaussian quadrature. The regular Gaussian quadrature is used to evaluate most of the integrals along the boundary, and the combined scheme is employed for integrals that are singular. Individual element contributions are assembled into the global matrices of the standard boundary element method, manipulated to form a system of linear equations, and the resulting system is solved. The interior displacements and stresses are found through a separate set of auxiliary equations that are derived using an Airy-type stress function in terms of complex variables. The capabilities and accuracy of this method are demonstrated for a laminated-composite plate with a central, elliptical cutout that is subjected to uniform tension along one of the straight edges of the plate. Comparison of the boundary element results for this problem with corresponding results from an analytical model show a difference of less than 1%.
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.
Three dimensional boundary element solutions for eddy current nondestructive evaluation
NASA Astrophysics Data System (ADS)
Yang, Ming; Song, Jiming; Nakagawa, Norio
2014-02-01
The boundary integral equations (BIE) method is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations. It can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, and fracture mechanics. The eddy current problem is formulated by the BIE and discretized into matrix equations by the method of moments (MoM) or the boundary element method (BEM). The three dimensional arbitrarily shaped objects are described by a number of triangular patches. The Stratton-Chu formulation is specialized for the conductive medium. The equivalent electric and magnetic surface currents are expanded in terms of Rao-Wilton-Glisson (RWG) vector basis function while the normal component of magnetic field is expanded in terms of the pulse basis function. Also, a low frequency approximation is applied in the external medium. Additionally, we introduce Auld's impedance formulas to calculate impedance variation. There are very good agreements between numerical results and those from theory and/or experiments for a finite cross-section above a wedge.
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.
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.
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.
Virtual boundary element method for multistage depressed collector of traveling-wave tubes
Lai Jianqiang; Gong Yubin; Yin Hairong; Duan Zhaoyun; Wei Yanyu
2011-04-15
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.
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 multi-patch nonsingular isogeometric boundary element method using trimmed elements
NASA Astrophysics Data System (ADS)
Wang, Yingjun; Benson, David J.; Nagy, Attila P.
2015-07-01
One of the major goals of isogeometric analysis is direct design-to-analysis, i.e., using computer-aided design (CAD) files for analysis without the need for mesh generation. One of the primary obstacles to achieving this goal is CAD models are based on surfaces, and not volumes. The boundary element method (BEM) circumvents this difficulty by directly working with the surfaces. The standard basis functions in CAD are trimmed nonuniform rational B-spline (NURBS). NURBS patches are the tensor product of one-dimensional NURBS, making the construction of arbitrary surfaces difficult. Trimmed NURBS use curves to trim away regions of the patch to obtain the desired shape. By coupling trimmed NURBS with a nonsingular BEM, the formulation proposed here comes close achieving the goal of direct design to analysis. Example calculations demonstrate its efficiency and accuracy.
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)
Interpolation functions in the immersed boundary and finite element methods
NASA Astrophysics Data System (ADS)
Wang, Xingshi; Zhang, Lucy T.
2010-03-01
In this paper, we review the existing interpolation functions and introduce a finite element interpolation function to be used in the immersed boundary and finite element methods. This straightforward finite element interpolation function for unstructured grids enables us to obtain a sharper interface that yields more accurate interfacial solutions. The solution accuracy is compared with the existing interpolation functions such as the discretized Dirac delta function and the reproducing kernel interpolation function. The finite element shape function is easy to implement and it naturally satisfies the reproducing condition. They are interpolated through only one element layer instead of smearing to several elements. A pressure jump is clearly captured at the fluid-solid interface. Two example problems are studied and results are compared with other numerical methods. A convergence test is thoroughly conducted for the independent fluid and solid meshes in a fluid-structure interaction system. The required mesh size ratio between the fluid and solid domains is obtained.
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.
Boundary control of parabolic systems - Finite-element approximation
NASA Technical Reports Server (NTRS)
Lasiecka, I.
1980-01-01
The finite element approximation of a Dirichlet type boundary control problem for parabolic systems is considered. An approach based on the direct approximation of an input-output semigroup formula is applied. Error estimates are derived for optimal state and optimal control, and it is noted that these estimates are actually optimal with respect to the approximation theoretic properties.
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.
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 Technical Reports Server (NTRS)
Strong, Stuart L.; Meade, Andrew J., Jr.
1992-01-01
Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.
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.
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.
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 New Boundary Condition for Computer Simulations of Interfacial Systems
Wong, Ka-Yiu; Pettitt, Bernard M.; Montgomery, B.
2000-08-18
A new boundary condition for computer simulations of interfacial systems is presented. The simulation box used in this boundary condition is the asymmetric unit of space group Pb, and it contains only one interface. Compared to the simulation box using common periodic boundary conditions which contains two interfaces, the number of particles in the simulation is reduced by half. This boundary condition was tested against common periodic boundary conditions in molecular dynamic simulations of liquid water interacting with hydroxylated silica surfaces. It yielded results essentially identical to periodic boundary condition and consumed less CPU time for comparable statistics.
A new boundary condition for computer simulations of interfacial systems
NASA Astrophysics Data System (ADS)
Wong, Ka-Yiu; Pettitt, B. Montgomery
2000-08-01
A new boundary condition for computer simulations of interfacial systems is presented. The simulation box used in this boundary condition is the asymmetric unit of space group Pb, and it contains only one interface. Compared to the simulation box using common periodic boundary conditions which contains two interfaces, the number of particles in the simulation is reduced by half. This boundary condition was tested against common periodic boundary conditions in molecular dynamic simulations of liquid water interacting with hydroxylated silica surfaces. It yielded results essentially identical to periodic boundary condition and consumed less CPU time for comparable statistics.
Evaluation of Boundary Conditions for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Hixon, R.; Shih, S.-H.; Mankbadi, Reda R.
1995-01-01
The performance of three boundary conditions for aeroacoustics were investigated, namely, (1) Giles-1990; (2) Tam and Webb-1993, and (3) Thompson-1987. For each boundary condition, various implementations were tested to study the sensitivity of their performance to the implementation procedure. Details of all implementations are given. Results are shown for the acoustic field of a monopole in a uniform freestream.
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
NASA Technical Reports Server (NTRS)
Omori, S.; Krebsbach, A.; Gross, K. W.
1972-01-01
Modifications of the turbulent boundary layer (TBL) computer program refer to a more accurate representation of boundary layer edge conditions, internal calculation of the Prandtl number, a changed friction coefficient relationship, and computation of the performance degradation. Important input parameters of the modified TBL program such as wall temperature distribution, Prandtl number, Stanton number, and velocity profile exponent were changed and the individual effects on significant boundary layer parameters, heat transfer, and performance degradation are described.
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.
Stiffened plate bending analysis by the boundary element method
NASA Astrophysics Data System (ADS)
Fernandes, G. R.; Venturini, W. S.
In this work, the plate bending formulation of the boundary element method (BEM) based on the Kirchhoff's hypothesis, is extended to the analysis of stiffened elements usually present in building floor structures. Particular integral representations are derived to take directly into account the interactions between the beams forming grid and surface elements. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composite structure as a single body. Two possible procedures are shown for dealing with plate domain stiffened by beams. In the first, the beam element is considered as a stiffer region requiring therefore the discretization of two internal lines with two unknowns per node. In the second scheme, the number of degrees of freedom along the interface is reduced by two by assuming that the cross-section motion is defined by three independent components only.
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.
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.
NASA Astrophysics Data System (ADS)
Träuble, Markus; Kirchner, Carolina Nunes; Wittstock, Gunther
2007-12-01
The use of the boundary element method (BEM) in simulating steady-state experiments of scanning electrochemical microscopy in feedback mode and in generation-collection mode using complex three dimensional geometries has been shown in previous papers. In the context of generation-collection mode experiments, catalytic reaction mechanisms of immobilized enzymes are of great interest. Due to the catalytic reaction behaviour, which can be described by nonlinear Michaelis-Menten kinetics, the modelling of such systems results in solving a diffusion equation with nonlinear boundary conditions. In this article it is described how such nonlinear reaction mechanisms can be treated with the BEM.
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.
NASA Astrophysics Data System (ADS)
Li, L.; Wang, K.; Li, H.; Eibert, T. F.
2014-11-01
A hybrid higher-order finite element boundary integral (FE-BI) technique is discussed where the higher-order FE matrix elements are computed by a fully analytical procedure and where the gobal matrix assembly is organized by a self-identifying procedure of the local to global transformation. This assembly procedure applys to both, the FE part as well as the BI part of the algorithm. The geometry is meshed into three-dimensional tetrahedra as finite elements and nearly orthogonal hierarchical basis functions are employed. The boundary conditions are implemented in a strong sense such that the boundary values of the volume basis functions are directly utilized within the BI, either for the tangential electric and magnetic fields or for the asssociated equivalent surface current densities by applying a cross product with the unit surface normals. The self-identified method for the global matrix assembly automatically discerns the global order of the basis functions for generating the matrix elements. Higher order basis functions do need more unknowns for each single FE, however, fewer FEs are needed to achieve the same satisfiable accuracy. This improvement provides a lot more flexibility for meshing and allows the mesh size to raise up to λ/3. The performance of the implemented system is evaluated in terms of computation time, accuracy and memory occupation, where excellent results with respect to precision and computation times of large scale simulations are found.
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.
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.
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.
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.
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.
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.
BOOK REVIEW: Finite Element and Boundary Element Applications in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Ueta, Tsuyoshi
2003-08-01
L Ramdas Ram-Mohan Oxford: Oxford University Press (2002) £26.50 (paperback), ISBN 0-19-852522-2 Although this book is one of the Oxford Texts in Applied and Engineering Mathematics, we may think of it as a physics book. It explains how to solve the problem of quantum mechanics using the finite element method (FEM) and the boundary element method (BEM). Many examples analysing actual problems are also shown. As for the ratio of the number of pages of FEM and BEM, the former occupies about 80%. This is, however, reasonable reflecting the flexibility of FEM. Although many explanations of FEM and BEM exist, most are written using special mathematical expressions and numerical computation fields. However, this book is written in the `language of physicists' throughout. I think that it is very readable and easy to understand for physicists. In the derivation of FEM and the argument on calculation accuracy, the action integral and a variation principle are used consistently. In the numerical computation of matrices, such as simultaneous equations and eigen value problems, a description of important points is also fully given. Moreover, the practical problems which become important in the electron device design field and the condensed matter physics field are dealt with as example computations, so that this book is very practical and applicable. It is characteristic and interesting that FEM is applied to solve the Schrödinger and Poisson equations consistently, and to the solution of the Ginzburg--Landau equation in superconductivity. BEM is applied to treat electric field enhancements due to surface plasmon excitations at metallic surfaces. A number of references are cited at the end of all the chapters, and this is very helpful. The description of quantum mechanics is also made appropriately and the actual application of quantum mechanics in condensed matter physics can also be surveyed. In the appendices, the mathematical foundation, such as numerical quadrature
Webb, Christopher J.; Zakian, Virginia A.
2015-01-01
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. PMID:26305931
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.
Dynamics of free subduction from 3-D boundary element modeling
NASA Astrophysics Data System (ADS)
Li, Zhong-Hai; Ribe, Neil M.
2012-06-01
In order better to understand the physical mechanisms underlying free subduction, we perform three-dimensional boundary-element numerical simulations of a dense fluid sheet with thickness h and viscosity η2 sinking in an `ambient mantle' with viscosity η1. The mantle layer is bounded above by a traction-free surface, and is either (1) infinitely deep or (2) underlain by a rigid boundary at a finite depth H + d, similar to the typical geometry used in laboratory experiments. Instantaneous solutions in configuration (1) show that the sheet's dimensionless `stiffness' S determines whether the slab's sinking speed is controlled by the viscosity of the ambient mantle (S < 1) or the viscosity of the sheet itself (S > 10). Time-dependent solutions with tracers in configuration (2) demonstrate a partial return flow around the leading edge of a retreating slab and return flow around its sides. The extra `edge drag' exerted by the flow around the sides causes transverse deformation of the slab, and makes the sinking speed of a 3-D slab up to 40% less than that of a 2-D slab. A systematic investigation of the slab's interaction with the bottom boundary as a function of η2/η1 and H/h delineates a rich regime diagram of different subduction modes (trench retreating, slab folding, trench advancing) and reveals a new `advancing-folding' mode in which slab folding is preceded by advancing trench motion. The solutions demonstrate that mode selection is controlled by the dip of the leading edge of the slab at the time when it first encounters the bottom boundary.
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.
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.
Interactive-Boundary-Layer Computations For Oscillating Airfoil
NASA Technical Reports Server (NTRS)
Carr, L. W.; Cebeci, T.; Jang, Hong-Ming
1993-01-01
Interactive-boundary-layer method developed for computations of steady flow, extended under assumption of quasi-steady flow, to computations of evolution of two-dimensional flow about oscillating airfoil under light-dynamic-stall conditions. Represents advance toward ability to compute unsteady flows at even greater angles of attack with solutions of equations normally used for description of boundary-layer flows on airfoils prior to stall. Important in practical studies of flow on blades of helicopter rotors, axial compressors, and turbines.
Finite element computation with parallel VLSI
NASA Technical Reports Server (NTRS)
Mcgregor, J.; Salama, M.
1983-01-01
This paper describes a parallel processing computer consisting of a 16-bit microcomputer as a master processor which controls and coordinates the activities of 8086/8087 VLSI chip set slave processors working in parallel. The hardware is inexpensive and can be flexibly configured and programmed to perform various functions. This makes it a useful research tool for the development of, and experimentation with parallel mathematical algorithms. Application of the hardware to computational tasks involved in the finite element analysis method is demonstrated by the generation and assembly of beam finite element stiffness matrices. A number of possible schemes for the implementation of N-elements on N- or n-processors (N is greater than n) are described, and the speedup factors of their time consumption are determined as a function of the number of available parallel processors.
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
Boundary element method approach to magnetostatic wave problems
NASA Astrophysics Data System (ADS)
Yashiro, K.; Ohkawa, S.; Miyazaki, M.
1985-03-01
In this paper, the technique for application of the boundary element method (BEM) to analysis of magnetostatic waves (MSWs) is established. To show the availability of the technique, two types of waveguides for the MSW are studied; one is a waveguide constituting a YIG slab shielded with metal plates and the other is a waveguide consisting of an unshielded YIG slab. With the former structure the results obtained by the present technique are compared with the analytical solutions, and with the latter the BEM is compared with Marcatili's approximate method since there is no analytical solution in this case. Those comparisons are performed successfully for both cases. The paper concludes that the BEM is useful and effective for analysis of a wide range of MSW problems.
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.
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.
Numerical Boundary Conditions for Computational Aeroacoustics Benchmark Problems
NASA Technical Reports Server (NTRS)
Tam, Chritsopher K. W.; Kurbatskii, Konstantin A.; Fang, Jun
1997-01-01
Category 1, Problems 1 and 2, Category 2, Problem 2, and Category 3, Problem 2 are solved computationally using the Dispersion-Relation-Preserving (DRP) scheme. All these problems are governed by the linearized Euler equations. The resolution requirements of the DRP scheme for maintaining low numerical dispersion and dissipation as well as accurate wave speeds in solving the linearized Euler equations are now well understood. As long as 8 or more mesh points per wavelength is employed in the numerical computation, high quality results are assured. For the first three categories of benchmark problems, therefore, the real challenge is to develop high quality numerical boundary conditions. For Category 1, Problems 1 and 2, it is the curved wall boundary conditions. For Category 2, Problem 2, it is the internal radiation boundary conditions inside the duct. For Category 3, Problem 2, they are the inflow and outflow boundary conditions upstream and downstream of the blade row. These are the foci of the present investigation. Special nonhomogeneous radiation boundary conditions that generate the incoming disturbances and at the same time allow the outgoing reflected or scattered acoustic disturbances to leave the computation domain without significant reflection are developed. Numerical results based on these boundary conditions are provided.
A new simple multidomain fast multipole boundary element method
NASA Astrophysics Data System (ADS)
Huang, S.; Liu, Y. J.
2016-06-01
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.
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.
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.
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. PMID:19173406
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.
NASA Astrophysics Data System (ADS)
Perton, Mathieu; Contreras-Zazueta, Marcial A.; Sánchez-Sesma, Francisco J.
2016-06-01
A new implementation of indirect boundary element method allows simulating the elastic wave propagation in complex configurations made of embedded regions that are homogeneous with irregular boundaries or flat layers. In an older implementation, each layer of a flat layered region would have been treated as a separated homogeneous region without taking into account the flat boundary information. For both types of regions, the scattered field results from fictitious sources positioned along their boundaries. For the homogeneous regions, the fictitious sources emit as in a full-space and the wave field is given by analytical Green's functions. For flat layered regions, fictitious sources emit as in an unbounded flat layered region and the wave field is given by Green's functions obtained from the discrete wavenumber (DWN) method. The new implementation allows then reducing the length of the discretized boundaries but DWN Green's functions require much more computation time than the full-space Green's functions. Several optimization steps are then implemented and commented. Validations are presented for 2-D and 3-D problems. Higher efficiency is achieved in 3-D.
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.
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. PMID:25015666
Optimization of dynamic roughness elements for reducing drag in a laminar boundary layer
NASA Astrophysics Data System (ADS)
Sayadi, Taraneh; Sayadi, Peter
2015-11-01
Roughness elements can serve as controllers in both laminar and turbulent regimes to, for example, reduce the skin friction or drag. In this study, adjoint-based optimization is employed to extract the optimal shape of roughness elements for reducing drag, in a laminar setting, given an initial condition. The roughness elements considered here are of the ``dynamic'' type, varying both in space and time, which allows control over the spatial distribution of the roughness but also the inherent timescales of the flow. Dynamic roughness is modeled here using the linearized boundary conditions previously introduced by McKeon (2008), where the no-slip and impermeability boundary conditions are replaced by stream-wise and wall-normal distributions at the wall. The adjoint equation is then implemented using the discretized approach by Fosas et al. (2012). This approach is particularly efficient, since the linearized operators are computed simply by using the local differentiation technique, without explicitly forming the resulting matrices for both forward and adjoint operators. Using the described framework we investigate the effect of the initial condition on the spatial distribution of the roughness elements and their variation in time as the drag coefficient is minimized.
Isogeometric Boundary Element analysis with elasto-plastic inclusions. Part 1: Plane problems
NASA Astrophysics Data System (ADS)
Beer, Gernot; Marussig, Benjamin; Zechner, Jürgen; Dünser, Christian; Fries, Thomas-Peter
2016-08-01
In this work a novel approach is presented for the isogeometric Boundary Element analysis of domains that contain inclusions with different elastic properties than the ones used for computing the fundamental solutions. In addition the inclusion may exhibit inelastic material behavior. In this paper only plane stress/strain problems are considered. In our approach the geometry of the inclusion is described using NURBS basis functions. The advantage over currently used methods is that no discretization into cells is required in order to evaluate the arising volume integrals. The other difference to current approaches is that Kernels of lower singularity are used in the domain term. The implementation is verified on simple finite and infinite domain examples with various boundary conditions. Finally a practical application in geomechanics is presented.
A linear analytical boundary element method (BEM) for 2D homogeneous potential problems
NASA Astrophysics Data System (ADS)
Friedrich, Jürgen
2002-06-01
The solution of potential problems is not only fundamental for geosciences, but also an essential part of related subjects like electro- and fluid-mechanics. In all fields, solution algorithms are needed that should be as accurate as possible, robust, simple to program, easy to use, fast and small in computer memory. An ideal technique to fulfill these criteria is the boundary element method (BEM) which applies Green's identities to transform volume integrals into boundary integrals. This work describes a linear analytical BEM for 2D homogeneous potential problems that is more robust and precise than numerical methods because it avoids numerical schemes and coordinate transformations. After deriving the solution algorithm, the introduced approach is tested against different benchmarks. Finally, the gained method was incorporated into an existing software program described before in this journal by the same author.
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.
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.
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
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.
A time-domain finite element boundary integration method for ultrasonic nondestructive evaluation.
Shi, Fan; Choi, Wonjae; Skelton, Elizabeth A; Lowe, Michael J S; Craster, Richard V
2014-12-01
A 2-D and 3-D numerical modeling approach for calculating the elastic wave scattering signals from complex stress-free defects is evaluated. In this method, efficient boundary integration across the complex boundary of the defect is coupled with a time-domain finite element (FE) solver. The model is designed to simulate time-domain ultrasonic nondestructive evaluation in bulk media. This approach makes use of the hybrid concept of linking a local numerical model to compute the near-field scattering behavior and theoretical mathematical formulas for postprocessing to calculate the received signals. It minimizes the number of monitoring signals from the FE calculation so that the computation effort in postprocessing decreases significantly. In addition, by neglecting the conventional regular monitoring box, the region for FE calculation can be made smaller. In this paper, the boundary integral method is implemented in a commercial FE code, and it is validated by comparing the scattering signals with results from corresponding full FE models. The coupled method is then implemented in real inspection scenarios in both 2-D and 3-D, and the accuracy and the efficiency are demonstrated. The limitations of the proposed model and future works are also discussed. PMID:25474780
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.
3D Multi-spectral Image-guided Near-infrared Spectroscopy using Boundary Element Method
Srinivasan, Subhadra; Pogue, Brian W.; Paulsen, Keith D.
2010-01-01
Image guided (IG) Near-Infrared spectroscopy (NIRS) has the ability to provide high-resolution metabolic and vascular characterization of tissue, with clinical applications in diagnosis of breast cancer. This method is specific to multimodality imaging where tissue boundaries obtained from alternate modalities such as MRI/CT, are used for NIRS recovery. IG-NIRS is severely limited in 3D by challenges such as volumetric meshing of arbitrary anatomical shapes and computational burden encountered by existing models which use finite element method (FEM). We present an efficient and feasible alternative to FEM using boundary element method (BEM). The main advantage is the use of surface discretization which is reliable and more easily generated than volume grids in 3D and enables automation for large number of clinical data-sets. The BEM has been implemented for the diffusion equation to model light propagation in tissue. Image reconstruction based on BEM has been tested in a multi-threading environment using four processors which provides 60% improvement in computational time compared to a single processor. Spectral priors have been implemented in this framework and applied to a three-region problem with mean error of 6% in recovery of NIRS parameters. PMID:21179380
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.
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
NASA Astrophysics Data System (ADS)
Manguoglu, Murat; Takizawa, Kenji; Sameh, Ahmed H.; Tezduyar, Tayfun E.
2009-10-01
Computation of incompressible flows in arterial fluid mechanics, especially because it involves fluid-structure interaction, poses significant numerical challenges. Iterative solution of the fluid mechanics part of the equation systems involved is one of those challenges, and we address that in this paper, with the added complication of having boundary layer mesh refinement with thin layers of elements near the arterial wall. As test case, we use matrix data from stabilized finite element computation of a bifurcating middle cerebral artery segment with aneurysm. It is well known that solving linear systems that arise in incompressible flow computations consume most of the time required by such simulations. For solving these large sparse nonsymmetric systems, we present effective preconditioning techniques appropriate for different stages of the computation over a cardiac cycle.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Zou, Fangxin; Aliabadi, M. H.
2015-09-01
In this paper, for the first time, a boundary element method (BEM) for modelling the electro-mechanical responses of three-dimensional structures is reported. Within an electro-mechanically coupled system, the host structure is formulated using the 3D dual boundary element method in order to be able to take into account the possible existence of cracks, and the piezoelectric transducers, which are the key to measuring electro-mechanical impedance (EMI), are modelled using a semi-analytical finite element approach. The analyses of the coupled system are performed in the frequency domain. The EMI signatures computed by the BEM developed in this work show excellent agreement with those obtained using the finite element method and from experiments. Using parametric studies, the potential of using EMI signatures for the detection of damages in structures and for the self-diagnosis of transducers is assessed.
Computer constructed imagery of distant plasma interaction boundaries
NASA Astrophysics Data System (ADS)
Greenstadt, E. W.; Schurr, H. D.; Tsugawa, R. K.
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
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.
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
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
Immersed boundary conditions method for computational fluid dynamics problems
NASA Astrophysics Data System (ADS)
Husain, Syed Zahid
This dissertation presents implicit spectrally-accurate algorithms based on the concept of immersed boundary conditions (IBC) for solving a range of computational fluid dynamics (CFD) problems where the physical domains involve boundary irregularities. Both fixed and moving irregularities are considered with particular emphasis placed on the two-dimensional moving boundary problems. The physical model problems considered are comprised of the Laplace operator, the biharmonic operator and the Navier-Stokes equations, and thus cover the most commonly encountered types of operators in CFD analyses. The IBC algorithm uses a fixed and regular computational domain with flow domain immersed inside the computational domain. Boundary conditions along the edges of the time-dependent flow domain enter the algorithm in the form of internal constraints. Spectral spatial discretization for two-dimensional problems is based on Fourier expansions in the stream-wise direction and Chebyshev expansions in the normal-to-the-wall direction. Up to fourth-order implicit temporal discretization methods have been implemented. The IBC algorithm is shown to deliver the theoretically predicted accuracy in both time and space. Construction of the boundary constraints in the IBC algorithm provides degrees of freedom in excess of that required to formulate a closed system of algebraic equations. The 'classical IBC formulation' works by retaining number boundary constraints that are just sufficient to form a closed system of equations. The use of additional boundary constraints leads to the 'over-determined formulation' of the IBC algorithm. Over-determined systems are explored in order to improve the accuracy of the IBC method and to expand its applicability to more extreme geometries. Standard direct over-determined solvers based on evaluation of pseudo-inverses of the complete coefficient matrices have been tested on three model problems, namely, the Laplace equation, the biharmonic equation
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.
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.
On a 3-D singularity element for computation of combined mode stress intensities
NASA Technical Reports Server (NTRS)
Atluri, S. N.; Kathiresan, K.
1976-01-01
A special three-dimensional singularity element is developed for the computation of combined modes 1, 2, and 3 stress intensity factors, which vary along an arbitrarily curved crack front in three dimensional linear elastic fracture problems. The finite element method is based on a displacement-hybrid finite element model, based on a modified variational principle of potential energy, with arbitrary element interior displacements, interelement boundary displacements, and element boundary tractions as variables. The special crack-front element used in this analysis contains the square root singularity in strains and stresses, where the stress-intensity factors K(1), K(2), and K(3) are quadratically variable along the crack front and are solved directly along with the unknown nodal displacements.
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. PMID:24606256
Chromosome boundary elements and regulation of heterochromatin spreading
Wang, Jiyong; Lawry, Stephanie T.; Cohen, Allison L.; Jia, Songtao
2014-01-01
Chromatin is generally classified as euchromatin or heterochromatin, each with distinct histone modifications, compaction levels, and gene expression patterns. Although the proper formation of heterochromatin is essential for maintaining genome integrity and regulating gene expression, heterochromatin can also spread into neighboring regions in a sequence-independent manner, leading to the inactivation of genes. Because the distance of heterochromatin spreading is stochastic, the formation of boundaries, which block the spreading of heterochromatin, is critical for maintaining stable gene expression patterns. Here we review the current understanding of the mechanisms underlying heterochromatin spreading and boundary formation. PMID:25192661
A fast boundary element method for the scattering analysis of high-intensity focused ultrasound.
van 't Wout, Elwin; Gélat, Pierre; Betcke, Timo; Arridge, Simon
2015-11-01
High-intensity focused ultrasound (HIFU) techniques are promising modalities for the non-invasive treatment of cancer. For HIFU therapies of, e.g., liver cancer, one of the main challenges is the accurate focusing of the acoustic field inside a ribcage. Computational methods can play an important role in the patient-specific planning of these transcostal HIFU treatments. This requires the accurate modeling of acoustic scattering at ribcages. The use of a boundary element method (BEM) is an effective approach for this purpose because only the boundaries of the ribs have to be discretized instead of the standard approach to model the entire volume around the ribcage. This paper combines fast algorithms that improve the efficiency of BEM specifically for the high-frequency range necessary for transcostal HIFU applications. That is, a Galerkin discretized Burton-Miller formulation is used in combination with preconditioning and matrix compression techniques. In particular, quick convergence is achieved with the operator preconditioner that has been designed with on-surface radiation conditions for the high-frequency approximation of the Neumann-to-Dirichlet map. Realistic computations of acoustic scattering at 1 MHz on a human ribcage model demonstrate the effectiveness of this dedicated BEM algorithm for HIFU scattering analysis. PMID:26627749
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.
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.
NASA Astrophysics Data System (ADS)
Zeng, X.; Scovazzi, G.
2016-06-01
We present a monolithic arbitrary Lagrangian-Eulerian (ALE) finite element method for computing highly transient flows with strong shocks. We use a variational multiscale (VMS) approach to stabilize a piecewise-linear Galerkin formulation of the equations of compressible flows, and an entropy artificial viscosity to capture strong solution discontinuities. Our work demonstrates the feasibility of VMS methods for highly transient shock flows, an area of research for which the VMS literature is extremely scarce. In addition, the proposed monolithic ALE method is an alternative to the more commonly used Lagrangian+remap methods, in which, at each time step, a Lagrangian computation is followed by mesh smoothing and remap (conservative solution interpolation). Lagrangian+remap methods are the methods of choice in shock hydrodynamics computations because they provide nearly optimal mesh resolution in proximity of shock fronts. However, Lagrangian+remap methods are not well suited for imposing inflow and outflow boundary conditions. These issues offer an additional motivation for the proposed approach, in which we first perform the mesh motion, and then the flow computations using the monolithic ALE framework. The proposed method is second-order accurate and stable, as demonstrated by extensive numerical examples in two and three space dimensions.
NASA Astrophysics Data System (ADS)
Huang, Shu H.; Ma, Zhi Y.
The paper presents a formulation of the boundary element method for axisymmetric heat transfer. The main advantage of this technique compared with conventional methods is that it reduces the dimensionality of the problem, resulting in a smaller system of equations to be solved. The method is also well suited for solving problems where high gradients occur. The formulation is used to compute the temperature fields of a gas turbine disk and of a steam turbine rotor.
Prediction of metallic nano-optical trapping forces by finite element-boundary integral method.
Pan, Xiao-Min; Xu, Kai-Jiang; Yang, Ming-Lin; Sheng, Xin-Qing
2015-03-01
The hybrid of finite element and boundary integral (FE-BI) method is employed to predict nano-optical trapping forces of arbitrarily shaped metallic nanostructures. A preconditioning strategy is proposed to improve the convergence of the iterative solution. Skeletonization is employed to speed up the design and optimization where iteration has to be repeated for each beam configuration. The radiation pressure force (RPF) is computed by vector flux of the Maxwell's stress tensor. Numerical simulations are performed to validate the developed method in analyzing the plasmonic effects as well as the optical trapping forces. It is shown that the proposed method is capable of predicting the trapping forces of complex metallic nanostructures accurately and efficiently. PMID:25836836
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. PMID:24180751
Finite Element Modeling of Crustal Deformation in the North American Caribbean Plate Boundary Zone
NASA Technical Reports Server (NTRS)
Lundgren, P.; Russo, R.
1995-01-01
We have developed 2-dimensional spherical shell finite element models of elastic displacement in the North American-Caribbean (NA-Ca) plate boundary zone (PBZ) in order to quantify crust and fault motions in the PBZ.
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.
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.
Three-dimensional shape optimization using the boundary element method
NASA Astrophysics Data System (ADS)
Yamazaki, Koetsu; Sakamoto, Jiro; Kitano, Masami
1994-06-01
A practical design sensitivity calculation technique of displacements and stresses for three-dimensional bodies based on the direct differentiation method of discrete boundary integral equations is formulated in detail. Then the sensitivity calculation technique is applied to determine optimum shapes of minimum weight subjected to stress constraints, where an approximated subproblem is constructed repeatedly and solved sequentially by the mathematical programming method. The shape optimization technique suggested here is applied to determine optimum shapes of a cavity in a cube and a connecting rod.
Three-dimensional shape optimization using boundary element method
NASA Astrophysics Data System (ADS)
Yamazaki, Koetsu; Sakamoto, Jiro; Kitano, Masami
1993-04-01
A practical design sensitivity calculation technique of displacements and stresses for three-dimensional bodies based on the direct differentiation method of discrete boundary integral equations is formulated in detail. Then, the sensitivity calculation technique is applied to determine optimum shapes of minimum weight subjected to stress constraints, where an approximated subproblem is constructed repeatedly and solved sequentially by the mathematical programming method. The shape optimization technique suggested here is applied to determine optimum shapes of a cavity shape in a cube and a connecting rod.
Developments in the computation of turbulent boundary layers
NASA Technical Reports Server (NTRS)
Rubesin, M. W.
1979-01-01
Computational techniques applicable to turbulent boundary layers are classified into solutions of Reynolds-averaged equations, in which all the effects of the turbulence are modelled, and solutions of three-dimensional, time dependent Navier-Stokes equations, in which the large eddies are calculated and only the turbulence at scales smaller than the computational mesh spacings has to be modelled. Current computation costs place engineering computations in the first of these categories; large eddy simulations are appropriate currently for special studies of the dynamical processes of turbulence in idealized flow fields. It is shown that the two methods are interrelated and that each can gain from advances in the other. The degree of success of a pair of increasingly complex Reynolds stress models to broaden their range of applicability is examined through comparisons with experimental data for a variety of flow conditions. An example of a large-eddy simulation is presented, compared with experimental results, and used to evaluate the models for pressure rate-of-strain correlations and dissipation in the Reynolds-averaged equations.
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.
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
A coupled finite-element, boundary-integral method for simulating ultrasonic flowmeters.
Bezdĕk, Michal; Landes, Hermann; Rieder, Alfred; Lerch, Reinhard
2007-03-01
Today's most popular technology of ultrasonic flow measurement is based on the transit-time principle. In this paper, a numerical simulation technique applicable to the analysis of transit-time flowmeters is presented. A flowmeter represents a large simulation problem that also requires computation of acoustic fields in moving media. For this purpose, a novel boundary integral method, the Helmholtz integral-ray tracing method (HIRM), is derived and validated. HIRM is applicable to acoustic radiation problems in arbitrary mean flows at low Mach numbers and significantly reduces the memory demands in comparison with the finite-element method (FEM). It relies on an approximate free-space Green's function which makes use of the ray tracing technique. For simulation of practical acoustic devices, a hybrid simulation scheme consisting of FEM and HIRM is proposed. The coupling of FEM and HIRM is facilitated by means of absorbing boundaries in combination with a new, reflection-free, acoustic-source formulation. Using the coupled FEM-HIRM scheme, a full three-dimensional (3-D) simulation of a complete transit-time flowmeter is performed for the first time. The obtained simulation results are in good agreement with measurements both at zero flow and under flow conditions. PMID:17375833
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.
Critical Elements of Computer Literacy for Teachers.
ERIC Educational Resources Information Center
Overbaugh, Richard C.
A definition of computer literacy is developed that is broad enough to apply to educators in general, but which leaves room for specificity for particular situations and content areas. The following general domains that comprise computer literacy for all educators are addressed: (1) general computer operations; (2) software, including computer…
Variational Generation of Prismatic Boundary-Layer Meshes for Biomedical Computing
Dyedov, Volodymyr; Einstein, Daniel; Jiao, Xiangmin; Kuprat, Andrew; Carson, James; Pin, Facundo del
2009-01-01
SUMMARY Boundary-layer meshes are important for numerical simulations in computational fluid dynamics, including computational biofluid dynamics of air flow in lungs and blood flow in hearts. Generating boundary-layer meshes is challenging for complex biological geometries. In this paper, we propose a novel technique for generating prismatic boundary-layer meshes for such complex geometries. Our method computes a feature size of the geometry, adapts the surface mesh based on the feature size, and then generates the prismatic layers by propagating the triangulated surface using the face-offsetting method. We derive a new variational method to optimize the prismatic layers to improve the triangle shapes and edge orthogonality of the prismatic elements and also introduce simple and effective measures to guarantee the validity of the mesh. Coupled with a high-quality tetrahedral mesh generator for the interior of the domain, our method generates high-quality hybrid meshes for accurate and efficient numerical simulations. We present comparative study to demonstrate the robustness and quality of our method for complex biomedical geometries. PMID:20161102
Boundary element techniques - Applications in stress analysis and heat transfer
Brebbia, C.A.; Venturini, W.S.
1987-01-01
This volume includes contributions in the field of stress analysis, soil and rock mechanics, non-linear problems, dynamics and vibrations, plate bending and heat transfer. The companion volume includes contributions dealing with viscous and inviscid fluid flow, aerodynamics and hydrodynamics applications, elastostatics and computational and mathematical aspects.
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
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.
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
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
NASA Technical Reports Server (NTRS)
Tezduyar, T. E.; Liou, J.
1988-01-01
Preconditioner algorithms to reduce the computational effort in FEM analyses of large-scale fluid-dynamics problems are presented. A general model problem is constructed on the basis of the convection-diffusion equation and the two-dimensional vorticity/stream-function formulation of the Navier-Stokes equations; this problem is then analyzed using element-by-element, implicit-explicit, and adaptive implicit-explicit approximation schemes. Numerical results for the two-dimensional advection and rigid-body rotation of a cosine hill, flow past a circular cylinder, and driven cavity flow are presented in extensive graphs and shown to be in good agreement with those obtained using implicit methods.
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.
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.
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
Numerical improvement of the three-dimensional indirect boundary element method
NASA Astrophysics Data System (ADS)
Ortiz-Aleman, C.; Gil-Zepeda, S. A.; Luzon, F.; Sanchez-Sesma, F. J.
2003-04-01
In recent years, several numerical techniques for the estimation of the seismic response in complex geologic configurations have been developed. The flexibility and versatility of these techniques have increased along with the improvement of computational systems, and they altogether have allowed the study of 3D geometries to model several sedimentary basins around the world. In this article we study the structure of the linear systems derived from the Indirect Boundary Element Method (IBEM). We apply a LU-sparse decomposition solver to the inversion of the IBEM coefficient matrix in order to optimise the numerical burden of such method. As pointed out before, special emphasis is given to understanding the main features of ground motion in sedimentary basins. We compute the seismic response of a 3D alluvial valley of irregular shape, as originally proposed by Sánchez-Sesma and Luzón (1995), and we establish comparisons on time consumption and memory allocation. Inversion of linear systems by using this new algorithm lead us to a significant saving on CPU time and memory allocation relative to the original IBEM formulation. Results represent an extension in the range of application of the IBEM method.
NASA Astrophysics Data System (ADS)
Liu, B.; Arsenlis, A.; Aubry, S.
2016-06-01
Driven by the growing interest in numerical simulations of dislocation–interface interactions in general crystalline materials with elastic anisotropy, we develop algorithms for the integration of interface tractions needed to couple dislocation dynamics with a finite element or boundary element solver. The dislocation stress fields in elastically anisotropic media are made analytically accessible through the spherical harmonics expansion of the derivative of Green’s function, and analytical expressions for the forces on interface elements are derived by analytically integrating the spherical harmonics series recursively. Compared with numerical integration by Gaussian quadrature, the newly developed analytical algorithm for interface traction integration is highly beneficial in terms of both computation precision and speed.
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.
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)
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.
E-coil: an inverse boundary element method for a quasi-static problem.
Sanchez, Clemente Cobos; Garcia, Salvador Gonzalez; Power, Henry
2010-06-01
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. PMID:20463375
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
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.
Bhattacharyya, S K; Premkumar, R
2003-12-01
In a domain method of solution of exterior scalar wave equation, the radiation condition needs to be imposed on a truncation boundary of the modeling domain. The Bayliss, Gunzberger, and Turkel (BGT) boundary dampers, which require a circular cylindrical and spherical truncation boundaries in two-(2D) and three-(3D)-dimensional problems, respectively, have been particularly successful in the analysis of scattering and radiation problems. However, for an elongated body, elliptical (2D) or spheroidal (3D) truncation boundaries have potential to reduce the size of modeling domain and hence computational effort. For harmonic problems, such extensions of the first- and second-order BGT dampers are available in the literature. In this paper, BGT dampers in both elliptical and spheroidal coordinate systems have been developed for transient problems involving acoustic radiation as well as fluid-structure interaction and implemented in the context of finite-element method based upon unsymmetric pressure-displacement formulation. Applications to elongated radiators and shells are reported using several numerical examples with excellent comparisons. It is demonstrated that significant computational economy can be achieved for elongated bodies with the use of these dampers. PMID:14714787
NASA Astrophysics Data System (ADS)
Bhattacharyya, S. K.; Premkumar, R.
2003-12-01
In a domain method of solution of exterior scalar wave equation, the radiation condition needs to be imposed on a truncation boundary of the modeling domain. The Bayliss, Gunzberger, and Turkel (BGT) boundary dampers, which require a circular cylindrical and spherical truncation boundaries in two-(2D) and three-(3D)-dimensional problems, respectively, have been particularly successful in the analysis of scattering and radiation problems. However, for an elongated body, elliptical (2D) or spheroidal (3D) truncation boundaries have potential to reduce the size of modeling domain and hence computational effort. For harmonic problems, such extensions of the first- and second-order BGT dampers are available in the literature. In this paper, BGT dampers in both elliptical and spheroidal coordinate systems have been developed for transient problems involving acoustic radiation as well as fluid-structure interaction and implemented in the context of finite-element method based upon unsymmetric pressure-displacement formulation. Applications to elongated radiators and shells are reported using several numerical examples with excellent comparisons. It is demonstrated that significant computational economy can be achieved for elongated bodies with the use of these dampers.
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.
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
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.
Pingenot, J; Jandhyala, V
2007-03-01
This report summarizes the work performed for Lawrence Livermore National Laboratory (LLNL) at the University of Washington between September 2004 and May 2006. This project studied fast solvers and stability for time domain integral equations (TDIE), especially as applied to radiating boundary for a massively parallel FEM solver.
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
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.
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.
NASA Astrophysics Data System (ADS)
Anton, I.; Carte, I. N.; Ludescher, H.; Iosif, A.
1990-04-01
The application of the boundary element method to the analysis of axisymmetric motions is examined with particular reference to turbomachines. A procedure for determining the hydrodynamic field in the meridian plane of turbomachine blading using the boundary element method is presented. The method is applied to a Francis turbine impeller with lateral boundaries of the Bovet type. The results obtained are compared with calculations by the finite element method.
Depth-dependent target strengths of gadoids by the boundary-element method
NASA Astrophysics Data System (ADS)
Francis, David T. I.; Foote, Kenneth G.
2003-12-01
The depth dependence of fish target strength has mostly eluded experimental investigation because of the need to distinguish it from depth-dependent behavioral effects, which may change the orientation distribution. The boundary-element method (BEM) offers an avenue of approach. Based on detailed morphometric data on 15 gadoid swimbladders, the BEM has been exercised to determine how the orientation dependence of target strength changes with pressure under the assumption that the fish swimbladder remains constant in shape and volume. The backscattering cross section has been computed at a nominal frequency of 38 kHz as a function of orientation for each of three pressures: 1, 11, and 51 atm. Increased variability in target strength and more abundant and stronger resonances are both observed with increasing depth. The respective backscattering cross sections have been averaged with respect to each of four normal distributions of tilt angle, and the corresponding target strengths have been regressed on the logarithm of fish length. The tilt-angle-averaged backscattering cross sections at the highest pressure have also been averaged with respect to frequency over a 2-kHz band for representative conditions of insonification. For all averaging methods, the mean target strength changes only slightly with depth.
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.
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.
Kerwien, Norbert; Schuster, Thomas; Rafler, Stephan; Osten, Wolfgang; Totzeck, Michael
2007-04-01
A semirigorous model is presented that bridges the gap between classical scalar diffraction theory on the one hand and fully rigorous simulation models on the other. It falls back on the basic ideas of scalar diffraction theory, especially the Kirchhoff approximation. In contrast to classical techniques, however, the boundary values are determined by rigorous methods of the stratified medium theory in the scope of a fully vectorial formulation. By this means the proposed approach takes vertical rigorous coupling effects inside the grating into account while neglecting the lateral ones. We therefore call this method semirigorous and use the name vectorial thin-element approximation. A direct comparison with rigorous coupled-wave analysis as a fully rigorous simulation model allows a detailed discussion of its range of validity and demonstrates a reduction of computation time of the order of 3 magnitudes. In addition, it also reveals deeper insight into the details of the electrodynamics inside diffracting structures. Some examples will demonstrate this benefit. PMID:17361295
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
Secular perturbation theory and computation of asteroid proper elements
NASA Technical Reports Server (NTRS)
Milani, Andrea; Knezevic, Zoran
1991-01-01
A new theory for the calculation of proper elements is presented. This theory defines an explicit algorithm applicable to any chosen set of orbits and accounts for the effect of shallow resonances on secular frequencies. The proper elements are computed with an iterative algorithm and the behavior of the iteration can be used to define a quality code.
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.
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.
Computing the Casimir force using regularized boundary integral equations
NASA Astrophysics Data System (ADS)
Kilen, Isak; Jakobsen, Per Kristen
2014-11-01
In this paper we use a novel regularization procedure to reduce the calculation of the Casimir force for 2D scalar fields between compact objects to the solution of a classical integral equation defined on the boundaries of the objects. The scalar fields are subject to Dirichlet boundary conditions on the object boundaries. We test the integral equation by comparing with what we get for parallel plates, concentric circles and adjacent circles using mode summation and the functional integral method. We show how symmetries in the shapes and configuration of boundaries can easily be incorporated into our method and that it leads to fast evaluation of the Casimir force for symmetric situations.
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 Technical Reports Server (NTRS)
Fulton, R. E.
1986-01-01
The requirements of complex aerospace vehicles combined with the age of structural analysis systems enhance the need to advance technology toward a new generation of structural analysis capability. Recent and impeding advances in parallel and supercomputers provide the opportunity to significantly improve these structural analysis capabilities for large order finite element problems. Long-term research in parallel computing, associated with the NASA Finite Element Machine project, is discussed. The results show the potential of parallel computers to provide substantial increases in computation speed over sequential computers. Results are given for sample problems in the areas of eigenvalue analysis and transient response.
A Advanced Boundary Element Formulation for Acoustic Radiation and Scattering in Three Dimensions.
NASA Astrophysics Data System (ADS)
Soenarko, Benjamin
A computational method is presented for determining acoustic fields produced by arbitrary shaped three-dimensional bodies. The formulation includes both radiation and scattering problems. In particular an isoparametric element formulation is introduced in which both the surface geometry and the acoustic variables on the surface of the body are represented by second order shape functions within the local coordinate system. A general result for the surface velocity potential and the exterior field is derived. This result is applicable to non-smooth bodies, i.e. it includes the case where the surface may have a non-unique normal (e.g. at the edge of a cube). Test cases are shown involving spherical, cylindrical and cubical geometry for both radiation and scattering problems. The present formulation is also extended to include half-space problems in which the effect of the reflected wave from an infinite plane is taken into account. By selecting an appropriate Green's function, the surface integral over the plane is nullified; thus all the computational efforts can be performed only on the radiating or scattering body at issue and thereby greatly simplify the solution. A special formulation involving axisymmetric bodies and boundary conditions is also presented. For this special case, the surface integrals are reduced to line integrals and an integral over the angle of revolution. The integration over the angle is performed partly analytically in terms of elliptic integrals and partly numerically using simple Gaussian quadrature formula. Since the rest of the integrals involve only line integrals along the generator of the body, any discretization scheme can be easily obtained to achieve a desired degree of accuracy in evaluating these integrals.
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,…
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)
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.
A finite element computational method for high Reynolds number laminar flows
NASA Technical Reports Server (NTRS)
Kim, Sang-Wook
1987-01-01
A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables are interpolated using complete quadratic shape functions, and the pressure is interpolated using linear shape functions which are defined on a triangular element for the two-dimensional case and on a tetrahedral element for the three-dimensional case. The triangular element and the tetrahedral element are contained inside the complete bi- and tri-quadratic elements for velocity variables for two and three dimensional cases, respectively, so that the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow of Reynolds numbers 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorably with the finite difference computational results and/or experimental data available. It was found that the present method can capture the delicate pressure driven recirculation zones, that the method did not yield any spurious pressure modes, and that the method requires fewer grid points than the finite difference methods to obtain comparable computational results.
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.
NASA Astrophysics Data System (ADS)
Gartling, D. K.
1987-04-01
The theoretical and numerical background for the finite element computer program, NACHOS 2, is presented in detail. The NACHOS 2 code is designed for the two-dimensional analysis of viscous incompressible fluid flows, including the effects of heat transfer and/or other transport processes. A general description of the boundary value problems treated by the program is presented. The finite element formulations and the associated numerical methods used in the NACHOS 2 code are also outlined. Instructions for use of the program are documented in SAND-86-1817; examples of problems analyzed by the code are provided in SAND-86-1818.
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.
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.
A mixed-grid finite element method with PML absorbing boundary conditions for seismic wave modelling
NASA Astrophysics Data System (ADS)
Liu, Shaolin; Li, Xiaofan; Wang, Wenshuai; Liu, Youshan
2014-10-01
We have developed a mixed-grid finite element method (MGFEM) to simulate seismic wave propagation in 2D structurally complex media. This method divides the physical domain into two subdomains. One subdomain covering the major part of the physical domain is divided by regular quadrilateral elements, while the other subdomain uses triangular elements to correctly fit a rugged free surface topography. The local stiffness matrix of any quadrilateral element is identical and matrix-vector production is calculated using an element-by-element technique, which avoids assembling a huge global stiffness matrix. As only a few triangular elements exist in the subdomain containing the rugged free surface topography, the memory requirements for storing the assembled subdomain global stiffness matrix are significantly reduced. To eliminate artificial boundary reflections, the MGFEM is also implemented to solve the system equations of PML absorbing boundary conditions (PML ABC). The accuracy and efficiency of the MGFEM is tested in numerical experiments by comparing it with conventional methods, and numerical comparisons also indicate its tremendous ability to describe rugged surfaces.
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.
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.
Protein:protein interactions and the pairing of boundary elements in vivo
Blanton, Jason; Gaszner, Miklos; Schedl, Paul
2003-01-01
Although it is now well-established that boundary elements/insulators function to subdivide eukaryotic chromosomes into autonomous regulatory domains, the underlying mechanisms remain elusive. One idea is that boundaries act as barriers, preventing the processive spreading of “active” or “silenced” chromatin between domains. Another is that the partitioning into autonomous functional units is a consequence of an underlying structural subdivision of the chromosome into higher order “looped” domains. In this view, boundaries are thought to delimit structural domains by interacting with each other or with some other nuclear structure. The studies reported here provide support for the looped domain model. We show that the Drosophila scs and scs‘ boundary proteins, Zw5 and BEAF, respectively, interact with each other in vitro and in vivo. Moreover, consistent with idea that this protein:protein interaction might facilitate pairing of boundary elements, we find that that scs and scs‘ are in close proximity to each other in Drosophila nuclei. PMID:12629048
Coupling finite element and integral equation solutions using decoupled boundary meshes
NASA Technical Reports Server (NTRS)
Cwik, Tom
1992-01-01
A method is outlined for calculating scattered fields from inhomogeneous penetrable objects using a coupled finite element-integral equation solution. The finite element equation can efficiently model fields in penetrable and inhomogeneous regions, while the integral equation exactly models fields on the finite element mesh boundary and in the exterior region. By decoupling the interior finite element and exterior integral equation meshes, considerable flexibility is found in both the number of field expansion points as well as their density. Only the nonmetal portions of the object need be modeled using a finite element expansion; exterior perfect conducting surfaces are modeled using an integral equation with a single unknown field since E(tan) is identically zero on these surfaces. Numerical convergence, accuracy, and stability at interior resonant frequencies are studied in detail.
Boundary element simulation of surface waves on a deformed half-space
NASA Astrophysics Data System (ADS)
Litvinchuk, S. Yu.; Belov, A. A.; Markov, I. P.; Ipatov, A. A.; Petrov, A. N.
2015-11-01
Homogeneous and two-layer half-spaces consisting of an anisotropic elastic, isotropic viscoelastic, or poroelastic material are considered. The Kelvin-Voigt model and the model with the Abel kernel are used as models of the viscoelastic material; the poroelastic material is studied within the framework of the model of the compressible Biot material. The case where the half-space contains a cavity is also considered. Propagation of surface waves is studied by the boundary element method. The numerical solution involves the method of collocations for a regularized boundary integral equation.
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)
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.
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.
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.
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.
Quantum corrected model for plasmonic nanoparticles: A boundary element method implementation
NASA Astrophysics Data System (ADS)
Hohenester, Ulrich
2015-05-01
We present a variant of the recently developed quantum corrected model (QCM) for plasmonic nanoparticles [Nat. Commun. 3, 825 (2012), 10.1038/ncomms1806] using nonlocal boundary conditions. The QCM accounts for electron tunneling in narrow gap regions of coupled metallic nanoparticles, leading to the appearance of new charge-transfer plasmons. Our approach has the advantages that it emphasizes the nonlocal nature of tunneling and introduces only contact resistance, but not ohmic losses through tunneling. Additionally, it can be implemented much more easily in boundary element method (BEM) approaches. We develop the methodology for the QCM using nonlocal boundary conditions and present simulation results of our BEM implementation, which are in good agreement with those of the original QCM.
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.
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.
Wu, Shih-Jeh; Kuo, Ihyuan; Shung, K Kirk
2005-01-01
High frequency ultrasonic imaging (e.g. >30 MHz) from blood is difficult due to its tenuous backscattered pressure and the interference from adjacent tissues as well. To increase the sensitivity focused transducer has to be used, thus raising the complexity of interpreting the received signals. A numerical simulation of the ultrasonic scattering property from erythrocyte and rouleaux based on boundary element method was performed with experimental results based on a modified substitution method. The results (proportional relationship between backscattered pressure and frequency and the frequency limit for Rayleigh scattering) closely coincide with experimental data for erythrocyte. Rouleaux model results also show the dependence of degree of red cell aggregation on backscattering properties. The boundary element method serves as a good means to calculate the acoustic scattering from blood cells under arbitrary incident waves. PMID:15556649
Tang, Y.; Kline, J.A. Sr.
1996-12-01
Nonlinear boundary element analysis provides a more accurate and detailing tool for the design of switched reluctance machines, than the conventional equivalent-circuit methods. Design optimization through more detailed analysis and simulation can reduce development and prototyping costs and time to market. Firstly, magnetic field modeling of an industrial switched reluctance machine by boundary element method is reported in this paper. Secondly, performance prediction and dynamic simulation of motor and control design are presented. Thirdly, magnetic forces that cause noise and vibration are studied, to include the effects of motor and control design variations on noise in the design process. Testing of the motor in NEMA 215-Frame size is carried out to verify the accuracy of modeling and simulation.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Yang, Zhiguo; Wang, Li-Lian; Rong, Zhijian; Wang, Bo; Zhang, Baile
2016-04-01
In this paper, we present an efficient spectral-element method (SEM) for solving general two-dimensional Helmholtz equations in anisotropic media, with particular applications in accurate simulation of polygonal invisibility cloaks, concentrators and circular rotators arisen from the field of transformation electromagnetics (TE). In practice, we adopt a transparent boundary condition (TBC) characterized by the Dirichlet-to-Neumann (DtN) map to reduce wave propagation in an unbounded domain to a bounded domain. We then introduce a semi-analytic technique to integrate the global TBC with local curvilinear elements seamlessly, which is accomplished by using a novel elemental mapping and analytic formulas for evaluating global Fourier coefficients on spectral-element grids exactly. From the perspective of TE, an invisibility cloak is devised by a singular coordinate transformation of Maxwell's equations that leads to anisotropic materials coating the cloaked region to render any object inside invisible to observers outside. An important issue resides in the imposition of appropriate conditions at the outer boundary of the cloaked region, i.e., cloaking boundary conditions (CBCs), in order to achieve perfect invisibility. Following the spirit of [48], we propose new CBCs for polygonal invisibility cloaks from the essential "pole" conditions related to singular transformations. This allows for the decoupling of the governing equations of inside and outside the cloaked regions. With this efficient spectral-element solver at our disposal, we can study the interesting phenomena when some defects and lossy or dispersive media are placed in the cloaking layer of an ideal polygonal cloak.
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.
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.
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.
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.
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.
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.
Stability of the laminar boundary-layer flow behind a roughness element
NASA Astrophysics Data System (ADS)
Shin, Yong-su; Rist, Ulrich; Krämer, Ewald
2015-01-01
Roughness elements in laminar boundary layers generate both high shear layers and streaky structures. Because these phenomena interact, it is difficult to precisely ascertain the dominant instability mechanisms. With the goal of explicating such interactions, we study the stability of a laminar boundary layer subject to a single roughness element at a Reynolds number subcritical of bypass transition. Our work involves two parts: bi-global linear stability theory (LST) analysis and corroborating experimental measurements. Linear stability analysis of a flat-plate boundary layer perturbed by streamwise streaks reveals the presence of several unstable modes. Of the dominant two modes, one exhibits spanwise symmetry and the other is antisymmetric. These modes are termed `varicose' and `sinuous,' respectively. Corroborating experiments were conducted in the laminar water channel of the University of Stuttgart. By simultaneously traversing two hot-film probes, we are able to confirm the presence of both eigenmodes predicted by LST and to extract relevant data for each: eigenvalues, eigenfunctions, growth rates and phase distributions. The main part of the experiments has been performed under `natural' conditions, i.e., in the absence of external forcing. As the amplitude of the sinuous part of the results is much smaller than the varicose one and hence affected by measurement noise, a case with asymmetric external forcing is presented as well. Despite some deficiencies of the setup, it is possible to enhance the sinuous mode with respect to the unforced case and to confirm its existence as an eigenmode of the flow.
Movement of a spherical cell in capillaries using a boundary element method.
Wen, P H; Aliabadi, M H; Wang, W
2007-01-01
This study aims to investigate the translation and rotation of a spherical particle in capillaries and overcomes limitations in previous studies by using a boundary element method. The capillary, a straight cylindrical tube, is filled with a Newtonian viscous fluid. A spherical particle is arbitrarily positioned in the capillary either co-centrically or eccentrically and is free to translate and rotate. Flow in the capillary is first assumed to be caused solely by the movement of the sphere under the gravity. When a steady state is reached, the net force and torque on the sphere are zero. The translating velocity and rotation of the particle are calculated from equilibrium equations. For a co-centric sphere, our result agrees to Bohlin's analytical solution (Bohlin, 1960) and the difference is less than 1%. For an eccentrically positioned sphere in the tube, there are no analytical solutions unless the eccentricity is infinitesimal. Results by boundary element method (BEM) give an improved estimations on the velocity and rotation of the sphere than earlier results by a boundary singularity method (BSM), particularly when the clearance between the tube and the sphere becomes small. Movement of a spherical particle in a capillary driven by a pressure gradient is further investigated, which has closer relevance to movement of blood cells in capillaries. The current study using BEM enables investigation on cell movement in close proximities of the capillary wall. PMID:17027993
Hromadka, T.V., II; 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.
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.
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.
NASA Astrophysics Data System (ADS)
Citro, V.; Giannetti, F.; Luchini, P.; Auteri, F.
2015-08-01
We study the full three-dimensional instability mechanism past a hemispherical roughness element immersed in a laminar Blasius boundary layer. The inherent three-dimensional flow pattern beyond the Hopf bifurcation is characterized by coherent vortical structures usually called hairpin vortices. Direct numerical simulation results are used to analyze the formation and the shedding of hairpin vortices inside the shear layer. The first bifurcation is investigated by global-stability tools. We show the spatial structure of the linear direct and adjoint global eigenmodes of the linearized Navier-Stokes equations and use the structural-sensitivity field to locate the region where the instability mechanism acts. The core of this instability is found to be symmetric and spatially localized in the region immediately downstream of the roughness element. The effect of the variation of the ratio between the obstacle height k and the boundary layer thickness δk ∗ is also considered. The resulting bifurcation scenario is found to agree well with previous experimental investigations. A limit regime for k / δk ∗ < 1 . 5 is attained where the critical Reynolds number is almost constant, Rek ≈ 580. This result indicates that, in these conditions, the only important parameter identifying the bifurcation is the unperturbed (i.e., without the roughness element) velocity slope at the wall.
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.
Dynamics of ULVZ-mantle interaction using fast multipole boundary element method
NASA Astrophysics Data System (ADS)
Drombosky, T.; Hier-Majumder, S.
2012-12-01
Seismic observations over the past two decades show evidence of areas immediately above the core-mantle boundary characterized by sharp, differential drops in seismic velocities. These aptly named UltraLow Velocity Zones (ULVZs) are typically localized (50-100km wide) and thin (10-40 km thick). High concentration of the observed ULVZ patches near the edges of Large Low Shear Velocity Provinces (LLSVPs) indicate that the shape and distribution of the dynamic ULVZ patches are strongly coupled with the flow in the adjacent mantle. Two important properties modulating the extent of this coupling are the contrasts in density and viscosity between the ULVZ patches and the surrounding mantle. This work explores the interaction, coalescence, and break-up of ULVZ patches excited by an imposed mantle flow using the Fast Multipole Boundary Element Method (FMBEM). We model the ambient mantle as a high viscosity medium containing viscous, deformable ULVZ patches. The ambient mantle and ULVZ patches are both homogeneous but may differ from each other in viscosity and density. Mass and momentum conservation within each patch and the mantle are governed by the Stokes flow equation. The governing partial differential equations, aided with stress jump and no-slip boundary conditions at the ULVZ-mantle interfaces, are converted into a set of Fredholm integral equations of the second kind. Unlike traditional Boundary Element Methods (BEM), discretization of this integral equation using FMBEM produces a system of linear equations solvable by iterative sparse solver methods. This work reports a set of numerical experiments over a range of viscosity and density contrasts.
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. PMID:19475122
Otsuru, Toru; Tomiku, Reiji; Din, Nazli Bin Che; Okamoto, Noriko; Murakami, Masahiko
2009-06-01
An in-situ measurement technique of a material surface normal impedance is proposed. It includes a concept of "ensemble averaged" surface normal impedance that extends the usage of obtained values to various applications such as architectural acoustics and computational simulations, especially those based on the wave theory. The measurement technique itself is a refinement of a method using a two-microphone technique and environmental anonymous noise, or diffused ambient noise, as proposed by Takahashi et al. [Appl. Acoust. 66, 845-865 (2005)]. Measured impedance can be regarded as time-space averaged normal impedance at the material surface. As a preliminary study using numerical simulations based on the boundary element method, normal incidence and random incidence measurements are compared numerically: results clarify that ensemble averaging is an effective mode of measuring sound absorption characteristics of materials with practical sizes in the lower frequency range of 100-1000 Hz, as confirmed by practical measurements. PMID:19507960
Nonreflecting far-field boundary conditions for unsteady transonic flow computation
NASA Technical Reports Server (NTRS)
Kwak, D.
1980-01-01
The approximate nonreflecting far-field boundary condition, as proposed by Engquist 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 are discussed. Various cases are 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 time required to obtain the solution through the use of fewer mesh points.
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.
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.
NASA Astrophysics Data System (ADS)
Perton, Mathieu; Contreras-Zazueta, Marcial A.; Sánchez-Sesma, Francisco J.
2016-04-01
A new implementation of IBEM allows simulating the elastic wave propagation in complex configurations made of embedded regions that are or homogeneous with irregular boundaries or flat layers. In an older implementation, each layer of a flat layered region would have been treated as a separated homogeneous region without taking into account the flat boundary information. For both types of regions, the scattered field results from fictitious sources positioned along their boundaries. For the homogeneous regions, the fictitious sources emit as in a full-space and the wave field is given by analytical Green's functions. For flat layered regions, fictitious sources emit as in an unbounded flat layered region and the wave field is given by Green's functions obtained from the Discrete Wave Number (DWN) method. The new implementation allows then reducing the length of the discretized boundaries but DWN Green's functions require much more computation time than the full space Green's functions. Several optimization steps are then implemented and commented. Validations are presented for 2D and 3D problems. Higher efficiency is achieved in 3D.