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Artigos de revistas sobre o tema "Fast Boundary Element Methods"

Autor: Grafiati

Publicado: 23 de novembro de 2024

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1

Kravčenko, Michal, Michal Merta, and Jan Zapletal. "Distributed fast boundary element methods for Helmholtz problems." Applied Mathematics and Computation 362 (December 2019): 124503. http://dx.doi.org/10.1016/j.amc.2019.06.017.

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2

Gumerov, Nail A., and Ramani Duraiswami. "Fast multipole accelerated boundary element methods for room acoustics." Journal of the Acoustical Society of America 150, no. 3 (2021): 1707–20. http://dx.doi.org/10.1121/10.0006102.

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3

Of, G., O. Steinbach, and P. Urthaler. "Fast Evaluation of Volume Potentials in Boundary Element Methods." SIAM Journal on Scientific Computing 32, no. 2 (2010): 585–602. http://dx.doi.org/10.1137/080744359.

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4

Harbrecht, H., and M. Peters. "Comparison of fast boundary element methods on parametric surfaces." Computer Methods in Applied Mechanics and Engineering 261-262 (July 2013): 39–55. http://dx.doi.org/10.1016/j.cma.2013.03.022.

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5

Gumerov, Nail, and Ramani Duraiswami. "Simulations of room acoustics using fast multipole boundary element methods." Journal of the Acoustical Society of America 148, no. 4 (2020): 2693–94. http://dx.doi.org/10.1121/1.5147458.

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6

MUKHERJEE, SUBRATA, and YIJUN LIU. "THE BOUNDARY ELEMENT METHOD." International Journal of Computational Methods 10, no. 06 (2013): 1350037. http://dx.doi.org/10.1142/s0219876213500370.

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The boundary element method (BEM), along with the finite element and finite difference methods, is commonly used to carry out numerical simulations in a wide variety of subjects in science and engineering. The BEM, rooted in classical mathematics of integral equations, started becoming a useful computational tool around 50 years ago. Many researchers have worked on computational aspects of this method during this time.This paper presents an overview of the BEM and related methods. It has three sections. The first, relatively short section, presents the governing equations for classical applica

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7

Dargush, G. F., and M. M. Grigoriev. "Fast and Accurate Solutions of Steady Stokes Flows Using Multilevel Boundary Element Methods." Journal of Fluids Engineering 127, no. 4 (2005): 640–46. http://dx.doi.org/10.1115/1.1949648.

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Most recently, we have developed a novel multilevel boundary element method (MLBEM) for steady Stokes flows in irregular two-dimensional domains (Grigoriev, M.M., and Dargush, G.F., Comput. Methods. Appl. Mech. Eng., 2005). The multilevel algorithm permitted boundary element solutions with slightly over 16,000 degrees of freedom, for which approximately 40-fold speedups were demonstrated for the fast MLBEM algorithm compared to a conventional Gauss elimination approach. Meanwhile, the sevenfold memory savings were attained for the fast algorithm. This paper extends the MLBEM methodology to dra

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8

van 't Wout, Elwin, Reza Haqshenas, Pierre Gélat, and Nader Saffari. "Fast and accurate boundary element methods for large-scale computational acoustics." Journal of the Acoustical Society of America 154, no. 4_supplement (2023): A179. http://dx.doi.org/10.1121/10.0023190.

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The boundary element method (BEM) is a powerful algorithm to solve the Helmholtz equation for harmonic acoustic waves. The explicit use of Green’s functions avoids domain truncation of unbounded regions and accurately models wave propagation through homogeneous materials. Furthermore, fast multipole and hierarchical compression techniques provide efficient computations for dense matrix multiplications. However, the convergence of the iterative linear solvers deteriorates significantly when frequencies are high or materials have large contrasts in density or speed of sound. This talk presents s

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9

Newman, J. N., and C. H. Lee. "Boundary-Element Methods In Offshore Structure Analysis." Journal of Offshore Mechanics and Arctic Engineering 124, no. 2 (2002): 81–89. http://dx.doi.org/10.1115/1.1464561.

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Boundary-element methods, also known as panel methods, have been widely used for computations of wave loads and other hydrodynamic characteristics associated with the interactions of offshore structures with waves. In the conventional approach, based on the low-order panel method, the submerged surface of the structure is represented by a large number of small quadrilateral plane elements, and the solution for the velocity potential or source strength is approximated by a constant value on each element. In this paper, we describe two recent developments of the panel method. One is a higher-ord

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10

Chen, Leilei, Steffen Marburg, Wenchang Zhao, Cheng Liu, and Haibo Chen. "Implementation of Isogeometric Fast Multipole Boundary Element Methods for 2D Half-Space Acoustic Scattering Problems with Absorbing Boundary Condition." Journal of Theoretical and Computational Acoustics 27, no. 02 (2019): 1850024. http://dx.doi.org/10.1142/s259172851850024x.

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Isogeometric Analysis (IGA), which tries to bridge the gap between Computer Aided Engineering (CAE) and Computer Aided Design (CAD), has been widely proposed in recent research. According to the concept of IGA, this work develops a boundary element method (BEM) using non-Uniform Rational B-Splines (NURBS) as basis functions for the 2D half-space acoustic problems with absorbing boundary condition. Fast multipole method (FMM) is applied to accelerate the solution of an isogeometric BEM (IGA-BEM). Several examples are tested and it is shown that this advancement on isogeometric fast multipole bo

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11

Proskurov, S., R. Ewert, M. Lummer, M. Mößner, and J. W. Delfs. "Sound shielding simulation by coupled discontinuous Galerkin and fast boundary element methods." Engineering Applications of Computational Fluid Mechanics 16, no. 1 (2022): 1690–705. http://dx.doi.org/10.1080/19942060.2022.2098827.

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12

Buchau, Andre, and Wolfgang M. Rucker. "Meshfree Computation of Field Lines Across Multiple Domains Using Fast Boundary Element Methods." IEEE Transactions on Magnetics 51, no. 3 (2015): 1–4. http://dx.doi.org/10.1109/tmag.2014.2359520.

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13

Chaillat, Stéphanie, Marion Darbas, and Frédérique Le Louër. "Fast iterative boundary element methods for high-frequency scattering problems in 3D elastodynamics." Journal of Computational Physics 341 (July 2017): 429–46. http://dx.doi.org/10.1016/j.jcp.2017.04.020.

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14

Gumerov, Nail A., and Ramani Duraiswami. "Wideband fast multipole accelerated boundary element methods for the three‐dimensional Helmholtz equation." Journal of the Acoustical Society of America 125, no. 4 (2009): 2566. http://dx.doi.org/10.1121/1.4808753.

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15

Rodgers, Michael J., Shuangbiao Liu, Q. Jane Wang, and Leon M. Keer. "Boundary Element Methods for Steady-State Thermal-Mechanical Problems of Counterformal Contact." Journal of Tribology 126, no. 3 (2004): 443–49. http://dx.doi.org/10.1115/1.1757492.

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This paper presents a concise boundary integral equation framework for relating the thermal-mechanical surface load (the three traction components and the normal heat flux) to the thermal-mechanical response (the three quasi-static displacement components and the steady-state temperature). This uncoupled thermoelastic framework allows the simultaneous calculation of displacement and temperature—without subsurface discretization—because it is based on classical Green’s functions for displacement and for temperature and on newly derived Green’s functions for thermoelastic displacement. In genera

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16

Pozrikidis, C. "Boundary Element Grid Optimization for Stokes Flow With Corner Singularities." Journal of Fluids Engineering 124, no. 1 (2001): 22–28. http://dx.doi.org/10.1115/1.1436091.

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The accuracy of boundary-element methods for computing Stokes flow past boundaries with sharp corners where singularities occur is discussed. To resolve the singular behavior, a graded mesh of boundary elements whose length increases in a geometrical fashion with respect to distance from the corners according to a prescribed stretch ratio is used. Numerical results for two-dimensional Stokes flow past bodies with polygonal shapes reveal the existence of an optimal value of the stretch ratio for best accuracy in the computation of the force and torque. When the optimal value is used, fast conve

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17

Preuss, Simone. "A fast multipole boundary element method for acoustics in viscothermal fluids." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 267, no. 1 (2023): 326–29. http://dx.doi.org/10.3397/no_2023_0071.

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Standard numerical models in acoustics rely on the isentropic Helmholtz equation. Its derivation assumes adiabatic and reversible, i.e., dissipation-free, wave propagation. Sound waves in fluids are, however, subject to viscous and thermal losses. These losses originate from viscous friction and heat conduction, leading to the formation of acoustic boundary layers. Considering these effects becomes significant in setups with acoustic cavities of similar dimension as the boundary layers. Recently, boundary element methods (BEM) accounting for the viscothermal dissipation have been proposed. The

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18

TAKAHASHI, Toru, and Toshikazu EBISUZAKI. "Fast Computing of Boundary Element Methods using the Special-Purpose Computer for Molecular Dynamics." Proceedings of The Computational Mechanics Conference 2002.15 (2002): 823–24. http://dx.doi.org/10.1299/jsmecmd.2002.15.823.

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19

Wang, Haitao, Zhenhan Yao, and Pengbo Wang. "On the preconditioners for fast multipole boundary element methods for 2D multi-domain elastostatics." Engineering Analysis with Boundary Elements 29, no. 7 (2005): 673–88. http://dx.doi.org/10.1016/j.enganabound.2005.03.002.

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20

Chen, Zejun, and Hong Xiao. "The fast multipole boundary element methods (FMBEM) and its applications in rolling engineering analysis." Computational Mechanics 50, no. 5 (2012): 513–31. http://dx.doi.org/10.1007/s00466-012-0692-z.

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21

Wang, Qiao, Wei Zhou, Yonggang Cheng, Gang Ma, and Xiaolin Chang. "Fast multipole cell-based domain integration method for treatment of volume potentials in 3D elasticity problems." Engineering Computations 34, no. 6 (2017): 1849–73. http://dx.doi.org/10.1108/ec-03-2016-0111.

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Purpose Domain integrals, known as volume potentials in 3D elasticity problems, exist in many boundary-type methods, such as the boundary element method (BEM) for inhomogeneous partial differential equations. The purpose of this paper is to develop an accurate and reliable technique to effectively evaluate the volume potentials in 3D elasticity problems. Design/methodology/approach An adaptive background cell-based domain integration method is proposed for treatment of volume potentials in 3D elasticity problems. The background cells are constructed from the information of the boundary element

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22

Fan, Hong Ling. "Fast Algorithm for the Inverse Matrices of Periodic Adding Element Tridiagonal Matrices." Advanced Materials Research 159 (December 2010): 464–68. http://dx.doi.org/10.4028/www.scientific.net/amr.159.464.

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Adding element tridiagonal periodic matrices have an important effect for the algorithms of solving linear systems，computing the inverses, the triangular factorization，the boundary value problems by finite difference methods, interpolation by cubic splines, three-term difference equations and so on. In this paper, we give a fast algorithm for the Inverse Matrices of periodic adding element tridiagonal matrices.

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23

Nadimi, Sadegh, Ali Ghanbarzadeh, Anne Neville, and Mojtaba Ghadiri. "Effect of particle roughness on the bulk deformation using coupled boundary element and discrete element methods." Computational Particle Mechanics 7, no. 3 (2019): 603–13. http://dx.doi.org/10.1007/s40571-019-00288-3.

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Abstract Particles slide and roll on each other when a granular medium is sheared. Consequently, the tribological properties, such as inter-particle friction and adhesion, play a major role in influencing their bulk failure and rheology. Although the influence of roughness on adhesion and friction of contacting surfaces is known, the incorporation of the surface roughness in the numerical modelling of granular materials has received little attention. In this study, the boundary element method (BEM), which is widely used for simulating the mechanics of interacting surfaces, is coupled with disc

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24

MAGOULÈS, FRÉDÉRIC, and ROMAN PUTANOWICZ. "OPTIMAL CONVERGENCE OF NON-OVERLAPPING SCHWARZ METHODS FOR THE HELMHOLTZ EQUATION." Journal of Computational Acoustics 13, no. 03 (2005): 525–45. http://dx.doi.org/10.1142/s0218396x05002748.

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The non-overlapping Schwarz method with absorbing boundary conditions instead of the Dirichlet boundary conditions is an efficient variant of the overlapping Schwarz method for the Helmholtz equation. These absorbing boundary conditions defined on the interface between the subdomains are the key ingredients to obtain a fast convergence of the iterative Schwarz algorithm. In a one-way subdomains splitting, non-local optimal absorbing boundary conditions can be obtained and leads to the convergence of the Schwarz algorithm in a number of iterations equal to the number of subdomains minus one. Th

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25

Achdou, Y., and O. Pironneau. "A Fast Solver for Navier–Stokes Equations in the Laminar Regime Using Mortar Finite Element and Boundary Element Methods." SIAM Journal on Numerical Analysis 32, no. 4 (1995): 985–1016. http://dx.doi.org/10.1137/0732046.

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26

Fedelinski, Piotr. "Computer Modelling of Dynamic Fracture Experiments." Key Engineering Materials 454 (December 2010): 113–25. http://dx.doi.org/10.4028/www.scientific.net/kem.454.113.

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In this work the time-domain boundary element method (BEM) is applied to simulate dynamic fracture experiments. The fast fracture is modelled by adding new boundary elements at the crack tip. The direction of crack growth is perpendicular to the direction of maximum circumferencial stress. The time dependent loading of specimens and velocities of crack growth are taken from experiments as input data for computer simulations. The method is used to analyze: a short beam specimen, a special mixed-mode specimen and a three-point bend specimen subjected to impact loads. The dynamic stress intensity

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27

Zhao, Yan Lei, and Xue Ting Liu. "Fast Algorithm for the Inverse Matrices of Adding Element Tridiagonal Periodic Matrices in Signal Processing." Advanced Materials Research 121-122 (June 2010): 682–86. http://dx.doi.org/10.4028/www.scientific.net/amr.121-122.682.

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Adding element tridiagonal matrices play a very important role in the theory and practical applications, such as the boundary value problems by finite difference methods, interpolation by cubic splines, three-term difference equations and so on. In this paper, we give a fast algorithm for the Inverse Matrices of periodic adding element tridiagonal matrices.

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28

Dölz, Jürgen, Stefan Kurz, Sebastian Schöps, and Felix Wolf. "Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples." SIAM Journal on Scientific Computing 41, no. 5 (2019): B983—B1010. http://dx.doi.org/10.1137/18m1227251.

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29

Ping, Xuecheng, Mengcheng Chen, Wei Zhu, Yihua Xiao, and Weixing Wu. "Computations of Singular Stresses Along Three-Dimensional Corner Fronts by a Super Singular Element Method." International Journal of Computational Methods 14, no. 06 (2017): 1750065. http://dx.doi.org/10.1142/s0219876217500657.

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In order to consider corner configurations with straight corner fronts in three-dimensional (3D) solids, a super polygonal prismatic element containing a straight corner front is established by using the numerical eigensolutions of singular stress fields and the Hellinger–Reissner variational principle. Singular stresses near the corner front subject to far-field boundary conditions can be obtained by incorporating the super singular element with conventional 3D brick elements. The numerical studies are conducted to demonstrate the simplicity of the proposed technique in handling fracture prob

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30

YASUDA, Y., S. SAKAMOTO, Y. KOSAKA, T. SAKUMA, N. OKAMOTO, and T. OSHIMA. "NUMERICAL ANALYSIS OF LARGE-SCALE SOUND FIELDS USING ITERATIVE METHODS PART I: APPLICATION OF KRYLOV SUBSPACE METHODS TO BOUNDARY ELEMENT ANALYSIS." Journal of Computational Acoustics 15, no. 04 (2007): 449–71. http://dx.doi.org/10.1142/s0218396x07003470.

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The convergence behavior of the Krylov subspace iterative solvers towards the systems with the 3D acoustical BEM is investigated through numerical experiments. The fast multipole BEM, which is an efficient BEM based on the fast multipole method, is used for solving problems with up to about 100,000 DOF. It is verified that the convergence behavior of solvers is much affected by the formulation of the BEM (singular, hypersingular, and Burton-Miller formulation), the complexity of the shape of the problem, and the sound absorption property of the boundaries. In BiCG-like solvers, GPBiCG and BiCG

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31

Winckelmans, G. S., J. K. Salmon, M. S. Warren, A. Leonard, and B. Jodoin. "Application of fast parallel and sequential tree codes to computing three-dimensional flows with the vortex element and boundary element methods." ESAIM: Proceedings 1 (1996): 225–40. http://dx.doi.org/10.1051/proc:1996039.

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32

Zhou, H., Y. Zhang, J. Wen, and S. Cui. "Mould cooling simulation for injection moulding using a fast boundary element method approach." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 224, no. 4 (2009): 653–62. http://dx.doi.org/10.1243/09544054jem1407.

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The existing cooling simulations for injection moulding are mostly based on the boundary element method (BEM). In this paper, a fast BEM approach for mould cooling analysis is developed. The actual problem is decoupled into a one-dimensional transient heat conduction problem within the thin part and a cycle-averaged steady state three-dimensional heat conduction problem of the mould. The BEM is formulated for the solution of the mould heat transfer problem. A dynamic allocation strategy of integral points is proposed when using the Gaussian integral formula to generate the BEM matrix. Consider

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33

Ma, F., J. Chatterjee, and P. K. Banerjee. "New Fast Convolution Algorithm in Boundary-Element Methods for Two- and Three-Dimensional Linear Soil Consolidation Analysis." International Journal of Geomechanics 7, no. 3 (2007): 236–49. http://dx.doi.org/10.1061/(asce)1532-3641(2007)7:3(236).

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34

TAKAHASHI, Toru, Hiroshi ISAKARI, and Toshiro MATSUMOTO. "An implementation and benchmark of a fast-multipole-type direct-solver for two-dimensional boundary element methods." Proceedings of The Computational Mechanics Conference 2014.27 (2014): 296–98. http://dx.doi.org/10.1299/jsmecmd.2014.27.296.

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35

Ochmann, Martin. "Two fast methods for the calculation of sound radiation: Multipol radiator synthesis and boundary element multigrid method." Journal of the Acoustical Society of America 87, S1 (1990): S74. http://dx.doi.org/10.1121/1.2028356.

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36

Song, Haiming, Kai Zhang, and Yutian Li. "Finite Element and Discontinuous Galerkin Methods with Perfect Matched Layers for American Options." Numerical Mathematics: Theory, Methods and Applications 10, no. 4 (2017): 829–51. http://dx.doi.org/10.4208/nmtma.2017.0020.

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AbstractThis paper is devoted to the American option pricing problem governed by the Black-Scholes equation. The existence of an optimal exercise policy makes the problem a free boundary value problem of a parabolic equation on an unbounded domain. The optimal exercise boundary satisfies a nonlinear Volterra integral equation and is solved by a high-order collocation method based on graded meshes. This free boundary is then deformed to a fixed boundary by the front-fixing transformation. The boundary condition at infinity (due to the fact that the underlying asset's price could be arbitrarily

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37

Ebrahimnejad, Latif, and Reza Attarnejad. "A novel way of using fast wavelet transforms to solve dense linear systems arising from boundary element methods." Engineering Computations 26, no. 5 (2009): 483–99. http://dx.doi.org/10.1108/02644400910970167.

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38

Amlani, Faisal, Stéphanie Chaillat, and Adrien Loseille. "An efficient preconditioner for adaptive Fast Multipole accelerated Boundary Element Methods to model time-harmonic 3D wave propagation." Computer Methods in Applied Mechanics and Engineering 352 (August 2019): 189–210. http://dx.doi.org/10.1016/j.cma.2019.04.026.

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39

Pan, Jie, Jingwei Huang, Yunli Wang, Gengdong Cheng, and Yong Zeng. "A self-learning finite element extraction system based on reinforcement learning." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 35, no. 2 (2021): 180–208. http://dx.doi.org/10.1017/s089006042100007x.

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AbstractAutomatic generation of high-quality meshes is a base of CAD/CAE systems. The element extraction is a major mesh generation method for its capabilities to generate high-quality meshes around the domain boundary and to control local mesh densities. However, its widespread applications have been inhibited by the difficulties in generating satisfactory meshes in the interior of a domain or even in generating a complete mesh. The element extraction method's primary challenge is to define element extraction rules for achieving high-quality meshes in both the boundary and the interior of a g

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40

Chatzipantelidis, Panagiotis, Zoltan Horváth, and Vidar Thomée. "On Preservation of Positivity in Some Finite Element Methods for the Heat Equation." Computational Methods in Applied Mathematics 15, no. 4 (2015): 417–37. http://dx.doi.org/10.1515/cmam-2015-0018.

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AbstractWe consider the initial boundary value problem for the homogeneous heat equation, with homogeneous Dirichlet boundary conditions. By the maximum principle the solution is nonnegative for positive time if the initial data are nonnegative. We complement in a number of ways earlier studies of the possible extension of this fact to spatially semidiscrete and fully discrete piecewise linear finite element discretizations, based on the standard Galerkin method, the lumped mass method, and the finite volume element method. We also provide numerical examples that illustrate our findings.

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41

Illyashenko, Ludmila, and Alexander Nerukh. "APPLICATION OF SPECTRAL METHODS OF BOUNDARY INTEGRAL EQUATIONS FOR MODELING OF NANOOPTICAL DEVICES." Bulletin of the National Technical University "KhPI". Series: Mathematical modeling in engineering and technologies, no. 1 (August 1, 2023): 122–27. http://dx.doi.org/10.20998/2222-0631.2023.01.18.

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Efficiency of modeling of optical nanostructures depends not only on the accuracy of the description of the new physical processes which appear in the new configurations of resonantly scattering and resonantly absorbing structures, but also on the selection of appropriate algorithms for solving the corresponding mathematical problem and numerical parameters of modeling depending on parameters of elements. This is why solving complicated problems of modeling complex resonantly scattering and resonantly absorbing electrodynamic nanostructures involves deep learning of all groups of new unknown e

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42

Wang, Junpeng, Jinyou Xiao, and Lihua Wen. "A Numerical Method for Estimating the Nonlinear Eigenvalue Numbers of Boundary Element." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 37, no. 1 (2019): 28–34. http://dx.doi.org/10.1051/jnwpu/20193710028.

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Recently, some new proposed methods for solving nonlinear eigenvalue problems (NEPs) have promoted the development of large-scale modal analysis using BEM. However, the efficiency and robustness of such methods are generally still dependent on input parameters, especially on the parameters related to the number of eigenvalues to be solved. This limitation obviously restricts the popularization of the practical engineering application of modal analysis using BEM. Therefore, this paper develops a numerical method for estimating the number of nonlinear eigenvalues of the boundary element method.

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43

Li, Chengxi, and Jijian Lian. "Development and Application of a Pre-Corrected Fast Fourier Transform Accelerated Multi-Layer Boundary Element Method for the Simulation of Shallow Water Acoustic Propagation." Applied Sciences 10, no. 7 (2020): 2393. http://dx.doi.org/10.3390/app10072393.

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Because of the complexities associated with the domain geometry and environments, accurate prediction of acoustics propagation and scattering in realistic shallow water environments by direct numerical simulation is challenging. Based on the pre-corrected Fast Fourier Transform (PFFT) method, we accelerated the classical boundary element method (BEM) to predict the acoustic propagation in a multi-layer shallow water environment. The classical boundary element method formulate the acoustics propagation problem as a linear equation system in the form of [A]{x}={b}, where [A] is an N×N dense matr

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44

SHERBAKOV, Sergei S., Mikhail M. POLESTCHUK, and Dzianis E. MARMYSH. "PARALLELIZING OF COMPUTATIONS ON A GRAPHICS PROCESSING UNIT FOR ACCELERATING BOUNDARY ELEMENT CALCULATIONS IN MECHANICS." Mechanics of Machines, Mechanisms and Materials 1, no. 66 (2024): 80–85. http://dx.doi.org/10.46864/1995-0470-2024-1-66-80-85.

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In solving problems of computer modeling using various methods, accuracy and computational efficiency questions always arise. This study explores the application of two modifications of the boundary element method to solve the problem of potential distribution within a closed two-dimensional domain with a uniform potential distribution on its boundary. The first modification involves using three nonlinear shape functions instead of one. The second modification applies the Galerkin method to the boundary element approach with three nonlinear shape functions. The essence of this modification lie

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45

Chernukha, Nikita. "New Numerical Methods for Structural Mechanics Problems in Unbounded Domains." Applied Mechanics and Materials 725-726 (January 2015): 848–53. http://dx.doi.org/10.4028/www.scientific.net/amm.725-726.848.

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The article is devoted to the problem of numerical simulation of unbounded domains in structural mechanics. Nowadays there are many numerical methods to analyze structural mechanics problems in infinite domains. A brief analytical review of existing numerical methods is presented. Among them are finite difference method, boundary element method (BEM), finite element method (FEM) and scaled boundary finite element method (SBFEM). No one suggests general approach for all kinds of problem statements. Vast majority of industrial software realize FEM. Considering this fact it is more reasonable to

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Fochesato, Christophe, and Frédéric Dias. "A fast method for nonlinear three-dimensional free-surface waves." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2073 (2006): 2715–35. http://dx.doi.org/10.1098/rspa.2006.1706.

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An efficient numerical model for solving fully nonlinear potential flow equations with a free surface is presented. Like the code that was developed by Grilli et al . (Grilli et al . 2001 Int. J. Numer. Methods Fluids 35 , 829–867), it uses a high-order three-dimensional boundary-element method combined with mixed Eulerian–Lagrangian time updating, based on second-order explicit Taylor expansions with adaptive time-steps. Such methods are known to be accurate but expensive. The efficiency of the code has been greatly improved by introducing the fast multipole algorithm. By replacing every matr

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Oliveira, Tiago, Wilber Vélez, and Artur Portela. "Formulation of local numerical methods in linear elasticity." Multidiscipline Modeling in Materials and Structures 16, no. 5 (2020): 853–86. http://dx.doi.org/10.1108/mmms-05-2018-0094.

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PurposeThis paper is concerned with new formulations of local meshfree and finite element numerical methods, for the solution of two-dimensional problems in linear elasticity.Design/methodology/approachIn the local domain, assigned to each node of a discretization, the work theorem establishes an energy relationship between a statically admissible stress field and an independent kinematically admissible strain field. This relationship, derived as a weighted residual weak form, is expressed as an integral local form. Based on the independence of the stress and strain fields, this local form of

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Yari, Ehsan, and Hassan Ghassemi. "Boundary Element Method Applied to Added Mass Coefficient Calculation of the Skewed Marine Propellers." Polish Maritime Research 23, no. 2 (2016): 25–31. http://dx.doi.org/10.1515/pomr-2016-0017.

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AbstractThe paper mainly aims to study computation of added mass coefficients for marine propellers. A three-dimensional boundary element method (BEM) is developed to predict the propeller added mass and moment of inertia coefficients. Actually, only few experimental data sets are available as the validation reference. Here the method is validated with experimental measurements of the B-series marine propeller. The behavior of the added mass coefficients predicted based on variation of geometric and flow parameters of the propeller is calculated and analyzed. BEM is more accurate in obtaining

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Mora, Jaime, and Leszek Demkowicz. "Fast Integration of DPG Matrices Based on Sum Factorization for all the Energy Spaces." Computational Methods in Applied Mathematics 19, no. 3 (2019): 523–55. http://dx.doi.org/10.1515/cmam-2018-0205.

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AbstractNumerical integration of the stiffness matrix in higher-order finite element (FE) methods is recognized as one of the heaviest computational tasks in an FE solver. The problem becomes even more relevant when computing the Gram matrix in the algorithm of the Discontinuous Petrov Galerkin (DPG) FE methodology. Making use of 3D tensor-product shape functions, and the concept of sum factorization, known from standard high-order FE and spectral methods, here we take advantage of this idea for the entire exact sequence of FE spaces defined on the hexahedron. The key piece to the presented al

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MENG, WENHUI, and JUNZHI CUI. "COMPARATIVE STUDY OF TWO DIFFERENT FMM–BEM METHODS IN SOLVING 2-D ACOUSTIC TRANSMISSION PROBLEMS WITH A MULTILAYERED OBSTACLE." International Journal of Structural Stability and Dynamics 11, no. 01 (2011): 197–214. http://dx.doi.org/10.1142/s021945541100404x.

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The fast multipole method (FMM) is an effective approach for accelerating the computation efficiency of the boundary element method (BEM) in solving problems that are computationally intensive. This paper presents two different BEMs, i.e., Kress' and Seydou's methods, for solving two-dimensional (2D) acoustic transmission problems with a multilayered obstacle, along with application of the FMM to solution of the related boundary integral equations. Conventional BEM requires O(MN2) operations to compute the equations for this problem. By using the FMM, both the amount of computation and the mem

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