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Journal articles on the topic 'Indirect boundary element method'

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Published: 4 June 2021

Last updated: 21 February 2023

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1

Zhuravchak, L. M., and N. V. Zabrodska. "Using of partly-boundary elements as a version of the indirect near-boundary element method for potential field modeling." Mathematical Modeling and Computing 8, no. 1 (2020): 1–10. http://dx.doi.org/10.23939/mmc2021.01.001.

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In this paper, the partly-boundary elements as a version of the indirect near-boundary element method has been considered. Accuracy and effectiveness of their using for 2D problems of potential theory have been investigated. It is shown that using of partly-boundary elements for objects of canonical shape (circle, square, rectangle, ellipse) and arbitrary polygons allows us to achieve the solution accuracy, which is comparable with the accuracy of the indirect near-boundary element method, and its order of magnitude is higher than in the indirect boundary element method. In this case, the computation time is reduced by 2–2.5 times than in the near-boundary element method case. The software of the proposed approach has been implemented in Python. Practical testing was carried out for the tasks of electrical profiling and vertical electrical sounding in the half-plane with inclusion as a polygon. The recommendations for application of the partly-boundary elements in geophysical practice have been given.

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2

Gao, Sheng Yao, and De Shi Wang. "An Indirect Boundary Element Method for Computing Sound Field." Advanced Materials Research 476-478 (February 2012): 1173–77. http://dx.doi.org/10.4028/www.scientific.net/amr.476-478.1173.

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Computing sound field from an arbitrary radiator is of interest in acoustics, with many significant applications, one that includes the design of classical projectors and the noise prediction of underwater vehicle. To overcome the non-uniqueness of solution at eigenfrequencies in the boundary integral equation method for structural acoustic radiation, wave superposition method is introduced to study the acoustics. In this paper, the theoretical backgrounds to the direct boundary element method and the wave superposition method are presented. The wave superposition method does not solve the Kirchoff-Helmholtz integral equation directly. In the approach a lumped parameter model is estabiled from spatially averaged quantities, and the numerical method is implemented by using the acoustic field from a series of virtual sources which are collocated near the boundary surface to replace the acoustic field of the radiator. Then the sound field over the of a pulsating sphere is calculated. Finally, comparison between the analytical and numerical results is given, and the speed of solution is investigated. The results show that the agreement between the results from the above numerical methods is excellent. The wave superposition method requires fewer elements and hence is faster, which do not need as high a mesh density as traditionally associated with BEM.

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3

Rodríguez-Castellanos, A., E. Flores, F. J. Sánchez-Sesma, C. Ortiz-Alemán, M. Nava-Flores, and R. Martin. "Indirect Boundary Element Method applied to fluid–solid interfaces." Soil Dynamics and Earthquake Engineering 31, no. 3 (March 2011): 470–77. http://dx.doi.org/10.1016/j.soildyn.2010.10.007.

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4

Bedair, O. K., and J. C. Thompson. "Shape sensitivity analysis using the indirect boundary element method." Structural Optimization 6, no. 2 (June 1993): 116–22. http://dx.doi.org/10.1007/bf01743344.

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5

Shen, Shih-yu. "An indirect elastostatic boundary element method with analytic bases." Computers & Structures 89, no. 23-24 (December 2011): 2402–13. http://dx.doi.org/10.1016/j.compstruc.2011.06.008.

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6

VENTSEL, EDUARD S. "AN INDIRECT BOUNDARY ELEMENT METHOD FOR PLATE BENDING ANALYSIS." International Journal for Numerical Methods in Engineering 40, no. 9 (May 15, 1997): 1597–610. http://dx.doi.org/10.1002/(sici)1097-0207(19970515)40:9<1597::aid-nme129>3.0.co;2-t.

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7

Wearing, J. L., and M. A. Sheikh. "A regular indirect boundary element method for thermal analysis." International Journal for Numerical Methods in Engineering 25, no. 2 (June 1988): 495–515. http://dx.doi.org/10.1002/nme.1620250214.

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8

Shen, Shih-yu. "An indirect elastodynamic boundary element method with analytic bases." International Journal for Numerical Methods in Engineering 57, no. 6 (2003): 767–94. http://dx.doi.org/10.1002/nme.702.

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9

Akimov, Pavel A. "Correct Indirect Discrete-Continual Boundary Element Method of Structural Analysis." Advanced Materials Research 671-674 (March 2013): 1614–18. http://dx.doi.org/10.4028/www.scientific.net/amr.671-674.1614.

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This paper is devoted to so-called indirect discrete-continual boundary element method of structural analysis. Operational formulation of the problem is given. Using fundamental operational relations of indirect approach after construction of corresponding fundamental matrix-function in a special form convenient for problems of structural mechanics and its application resolving set of differential equations with operational coefficients is obtained. The discrete-continual design model for structures with constant physical and geometrical parameters in one direction is offered on the basis of so-called discrete-continual boundary elements. Basic pseudodifferential operators are approximated discretely by Fourier series. Fourier transformations and Wavelet analysis can be applied as well.

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10

PONOMAREVA, Maria Andreevna, Evgeniy Alekseevich SOBKO, and Vladimir Albertovich YAKUTENOK. "SOLVING AXISYMMETRIC POTENTIAL PROBLEMS USING THE INDIRECT BOUNDARY ELEMENT METHOD." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 37(5) (October 1, 2015): 84–96. http://dx.doi.org/10.17223/19988621/37/8.

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11

Wang, C., and B. C. Khoo. "An indirect boundary element method for three-dimensional explosion bubbles." Journal of Computational Physics 194, no. 2 (March 2004): 451–80. http://dx.doi.org/10.1016/j.jcp.2003.09.011.

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12

Kipp, C. R., and R. J. Bernhard. "Prediction of Acoustical Behavior in Cavities Using an Indirect Boundary Element Method." Journal of Vibration and Acoustics 109, no. 1 (January 1, 1987): 22–28. http://dx.doi.org/10.1115/1.3269390.

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An indirect boundary element method is developed to predict sound fields in acoustical cavities. An isoparametric quadratic boundary element is utilized. The formulations of pressure, velocity and/or impedance boundary conditions are developed and incorporated into the method. The capability to include acoustic point sources within the cavity is also implemented. The method is applied to the prediction of sound fields in spherical and rectangular cavities. All three boundary condition types are verified. Cases having 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.

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13

Pape, D. A., and P. K. Banerjee. "Treatment of Body Forces in 2D Elastostatic BEM Using Particular Integrals." Journal of Applied Mechanics 54, no. 4 (December 1, 1987): 866–71. http://dx.doi.org/10.1115/1.3173130.

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A new set of direct and indirect boundary element formulations for two-dimensional elastostatics have been developed. These new formulations differ from currently popular formulations in the treatment of body forces. The method of particular integrals is used resulting in a formulation which requires neither volume nor surface integration to solve the most general body force problem. This formulation is implemented in both direct and indirect boundary element methods using quadratic isoparametric elements. The efficiency and accuracy of this formulation for these two methods are compared for a range of problems. Finally, a multi-region problem with complicated geometry is run in order to show the complete generality of the particular integral method.

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14

Aliabadi, M. H. "Boundary Element Formulations in Fracture Mechanics." Applied Mechanics Reviews 50, no. 2 (February 1, 1997): 83–96. http://dx.doi.org/10.1115/1.3101690.

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This article reviews advances in the application of boundary element methods (BEM) to fracture mechanics which have taken place over the last 25 years. Applications discussed include linear, nonlinear and transient problems. Also reviewed are contributions using the indirect boundary element formulations. Over this period the method has emerged as the most efficient technique for the evaluation of stress intensity factors (SIF) and crack growth analysis in the context of linear elastic fracture mechanics (LEFM). Much has also been achieved in the application to dynamic fracture mechanics. This review article contains 289 references.

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15

Citarella, R. "Acoustic Analysis of an Exhaust MANIFOLD by INDIRECT Boundary Element Method." Open Mechanical Engineering Journal 5, no. 1 (November 29, 2011): 138–51. http://dx.doi.org/10.2174/1874155x01105010138.

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16

Bin Song and Junmei Fu. "Application of modified indirect boundary element method to electromagnetic field problems." IEEE Transactions on Microwave Theory and Techniques 42, no. 4 (April 1994): 654–60. http://dx.doi.org/10.1109/22.285072.

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17

Karabulut, Hayrullah, and John F. Ferguson. "An analysis of the indirect boundary element method for seismic modelling." Geophysical Journal International 147, no. 1 (September 2001): 68–76. http://dx.doi.org/10.1046/j.1365-246x.2001.00504.x.

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18

Vijayakumar, S., T. E. Yacoub, and J. H. Curran. "A node-centric indirect boundary element method: three-dimensional displacement discontinuities." Computers & Structures 74, no. 6 (February 2000): 687–703. http://dx.doi.org/10.1016/s0045-7949(99)00078-4.

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19

Chen, Jeng-Tzong, Yu-Lung Chang, Shing-Kai Kao, and Jie Jian. "Revisit of the Indirect Boundary Element Method: Necessary and Sufficient Formulation." Journal of Scientific Computing 65, no. 2 (December 28, 2014): 467–85. http://dx.doi.org/10.1007/s10915-014-9974-2.

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20

Goel, Narenda S., Fengshi Gang, and Zhonglin Ko. "Electrostatic Field in Inhomogeneous Dielectric Media I. Indirect Boundary Element Method." Journal of Computational Physics 118, no. 1 (April 1995): 172–79. http://dx.doi.org/10.1006/jcph.1995.1088.

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21

Wen, P. H., M. H. Aliabadi, and D. P. Rooke. "An indirect boundary element method for three-dimensional dynamic fracture mechanics." Engineering Analysis with Boundary Elements 16, no. 4 (December 1995): 351–62. http://dx.doi.org/10.1016/0955-7997(95)00082-8.

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22

Wu, Y. H., C. Y. Dong, and H. S. Yang. "Isogeometric indirect boundary element method for solving the 3D acoustic problems." Journal of Computational and Applied Mathematics 363 (January 2020): 273–99. http://dx.doi.org/10.1016/j.cam.2019.06.013.

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23

Coox, Laurens, Onur Atak, Dirk Vandepitte, and Wim Desmet. "An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains." Computer Methods in Applied Mechanics and Engineering 316 (April 2017): 186–208. http://dx.doi.org/10.1016/j.cma.2016.05.039.

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24

Hamada, Shoji. "GPU-accelerated indirect boundary element method for voxel model analyses with fast multipole method." Computer Physics Communications 182, no. 5 (May 2011): 1162–68. http://dx.doi.org/10.1016/j.cpc.2011.01.020.

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25

Ávila-Carrera, R., A. Rodríguez-Castellanos, F. J. Sánchez-Sesma, and C. Ortiz-Alemán. "Rayleigh-wave scattering by shallow cracks using the indirect boundary element method." Journal of Geophysics and Engineering 6, no. 3 (May 29, 2009): 221–30. http://dx.doi.org/10.1088/1742-2132/6/3/002.

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26

Cassidy, Matthew, Richard K. Cooper, Richard Gault, and Jian Wang. "Numerical study of sound transmission loss using an indirect boundary element method." Journal of the Acoustical Society of America 123, no. 5 (May 2008): 3500. http://dx.doi.org/10.1121/1.2934371.

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27

Bedair, Osama K. "The application of the indirect boundary element method to optimum shape design." Computers & Structures 65, no. 5 (December 1997): 651–68. http://dx.doi.org/10.1016/s0045-7949(96)00439-7.

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28

Abdollahipour, Abolfazl, Mohammad Fatehi Marji, Alireza Yarahmadi Bafghi, and Javad Gholamnejad. "A complete formulation of an indirect boundary element method for poroelastic rocks." Computers and Geotechnics 74 (April 2016): 15–25. http://dx.doi.org/10.1016/j.compgeo.2015.12.011.

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29

Poljak, Dragan, and Carlos A. Brebbia. "Indirect Galerkin–Bubnov boundary element method for solving integral equations in electromagnetics." Engineering Analysis with Boundary Elements 28, no. 7 (July 2004): 771–77. http://dx.doi.org/10.1016/j.enganabound.2003.11.004.

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30

Lefteriu, Sanda, Marcos Souza Lenzi, Hadrien Bériot, Michel Tournour, and Wim Desmet. "Fast frequency sweep method for indirect boundary element models arising in acoustics." Engineering Analysis with Boundary Elements 69 (August 2016): 32–45. http://dx.doi.org/10.1016/j.enganabound.2016.04.007.

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31

Auerbach, Markus, Andreas Bockstedte, Olgierd Zaleski, Marian Markiewicz, Otto von Estorff, and Wolfram Bartolomaeus. "Investigation of noise barriers with resonators by the indirect boundary element method." Journal of the Acoustical Society of America 127, no. 3 (March 2010): 1775. http://dx.doi.org/10.1121/1.3383879.

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32

Li, Li Jun, Xian Yue Gang, Hong Yan Li, Shan Chai, and Ying Zi Xu. "Study on Numerical Methods for Acoustic Radiation of Open Structure." Key Engineering Materials 439-440 (June 2010): 692–97. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.692.

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For acoustic radiation of open thin-walled structure, it was difficult to analyze directly by analytical method. The problem could be solved by several numerical methods. This paper had studied the basic theory of the numerical methods as FEM (Finite Element Method), BEM (Boundary Element Method) and IFEM (Infinite Element Method), and the numerical methods to solve open structure radiation problem. Under the premise of structure-acoustic coupling, this paper analyzed the theory and flow of the methods on acoustic radiation of open structure, including IBEM (Indirect Boundary Element Method), DBEM (Direct Boundary Element Method) coupling method of interior field and exterior field, FEM and BEM coupling method, FEM and IFEM coupling method. This paper took the open structure as practical example, and applied the several methods to analyze it, and analyzed and compared the several results to get relevant conclusions.

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33

ZHANG, YAOMING, ZHAOYAN LIU, and WENZHEN QU. "A NONSINGULAR BOUNDARY ELEMENT METHOD FOR THE TORSION PROBLEM OF THE ANISOTROPIC UNIFORM BAR." International Journal of Computational Methods 09, no. 01 (March 2012): 1240020. http://dx.doi.org/10.1142/s0219876212400208.

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The presentation is mainly devoted to the research on the regularized boundary integral equations (BIEs) with indirect unknowns for torsion problem of the anisotropic uniform bar. Based on a new view and idea, a novel regularization technique is pursued, in which the nonsingular indirect BIE (IBIE) excluding the CPV and HFP integrals is established. Such torsion problems can be solved directly by using the presented technique without transforming them into isotropic ones, for this reason, no inverse transform is required. Moreover, a unique feature of the shear stress BIEs expressed by density functions is that they are independent of the warp BIEs and, as such, can be collocated at the same locations as the warp BIEs. This provides additional and concurrently useable equations for various purposes. Besides, in the numerical implementation, the boundary geometric is depicted by exact elements, while the distribution of the boundary quantity on each element is approximated by a discontinuous quadratic element. Some numerical examples will be applied to validate the current scheme. It is shown that a better precision and high-computational efficiency can be achieved by the presentation.

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34

Velikanov, P. G., and D. M. Khalitova. "SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR ANISOTROPIC PLATES AND SHELLS BY BOUNDARY ELEMENTS METHOD." Vestnik of Samara University. Natural Science Series 27, no. 2 (March 30, 2022): 48–61. http://dx.doi.org/10.18287/2541-7525-2021-27-2-48-61.

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Modern mechanical engineering sets the tasks of calculating thin-walled structures that combine lightness and economy on the one hand and high strength and reliability on the other. In this regard, the use of anisotropic materials and plastics seems justified. The problems of the theory of plates and shells belong to the class of boundary value problems, the analytical solution of which, due to various circumstances (nonlinearity of differential equations, complexity of geometry and boundary conditions, etc.), cannot bedetermined. Numerical methods help to solve this problem. Among numerical methods, undeservedly little attention is paid to the boundary element method. In this regard, the further development of indirect method of compensating loads for solving problems of the anisotropic plates and shells theory based on the applicationof exact fundamental solutions is relevant.The paper considers the application of the indirect boundary element method for solving of an anisotropic plates and shells nonlinear deformation problem. Since the kernels of the system of singular integral equations to which the solution of the problem is reduced are expressed in terms of the fundamental solution and itsderivatives, first of all, the article provides a method for determining the fundamental solutions to the problem of bending and the plane stress state of an anisotropic plate. The displacement vector is determined from the solution of linear equations system describing the bending and plane stress state of an anisotropic plate. The solution of the system is performed by the method of compensating loads, according to which the area representing the plan of the shallow shell is supplemented to an infinite plane, and on the contour that limits the area, compensating loads are applied to the infinite plate. Integral equations of indirect BEM are given. In this paper, the study of nonlinear deformation of anisotropic plates and shallow shells is carried out using the deflection load dependencies. The deflection at a given point on the median surface of the shell was taken as the leading parameter.

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35

Moro, Federico, and Lorenzo Codecasa. "Coupling the Cell Method with the Boundary Element Method in Static and Quasi–Static Electromagnetic Problems." Mathematics 9, no. 12 (June 19, 2021): 1426. http://dx.doi.org/10.3390/math9121426.

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A unified discretization framework, based on the concept of augmented dual grids, is proposed for devising hybrid formulations which combine the Cell Method and the Boundary Element Method for static and quasi-static electromagnetic field problems. It is shown that hybrid approaches, already proposed in literature, can be rigorously formulated within this framework. As a main outcome, a novel direct hybrid approach amenable to iterative solution is derived. Both direct and indirect hybrid approaches, applied to an axisymmetric model, are compared with a reference third-order 2D FEM solution. The effectiveness of the indirect approach, equivalent to the direct approach, is finally tested on a fully 3D benchmark with more complex topology.

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36

Lu, Jiali, and J. O. Watson. "A quadratic variation indirect boundary element method for traction boundary-value problems of two-dimensional elastostatics." International Journal for Numerical and Analytical Methods in Geomechanics 12, no. 2 (March 1988): 183–96. http://dx.doi.org/10.1002/nag.1610120206.

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37

Sánchez-Sesma, Francisco J., Mauricio Arellano-Guzmán, Juan J. Pérez-Gavilán, Martha Suarez, Humberto Marengo-Mogollón, Stephanie Chaillat, Juan Diego Jaramillo, Juan Gómez, Ursula Iturrarán-Viveros, and Alejandro Rodríguez-Castellanos. "Seismic response of three-dimensional rockfill dams using the Indirect Boundary Element Method." IOP Conference Series: Materials Science and Engineering 10 (June 1, 2010): 012167. http://dx.doi.org/10.1088/1757-899x/10/1/012167.

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38

Zhu, G., A. A. Mammoli, and H. Power. "A 3-D indirect boundary element method for bounded creeping flow of drops." Engineering Analysis with Boundary Elements 30, no. 10 (October 2006): 856–68. http://dx.doi.org/10.1016/j.enganabound.2006.07.002.

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39

Shen, Baotang, and Jingyu Shi. "An indirect boundary element method for analysis of 3D thermoelastic problem with cracks." Engineering Analysis with Boundary Elements 115 (June 2020): 120–32. http://dx.doi.org/10.1016/j.enganabound.2020.03.008.

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40

Sadat Tayarani, Narges, and Mohammad Fatehi Marji. "Numerical Crack Analysis of Blunt Rock Indenters by an Indirect Boundary Element Method." Geomaterials 03, no. 04 (2013): 132–37. http://dx.doi.org/10.4236/gm.2013.34017.

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41

Provatidis, C. G., and N. K. Zafiropoulos. "A modified indirect boundary element method for solving two-dimensional sound radiation problems." Forschung im Ingenieurwesen 68, no. 1 (July 2003): 8–18. http://dx.doi.org/10.1007/s10010-003-0100-0.

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42

Chan, H. C. M., V. Li, and H. H. Einstein. "A hybridized displacement discontinuity and indirect boundary element method to model fracture propagation." International Journal of Fracture 45, no. 4 (October 1990): 263–82. http://dx.doi.org/10.1007/bf00036271.

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43

LIU, E., A. DOBSON, D. M. PAN, and D. H. YANG. "THE MATRIX FORMULATION OF BOUNDARY INTEGRAL MODELING OF ELASTIC WAVE PROPAGATION IN 2D MULTI-LAYERED MEDIA WITH IRREGULAR INTERFACES." Journal of Computational Acoustics 16, no. 03 (September 2008): 381–96. http://dx.doi.org/10.1142/s0218396x08003634.

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A semi-analytic method based on the propagation matrix formulation of indirect boundary element method to compute response of elastic (and acoustic) waves in multi-layered media with irregular interfaces is presented. The method works recursively starting from the top-most free surface at which a stress-free boundary condition is applied, and the displacement-stress boundary conditions are then subsequently applied at each interface. The basic idea behind this method is the matrix formulation of the propagation matrix (PM) or more recently the reflectivity method as wide used in the geophysics community for the computation of synthetic seismograms in stratified media. The reflected and transmitted wave fields between arbitrary shapes of layers can be computed using the indirect boundary element (BEM) method. Like any standard BEM methods, the primary task of the BEM-based propagation matrix method (thereafter called PM–BEM) is the evaluation of element boundary integral of the Green's function, for which there are standard method that can be adapted. In addition, effective absorbing boundary conditions as used in the finite difference numerical method is adapted in our implementation to suppress the spurious arrivals from the artificial boundaries due to limited model space. To our knowledge, such implementation has not appeared in the literature. Several examples are presented in this paper to demonstrate the effectiveness of this proposed PM–BEM method for modeling elastic waves in media with complex structure.

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44

Aldlemy, Mohammed. "EFFECT OF CONDUCTIVITY IN CORROSION PROBLEM USING BOUNDARY ELEMENT METHOD AND GENETIC ALGORITHM." Knowledge-Based Engineering and Sciences 1, no. 01 (December 31, 2020): 58–63. http://dx.doi.org/10.51526/kbes.2020.1.01.58-63.

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Boundary element method applications with inverse solution are used to apply the indirect analysis for modeling of corrosion problem. Laplace equation has been used to model the electrical potential in the electrolyte surface. In this paper a computer modeling has been developed to visualize the effect of conductivity value in corrosion problem. Genetic algorithm is used to create the conductivity value based on the mechanics of natural selection and genetics. The boundary element method is then calculating the potential value of the whole domain. FORTRAN and MATLAB program have been developed to calculate and visualize the potential distribution in the domain. Two-dimensional example problems are analyzed to demonstrate the application of the proposed boundary element modeling procedure.

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45

Mejía-López, Jimena, Oscar I. López-Sugahara, José Piña-Flores, Francisco J. Sánchez-Sesma, Zengxi Ge, Jia Wei, Mianshui Rong, and Zhenning Ba. "Seismic Response of 2D Topographic Profiles for Incident SH Waves: Iterative Solution and Comparison of Direct and Indirect BEM." Bulletin of the Seismological Society of America 112, no. 2 (November 23, 2021): 1031–40. http://dx.doi.org/10.1785/0120210148.

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ABSTRACT The scattering and diffraction of waves by irregular surface profiles is of interest in seismology and in many other areas. Diverse techniques have been proposed to quantitatively study the problem. Among them, domain approaches such as finite differences, spectral elements and finite elements have been used. Because the reduction of dimensionality boundary formulations is widely used. Recently, the direct boundary-element method has been applied using some series approximations for surface scattering, including the preconditioned splitting series, for the numerical description of rough surface scattering. Extending further and simplifying this approach, we use the indirect boundary-element method. The ensuing Fredholm integral equation of the second kind that arises in IBEM leads to a very efficient iterative scheme based on the classical Jacobi method. A discussion of direct and indirect approaches is presented. Assuming incident SH waves, results are obtained with the various approaches and compared among them for both a canyon and a hill, both of semicircular shape. Besides, an example is presented of a surface profile that produces strong scattering. This was inspired by the diverse problems that arise in the emerging field of metamaterials.

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46

Abdelkader, Benmessaoud, Badaoui Mohamed, Hachi Brahim El-Khalil, Nehar Camellia Khaira, and Guesmi Mohamed. "Modal Stress Intensity Factor Using Extended Finite Element Method." Applied Mechanics and Materials 232 (November 2012): 686–90. http://dx.doi.org/10.4028/www.scientific.net/amm.232.686.

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The aim of this paper is the determination of the evolution of the modal stress intensity factor (MSIF) for a non-propagating crack subjected to dynamic loading using the extended finite element method (X-FEM). The main advantage of this method coupled with the modal analysis is its capability in modeling cracks independently of the mesh and in a reduced computational time compared to the finite element method coupled with dynamic iterative method. The proposed procedure is applied to a reference problem (cracked plate). The MSIFs obtained agree well with those found by indirect boundary element (IBEM), weight function and Newmark’s explicit methods.

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47

Bessonova, M. P., and V. A. Yakutenok. "Numerical simulation of the non-Newtonian fluid flow using the indirect boundary element method." IOP Conference Series: Materials Science and Engineering 177 (February 2017): 012055. http://dx.doi.org/10.1088/1757-899x/177/1/012055.

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48

Yokoi, T. "Reflection and transmission operator for irregular interfaces derived from the indirect boundary element method." Geophysical Journal International 148, no. 1 (January 1, 2002): 88–102. http://dx.doi.org/10.1046/j.0956-540x.2001.01566.x.

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49

G�mez, J. E., and H. Power. "A parallel multipolar indirect boundary element method for the Neumann interior Stokes flow problem." International Journal for Numerical Methods in Engineering 48, no. 4 (June 10, 2000): 523–43. http://dx.doi.org/10.1002/(sici)1097-0207(20000610)48:4<523::aid-nme888>3.0.co;2-h.

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Prybytak, Dzmitry. "Application of the Boundary Element Method for the Simulation of Two-dimensional Viscous Incompressible Flow." Archives of Hydro-Engineering and Environmental Mechanics 61, no. 3-4 (December 1, 2014): 163–73. http://dx.doi.org/10.1515/heem-2015-0010.

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Abstract:

Abstract The paper presents the application of an indirect variant of the boundary element method (BEM) to solve the two-dimensional steady flow of a Stokes liquid. In the BEM, a system of differential equations is transformed into integral equations. This makes it possible to limit discretization to the border of the solution. Numerical discretization of the computational domain was performed with linear boundary elements, for which a constant value of unknown functions was assumed. The verification was carried out for the case of flow in a square cavity with one moving wall. The results obtained show that the use of approximations by simple linear functions is relatively easy for different shapes of the area, but the result may be affected by significant errors.

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