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Zeitschriftenartikel zum Thema „Boundary element methods“

Autor: Grafiati

Veröffentlicht am 4. Juni 2021

Zuletzt aktualisiert am 9. Juni 2025

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1

Nedelec, Jean-Claude, Goong Chen, and Jianxin Zhou. "Boundary Element Methods." Mathematics of Computation 60, no. 202 (April 1993): 851. http://dx.doi.org/10.2307/2153130.

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2

Chaillat-Loseille, Stéphanie, Ralf Hiptmair, and Olaf Steinbach. "Boundary Element Methods." Oberwolfach Reports 17, no. 1 (February 9, 2021): 273–376. http://dx.doi.org/10.4171/owr/2020/5.

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3

Feischl, Michael, Thomas Führer, Norbert Heuer, Michael Karkulik, and Dirk Praetorius. "Adaptive Boundary Element Methods." Archives of Computational Methods in Engineering 22, no. 3 (June 27, 2014): 309–89. http://dx.doi.org/10.1007/s11831-014-9114-z.

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4

Khoromskij, B. N., and J. M. Melenk. "Boundary Concentrated Finite Element Methods." SIAM Journal on Numerical Analysis 41, no. 1 (January 2003): 1–36. http://dx.doi.org/10.1137/s0036142901391852.

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5

Beskos, D. E., and U. Heise. "Boundary Element Methods in Mechanics." Journal of Applied Mechanics 55, no. 4 (December 1, 1988): 997. http://dx.doi.org/10.1115/1.3173761.

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6

Bonnet, Marc, Giulio Maier, and Castrenze Polizzotto. "Symmetric Galerkin Boundary Element Methods." Applied Mechanics Reviews 51, no. 11 (November 1, 1998): 669–704. http://dx.doi.org/10.1115/1.3098983.

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This review article concerns a methodology for solving numerically, for engineering purposes, boundary and initial-boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form. The discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager’s sense. As main consequences of the above provisions, symmetry is exhibited by matrices with a key role in the algebraized versions; some quadratic forms have a clear energy meaning; variational properties characterize the solutions and other results, invalid in traditional boundary element methods enrich the theory underlying the computational applications. The present survey outlines recent theoretical and computational developments of the title methodology with particular reference to linear elasticity, elastoplasticity, fracture mechanics, time-dependent problems, variational approaches, singular integrals, approximation issues, sensitivity analysis, coupling of boundary and finite elements, and computer implementations. Areas and aspects which at present require further research are identified, and comparative assessments are attempted with respect to traditional boundary integral-elements. This article includes 176 references.

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7

Costabel, Martin. "Principles of boundary element methods." Computer Physics Reports 6, no. 1-6 (August 1987): 243–74. http://dx.doi.org/10.1016/0167-7977(87)90014-1.

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8

Hsiao, George C. "Boundary element methods—An overview." Applied Numerical Mathematics 56, no. 10-11 (October 2006): 1356–69. http://dx.doi.org/10.1016/j.apnum.2006.03.030.

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9

Faust, G., and J. Szimmat. "Developments in boundary element methods." Computer Methods in Applied Mechanics and Engineering 60, no. 2 (February 1987): 253–54. http://dx.doi.org/10.1016/0045-7825(87)90112-5.

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10

Faermann, Birgit. "Adaptive galerkin boundary element methods." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 78, S3 (1998): 909–10. http://dx.doi.org/10.1002/zamm.19980781527.

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11

Liu, Shaolin, Dinghui Yang, Xingpeng Dong, Qiancheng Liu, and Yongchang Zheng. "Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling." Solid Earth 8, no. 5 (September 28, 2017): 969–86. http://dx.doi.org/10.5194/se-8-969-2017.

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Abstract. The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency–wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.

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12

Phan, Thanh Xuan, and Olaf Steinbach. "Boundary element methods for parabolic boundary control problems." Journal of Integral Equations and Applications 26, no. 1 (March 2014): 53–90. http://dx.doi.org/10.1216/jie-2014-26-1-53.

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13

Betcke, Timo, Erik Burman, and Matthew W. Scroggs. "Boundary Element Methods with Weakly Imposed Boundary Conditions." SIAM Journal on Scientific Computing 41, no. 3 (January 2019): A1357—A1384. http://dx.doi.org/10.1137/18m119625x.

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14

Of, Günther, Thanh Xuan Phan, and Olaf Steinbach. "Boundary element methods for Dirichlet boundary control problems." Mathematical Methods in the Applied Sciences 33, no. 18 (September 19, 2010): 2187–205. http://dx.doi.org/10.1002/mma.1356.

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15

Beskos, Dimitri E. "Boundary Element Methods in Dynamic Analysis." Applied Mechanics Reviews 40, no. 1 (January 1, 1987): 1–23. http://dx.doi.org/10.1115/1.3149529.

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A review of boundary element methods for the numerical solution of dynamic problems of linear elasticity is presented. The integral formulation and the corresponding numerical solution of three- and two-dimensional elastodynamics from the direct boundary element method viewpoint and in both the frequency and time domains are described. The special case of the anti-plane motion governed by the scalar wave equation is also considered. In all the cases both harmonic and transient dynamic disturbances are taken into account. Special features of material behavior such as viscoelasticity, inhomogeneity, anisotropy, and poroelasticity are briefly discussed. Some other nonconventional boundary element methods as well as the hybrid scheme that results from the combination of boundary and finite elements are also reviewed. All these boundary element methodologies are applied to: soil-structure interaction problems that include the dynamic analysis of underground and above-ground structures, foundations, piles, and vibration isolation devices; problems of crack propagation and wave diffraction by cracks; and problems dealing with the dynamics of beams, plates, and shells. Finally, a brief assessment of the progress achieved so far in dynamic analysis is made and areas where further research is needed are identified.

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16

Utzinger, Helmut Harbrecht and Manuela. "On Adaptive Wavelet Boundary Element Methods." Journal of Computational Mathematics 36, no. 1 (June 2018): 90–109. http://dx.doi.org/10.4208/jcm.1610-m2016-0496.

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17

Aliabadi, M. H. "Boundary Element Methods for Crack Dynamics." Key Engineering Materials 145-149 (October 1997): 323–28. http://dx.doi.org/10.4028/www.scientific.net/kem.145-149.323.

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18

Carstensen, Carsten, and Dirk Praetorius. "Convergence of adaptive boundary element methods." Journal of Integral Equations and Applications 24, no. 1 (March 2012): 1–23. http://dx.doi.org/10.1216/jie-2012-24-1-1.

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19

Ohl, Siew-Wan, Md Haiqal Haqim Bin Md. Rahim, Evert Klaseboer, and Boo Cheong Khoo. "Blake, bubbles and boundary element methods." IMA Journal of Applied Mathematics 85, no. 2 (December 18, 2019): 190–213. http://dx.doi.org/10.1093/imamat/hxz032.

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Abstract Professor John Blake spent a considerable part of his scientific career on studying bubble dynamics and acoustic cavitation. As Blake was a mathematician, we will be focusing on the theoretical and numerical studies (and much less on experimental results). Rather than repeating what is essentially already known, we will try to present the results from a different perspective as much as possible. This review will also be of interest for readers who wish to know more about the boundary element method in general, which is a method often used by Blake and his colleagues to simulate bubbles. We will, however, not limit the discussion to bubble dynamics but try to give a broad discussion on recent advances and improvements to this method, especially for potential problems (Laplace) and wave equations (Helmholtz). Based on examples from Blake’s work, we will guide the reader and show some of the mysteries of bubble dynamics, such as why jets form in collapsing bubbles near rigid surfaces. Where appropriate, we will illustrate the concepts with examples drawn from numerical simulations and experiments.

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20

Tausch, Johannes. "Equivariant Preconditioners for Boundary Element Methods." SIAM Journal on Scientific Computing 17, no. 1 (January 1996): 90–99. http://dx.doi.org/10.1137/0917008.

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21

Gaul, Lothar, Marcus Wagner, and Wolfgang Wenzel. "Teaching boundary element methods in acoustics." Journal of the Acoustical Society of America 105, no. 2 (February 1999): 1123. http://dx.doi.org/10.1121/1.425242.

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22

Syngellakis, Stavros. "Boundary element methods for polymer analysis." Engineering Analysis with Boundary Elements 27, no. 2 (February 2003): 125–35. http://dx.doi.org/10.1016/s0955-7997(02)00090-5.

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23

Wu, J. "Fundamental solutions and boundary element methods." Engineering Analysis with Boundary Elements 4, no. 1 (March 1987): 2–6. http://dx.doi.org/10.1016/0955-7997(87)90013-0.

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24

Portela, A. "Stress analysis by boundary element methods." Engineering Analysis with Boundary Elements 9, no. 2 (January 1992): 189–90. http://dx.doi.org/10.1016/0955-7997(92)90063-d.

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25

Martin, P. A. "Maurice Jaswon and boundary element methods." Engineering Analysis with Boundary Elements 36, no. 11 (November 2012): 1699–704. http://dx.doi.org/10.1016/j.enganabound.2012.05.003.

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26

Ylä-Oijala, Pasi, Sami P. Kiminki, and Seppo Järvenpää. "Conforming boundary element methods in acoustics." Engineering Analysis with Boundary Elements 50 (January 2015): 447–58. http://dx.doi.org/10.1016/j.enganabound.2014.10.002.

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27

Feischl, Michael, Gregor Gantner, Alexander Haberl, and Dirk Praetorius. "Adaptive 2D IGA boundary element methods." Engineering Analysis with Boundary Elements 62 (January 2016): 141–53. http://dx.doi.org/10.1016/j.enganabound.2015.10.003.

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28

Allgower, Eugene L., Klaus Böhmer, Kurt Georg, and Rick Miranda. "Exploiting Symmetry in Boundary Element Methods." SIAM Journal on Numerical Analysis 29, no. 2 (April 1992): 534–52. http://dx.doi.org/10.1137/0729034.

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29

Wu, J. C. "Fundamental solutions and boundary element methods." Engineering Analysis 4, no. 1 (March 1987): 2–6. http://dx.doi.org/10.1016/0264-682x(87)90025-6.

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30

Popescu, M. "Boundary element methods in solid mechanics." Earth-Science Reviews 22, no. 1 (May 1985): 96–97. http://dx.doi.org/10.1016/0012-8252(85)90044-3.

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31

Allgower, Eugene L., Kurt Georg, and Ralf Widmann. "Volume integrals for boundary element methods." Journal of Computational and Applied Mathematics 38, no. 1-3 (December 1991): 17–29. http://dx.doi.org/10.1016/0377-0427(91)90158-g.

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32

Steinbach, O. "Boundary element methods for variational inequalities." Numerische Mathematik 126, no. 1 (May 17, 2013): 173–97. http://dx.doi.org/10.1007/s00211-013-0554-4.

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33

Langer, U., and O. Steinbach. "Boundary Element Tearing and Interconnecting Methods." Computing 71, no. 3 (November 1, 2003): 205–28. http://dx.doi.org/10.1007/s00607-003-0018-2.

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34

Langer, Ulrich, and Olaf Steinbach. "Recent Advances in Boundary Element Methods." Computational Methods in Applied Mathematics 23, no. 2 (March 28, 2023): 297–99. http://dx.doi.org/10.1515/cmam-2023-0037.

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35

Carstensen, Carsten, and Ernst P. Stephan. "Adaptive boundary-element methods for transmission problems." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 38, no. 3 (January 1997): 336–67. http://dx.doi.org/10.1017/s0334270000000722.

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AbstractIn this paper we present an adaptive boundary-element method for a transmission prob-lem for the Laplacian in a two-dimensional Lipschitz domain. We are concerned with an equivalent system of boundary-integral equations of the first kind (on the transmission boundary) involving weakly-singular, singular and hypersingular integral operators. For the h-version boundary-element (Galerkin) discretization we derive an a posteriori error estimate which guarantees a given bound for the error in the energy norm (up to a multiplicative constant). Then, following Eriksson and Johnson this yields an adaptive algorithm steering the mesh refinement. Numerical examples confirm that our adaptive algorithms yield automatically good triangulations and are efficient.

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36

Ganesh, M., and O. Steinbach. "Boundary element methods for potential problems with nonlinear boundary conditions." Mathematics of Computation 70, no. 235 (June 12, 2000): 1031–43. http://dx.doi.org/10.1090/s0025-5718-00-01266-7.

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37

Tanaka, Masataka, Vladimir Sladek, and Jan Sladek. "Regularization Techniques Applied to Boundary Element Methods." Applied Mechanics Reviews 47, no. 10 (October 1, 1994): 457–99. http://dx.doi.org/10.1115/1.3111062.

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This review article deals with the regularization of the boundary element formulations for solution of boundary value problems of continuum mechanics. These formulations may be singular owing to the use of two-point singular fundamental solutions. When the physical interpretation is irrelevant for this topic of computational mechanics, we consider various mechanical problems simultaneously within particular sections selected according to the main topic. In spite of such a structure of the paper, applications of the regularization techniques to many mechanical problems are described. There are distinguished two main groups of regularization techniques according to their application to singular formulations either before or after the discretization. Further subclassification of each group is made with respect to basic principles employed in individual regularization techniques. This paper summarizes the substances of the regularization procedures which are illustrated on the boundary element formulation for a scalar potential field. We discuss the regularizations of both the strongly singular and hypersingular integrals, occurring in the boundary integral equations, as well as those of nearly singular and nearly hypersingular integrals arising when the source point is near the integration element (as compared to its size) but not on this element. The possible dimensional inconsistency (or scale dependence of results) of the regularization after discretization is pointed out. Finally, we discuss the numerical approximations in various boundary element formulations, as well as the implementations of solutions of some problems for which derivative boundary integral equations are required.

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38

Wu, K. L., G. Y. Delisle, D. G. Fang, and M. Lecours. "Coupled Finite Element and boundary Element Methods in Electromagnetic Scattering." Progress In Electromagnetics Research 02 (1990): 113–32. http://dx.doi.org/10.2528/pier89010300.

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39

Of, G., G. J. Rodin, O. Steinbach, and M. Taus. "Coupling of Discontinuous Galerkin Finite Element and Boundary Element Methods." SIAM Journal on Scientific Computing 34, no. 3 (January 2012): A1659—A1677. http://dx.doi.org/10.1137/110848530.

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40

Bernhard, Robert J. "General characteristics of the finite element and boundary element methods." Journal of the Acoustical Society of America 90, no. 4 (October 1991): 2250. http://dx.doi.org/10.1121/1.401507.

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41

Panchal, Piyush, and Ralf Hiptmair. "Electrostatic Force Computation with Boundary Element Methods." SMAI journal of computational mathematics 8 (April 8, 2022): 49–74. http://dx.doi.org/10.5802/smai-jcm.79.

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42

JEON, Youngmok, and Eun-Jae PARK. "Cell boundary element methods for elliptic problems." Hokkaido Mathematical Journal 36, no. 4 (November 2007): 669–85. http://dx.doi.org/10.14492/hokmj/1272848027.

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43

Georg, Kurt. "Approximation of Integrals for Boundary Element Methods." SIAM Journal on Scientific and Statistical Computing 12, no. 2 (March 1991): 443–53. http://dx.doi.org/10.1137/0912024.

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44

Nguyen, D. T., J. Qin, M. I. Sancer, and R. McClary. "Finite element–boundary integral methods in electromagnetics." Finite Elements in Analysis and Design 38, no. 5 (March 2002): 391–400. http://dx.doi.org/10.1016/s0168-874x(01)00066-x.

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45

Amaya, K., and S. Aoki. "Effective boundary element methods in corrosion analysis." Engineering Analysis with Boundary Elements 27, no. 5 (May 2003): 507–19. http://dx.doi.org/10.1016/s0955-7997(02)00158-3.

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46

Brebbia, C. "10th International conference on boundary element methods." Engineering Analysis with Boundary Elements 5, no. 4 (December 1988): 217–19. http://dx.doi.org/10.1016/0955-7997(88)90012-4.

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47

Aliabadi, M. H. "Developments in boundary element methods - volume 4." Engineering Analysis with Boundary Elements 8, no. 4 (August 1991): 215. http://dx.doi.org/10.1016/0955-7997(91)90016-m.

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48

Onishi, K. "Boundary element methods applied to transport phenomena." Advances in Water Resources 11, no. 3 (September 1988): 133–38. http://dx.doi.org/10.1016/0309-1708(88)90007-3.

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49

Brebbia, Carlos. "10th International Conference on Boundary Element Methods." Advances in Water Resources 11, no. 3 (September 1988): 150–52. http://dx.doi.org/10.1016/0309-1708(88)90010-3.

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50

Cross, M. "Developments in boundary element methods: Vol. 4." Applied Mathematical Modelling 11, no. 1 (February 1987): 73. http://dx.doi.org/10.1016/0307-904x(87)90188-0.

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