Journal articles: 'Boundary integral equations'

1

Bruk, V. M. "BOUNDARY VALUE PROBLEMS FOR INTEGRAL EQUATIONS WITH OPERATOR MEASURES." Issues of Analysis 24, no. 1 (June 2017): 19–40. http://dx.doi.org/10.15393/j3.art.2017.3810.

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Morino, Luigi. "Boundary Integral Equations in Aerodynamics." Applied Mechanics Reviews 46, no. 8 (August 1, 1993): 445–66. http://dx.doi.org/10.1115/1.3120373.

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A review of the use of boundary integral equations in aerodynamics is presented, with the objective of addressing what has been accomplished and, even more, what remains to be done. The paper is limited to aerodynamics of aeronautical type, with emphasis on unsteady flows (incompressible and compressible, potential and viscous). For potential flows, both incompressible and compressible flows are considered; the issue of the boundary conditions on the wake and on the trailing edge are addressed in some detail (in particular, some unresolved issues related to the impulsive start are pointed out). For incompressible viscous flows, the use of boundary integral equations in the non-primitive variable formulation are addressed: the Helmholtz decomposition and a decomposition recently introduced (and here referred to as the Poincare´ decomposition) are presented, along with their relationship. The latter is used to examine the relationship between potential and attached viscous flows (in particular, it is shown how the Poincare´ representation, for vortex layers of infinitesimal thickness, reduces to the potential-flow representation). The extension to compressible flows is also briefly outlined and the relative advantages of the two decompositions are discussed. Throughout the paper the emphasis is on the derivation and the interpretation of the boundary integral equations; issues related to the discretization (ie, panel methods, boundary element methods) are barely addressed. For numerical results, which are not included here, the reader is referred to the original references.

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3

Vavasis, Stephen A. "Preconditioning for Boundary Integral Equations." SIAM Journal on Matrix Analysis and Applications 13, no. 3 (July 1992): 905–25. http://dx.doi.org/10.1137/0613055.

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4

Amini, S., and N. D. Maines. "Regularization of strongly singular integrals in boundary integral equations." Communications in Numerical Methods in Engineering 12, no. 11 (November 1996): 787–93. http://dx.doi.org/10.1002/(sici)1099-0887(199611)12:11<787::aid-cnm19>3.0.co;2-5.

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5

Setukha, A. V. "Method of Boundary Integral Equations with Hypersingular Integrals in Boundary-Value Problems." Journal of Mathematical Sciences 257, no. 1 (July 29, 2021): 114–26. http://dx.doi.org/10.1007/s10958-021-05475-3.

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6

Sulym, Heorhiy, Iaroslav Pasternak, Mariia Smal, and Andrii Vasylyshyn. "Mixed Boundary Value Problem for an Anisotropic Thermoelastic Half-Space Containing Thin Inhomogeneities." Acta Mechanica et Automatica 13, no. 4 (December 1, 2019): 238–44. http://dx.doi.org/10.2478/ama-2019-0032.

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Abstract The paper presents a rigorous and straightforward approach for obtaining the 2D boundary integral equations for a thermoelastic half-space containing holes, cracks and thin foreign inclusions. It starts from the Cauchy integral formula and the extended Stroh formalism which allows writing the general solution of thermoelastic problems in terms of certain analytic functions. In addition, with the help of it, it is possible to convert the volume integrals included in the equation into contour integrals, which, in turn, will allow the use of the method of boundary elements. For modelling of solids with thin inhomogeneities, a coupling principle for continua of different dimensions is used. Applying the theory of complex variable functions, in particular, Cauchy integral formula and Sokhotski–Plemelj formula, the Somigliana type boundary integral equations are constructed for thermoelastic anisotropic half-space. The obtained integral equations are introduced into the modified boundary element method. A numerical analysis of the influence of boundary conditions on the half-space boundary and relative rigidity of the thin inhomogeneity on the intensity of stresses at the inclusions is carried out.

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Bukanay, N. U., A. E. Mirzakulova, M. K. Dauylbayev, and K. T. Konisbayeva. "A boundary jumps phenomenon in the integral boundary value problem for singularly perturbed differential equations." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 98, no. 2 (June 30, 2020): 46–58. http://dx.doi.org/10.31489/2020m2/46-58.

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8

Jankowski, Tadeusz. "Differential equations with integral boundary conditions." Journal of Computational and Applied Mathematics 147, no. 1 (October 2002): 1–8. http://dx.doi.org/10.1016/s0377-0427(02)00371-0.

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9

Schippers, H. "Multigrid methods for boundary integral equations." Numerische Mathematik 46, no. 3 (September 1985): 351–63. http://dx.doi.org/10.1007/bf01389491.

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10

Maczynski, J. "Boundary integral equations and reinforced bodies." Engineering Analysis with Boundary Elements 3, no. 3 (September 1986): 166–72. http://dx.doi.org/10.1016/0955-7997(86)90005-6.

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11

Grabacki, Jan. "Boundary integral equations in sensitivity analysis." Applied Mathematical Modelling 15, no. 4 (April 1991): 170–81. http://dx.doi.org/10.1016/0307-904x(91)90006-b.

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12

Vatul'yan, A. O., and V. L. Kublikov. "On boundary integral equations in electroelasticity." Journal of Applied Mathematics and Mechanics 53, no. 6 (January 1989): 824–27. http://dx.doi.org/10.1016/0021-8928(89)90095-6.

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13

Fairweather, G., P. A. Martin, and T. J. Rudolphi. "Frank Rizzo and boundary integral equations." Engineering Analysis with Boundary Elements 124 (March 2021): 137–41. http://dx.doi.org/10.1016/j.enganabound.2020.11.007.

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14

Maczyński, Jacek F. "Boundary integral equations and reinforced bodies." Engineering Analysis 3, no. 3 (September 1986): 166–72. http://dx.doi.org/10.1016/0264-682x(86)90055-9.

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15

Griebel, M., P. Oswald, and T. Schiekofer. "Sparse grids for boundary integral equations." Numerische Mathematik 83, no. 2 (August 1, 1999): 279–312. http://dx.doi.org/10.1007/s002110050450.

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16

Baderko, Elena A. "Parabolic Problems and Boundary Integral Equations." Mathematical Methods in the Applied Sciences 20, no. 5 (March 25, 1997): 449–59. http://dx.doi.org/10.1002/(sici)1099-1476(19970325)20:5<449::aid-mma818>3.0.co;2-e.

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17

Krishnasamy, Guna, Frank J. Rizzo, and Yijun Liu. "Boundary integral equations for thin bodies." International Journal for Numerical Methods in Engineering 37, no. 1 (January 15, 1994): 107–21. http://dx.doi.org/10.1002/nme.1620370108.

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18

REN, J. G. "WAVELET METHODS FOR BOUNDARY INTEGRAL EQUATIONS." Communications in Numerical Methods in Engineering 13, no. 5 (May 1997): 373–85. http://dx.doi.org/10.1002/(sici)1099-0887(199705)13:5<373::aid-cnm62>3.0.co;2-o.

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19

Iemma, Umberto. "Singing Integrals or wind instruments modeling using Boundary Integral Equations." Journal of the Acoustical Society of America 123, no. 5 (May 2008): 3523. http://dx.doi.org/10.1121/1.2934457.

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20

Belov, A. A., and A. N. Petrov. "NUMERICAL ANALYSIS OF THE DYNAMICS OF THREE-DIMENSIONAL ANISOTROPIC BODIES BASED ON NON-CLASSICAL BOUNDARY INTEGRAL EQUATIONS." Problems of strenght and plasticity 83, no. 1 (2021): 76–86. http://dx.doi.org/10.32326/1814-9146-2021-83-1-76-86.

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The application of non-classical approach of the boundary integral equation method in combination with the integral Laplace transform in time to anisotropic elastic wave modeling is considered. In contrast to the classical approach of the boundary integral equation method which is successfully implemented for solving three-dimensional isotropic problems of the dynamic theory of elasticity, viscoelasticity and poroelasticity, the alternative nonclassical formulation of the boundary integral equations method is presented that employs regular Fredholm integral equations of the first kind (integral equations on a plane wave). The construction of such boundary integral equations is based on the structure of the dynamic fundamental solution. The approach employs the explicit boundary integral equations. The inverse Laplace transform is constructed numerically by the Durbin method. A numerical solution of the dynamic problem of anisotropic elasticity theory based on the boundary integral equations method in a nonclassical formulation is presented. The boundary element scheme of the boundary integral equations method is built on the basis of a regular integral equation of the first kind. The problem is solved in anisotropic formulation for the load acting along the normal in the form of the Heaviside function on the cube face weakened by a cubic cavity. The obtained boundary element solutions are compared with finite element solutions. Numerical results prove the efficiency of using boundary integral equations on a single plane wave in solving three-dimensional anisotropic dynamic problems of elasticity theory. The convergence of boundary element solutions is studied on three schemes of surface discretization. The achieved calculation accuracy is not inferior to the accuracy of boundary element schemes for classical boundary integral equations. Boundary element analysis of solutions for a cube with and without a cavity is carried out.

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21

Stephan, Ernst P. "Boundary Integral Equations for Mixed Boundary Value Problems inR3." Mathematische Nachrichten 134, no. 1 (1987): 21–53. http://dx.doi.org/10.1002/mana.19871340103.

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22

Sloan, Ian H. "Error analysis of boundary integral methods." Acta Numerica 1 (January 1992): 287–339. http://dx.doi.org/10.1017/s0962492900002294.

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Many of the boundary value problems traditionally cast as partial differential equations can be reformulated as integral equations over the boundary. After an introduction to boundary integral equations, this review describes some of the methods which have been proposed for their approximate solution. It discusses, as simply as possible, some of the techniques used in their error analysis, and points to areas in which the theory is still unsatisfactory.

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23

Guiggiani, M., G. Krishnasamy, T. J. Rudolphi, and F. J. Rizzo. "A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations." Journal of Applied Mechanics 59, no. 3 (September 1, 1992): 604–14. http://dx.doi.org/10.1115/1.2893766.

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The limiting process that leads to the formulation of hypersingular boundary integral equations is first discussed in detail. It is shown that boundary integral equations with hypersingular kernels are perfectly meaningful even at non-smooth boundary points, and that special interpretations of the integrals involved are not necessary. Careful analysis of the limiting process has also strong relevance for the development of an appropriate numerical algorithm. In the second part, a new general method for the evaluation of hypersingular surface integrals in the boundary element method (BEM) is presented. The proposed method can be systematically applied in any BEM analysis, either with open or closed surfaces, and with curved boundary elements of any kind and order (of course, provided the density function meets necessary regularity requirements at each collocation point). The algorithm operates in the parameter plane of intrinsic coordinates and allows any hypersingular integral in the BEM to be directly transformed into a sum of a double and a one-dimensional regular integrals. Since all singular integrations are performed analytically, standard quadrature formulae can be used. For the first time, numerical results are presented for hypersingular integrals on curved (distorted) elements for three-dimensional problems.

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24

Benedetti, Ivano, Vincenzo Gulizzi, and Vincenzo Mallardo. "Boundary Element Crystal Plasticity Method." Journal of Multiscale Modelling 08, no. 03n04 (September 2017): 1740003. http://dx.doi.org/10.1142/s1756973717400030.

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A three-dimensional (3D) boundary element method for small strains crystal plasticity is described. The method, developed for polycrystalline aggregates, makes use of a set of boundary integral equations for modeling the individual grains, which are represented as anisotropic elasto-plastic domains. Crystal plasticity is modeled using an initial strains boundary integral approach. The integration of strongly singular volume integrals in the anisotropic elasto-plastic grain-boundary equations are discussed. Voronoi-tessellation micro-morphologies are discretized using nonstructured boundary and volume meshes. A grain-boundary incremental/iterative algorithm, with rate-dependent flow and hardening rules, is developed and discussed. The method has been assessed through several numerical simulations, which confirm robustness and accuracy.

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25

Roach, G. F. "Boundary integral equations and modified Green's functions." Banach Center Publications 19, no. 1 (1987): 237–61. http://dx.doi.org/10.4064/-19-1-237-261.

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26

Maher, Philip, V. G. Maz'ya, and S. M. Nikol'skii. "Analysis IV: Linear and Boundary Integral Equations." Mathematical Gazette 76, no. 476 (July 1992): 321. http://dx.doi.org/10.2307/3619185.

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27

Mudge, Michael R., and William McLean. "Strongly Elliptic Systems and Boundary Integral Equations." Mathematical Gazette 86, no. 505 (March 2002): 182. http://dx.doi.org/10.2307/3621632.

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28

Wang, Xuhuan, Liping Wang, and Qinghong Zeng. "Fractional differential equations with integral boundary conditions." Journal of Nonlinear Sciences and Applications 09, no. 04 (July 10, 2015): 309–14. http://dx.doi.org/10.22436/jnsa.008.04.03.

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29

TAKAKUDA, Kazuo, Takashi KOIZUMI, and Toshikazu SHIBUYA. "On numerical solutions of boundary integral equations." Transactions of the Japan Society of Mechanical Engineers Series A 51, no. 461 (1985): 81–89. http://dx.doi.org/10.1299/kikaia.51.81.

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30

Ganesh, M., and O. Steinbach. "Nonlinear Boundary Integral Equations for Harmonic Problems." Journal of Integral Equations and Applications 11, no. 4 (December 1999): 437–59. http://dx.doi.org/10.1216/jiea/1181074294.

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31

Creagh, Stephen C., Hanya Ben Hamdin, and Gregor Tanner. "In–out decomposition of boundary integral equations." Journal of Physics A: Mathematical and Theoretical 46, no. 43 (October 8, 2013): 435203. http://dx.doi.org/10.1088/1751-8113/46/43/435203.

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32

Atkinson, Kendall E., and David Chien. "Piecewise Polynomial Collocation for Boundary Integral Equations." SIAM Journal on Scientific Computing 16, no. 3 (May 1995): 651–81. http://dx.doi.org/10.1137/0916040.

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33

Hsiao, G. C., O. Steinbach, and W. L. Wendland. "Domain decomposition methods via boundary integral equations." Journal of Computational and Applied Mathematics 125, no. 1-2 (December 2000): 521–37. http://dx.doi.org/10.1016/s0377-0427(00)00488-x.

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34

Chandler, G. A., and I. H. Sloan. "Spline qualocation methods for boundary integral equations." Numerische Mathematik 62, no. 1 (December 1992): 295. http://dx.doi.org/10.1007/bf01396230.

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35

Miers, L. S., and J. C. F. Telles. "Meshless boundary integral equations with equilibrium satisfaction." Engineering Analysis with Boundary Elements 34, no. 3 (March 2010): 259–63. http://dx.doi.org/10.1016/j.enganabound.2009.09.008.

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36

Tausch, Johannes. "Nyström discretization of parabolic boundary integral equations." Applied Numerical Mathematics 59, no. 11 (November 2009): 2843–56. http://dx.doi.org/10.1016/j.apnum.2008.12.032.

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37

Hu, Haichang, Haojiang Ding, and Wenjun He. "Equivalent boundary integral equations for plane elasticity." Science in China Series A: Mathematics 40, no. 1 (January 1997): 76–82. http://dx.doi.org/10.1007/bf03182872.

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38

Kozlova, N. O., and V. A. Feruk. "Noetherian Boundary-Value Problems for Integral Equations." Journal of Mathematical Sciences 222, no. 3 (March 9, 2017): 266–75. http://dx.doi.org/10.1007/s10958-017-3298-3.

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39

Shi, Hualiang, Ya Yan Lu, and Qiang Du. "Calculating corner singularities by boundary integral equations." Journal of the Optical Society of America A 34, no. 6 (May 17, 2017): 961. http://dx.doi.org/10.1364/josaa.34.000961.

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40

Lage, Christian, and Christoph Schwab. "Wavelet Galerkin Algorithms for Boundary Integral Equations." SIAM Journal on Scientific Computing 20, no. 6 (January 1999): 2195–222. http://dx.doi.org/10.1137/s1064827597329989.

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41

TAKAKUDA, Kazuo, Takashi KOIZUMI, and Toshikazu SHIBUYA. "On Numerical Solutions of Boundary Integral Equations." Bulletin of JSME 28, no. 243 (1985): 1836–44. http://dx.doi.org/10.1299/jsme1958.28.1836.

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42

Chudinovich, Igor, and Christian Constanda. "Boundary Integral Equations for Multiply Connected Plates." Journal of Mathematical Analysis and Applications 244, no. 1 (April 2000): 184–99. http://dx.doi.org/10.1006/jmaa.1999.6700.

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43

Shakhmurov, Veli. "Abstract elliptic equations with integral boundary conditons." Chinese Annals of Mathematics, Series B 37, no. 4 (June 29, 2016): 625–42. http://dx.doi.org/10.1007/s11401-016-0948-6.

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44

Chandler, G. A., and I. H. Sloan. "Spline qualocation methods for boundary integral equations." Numerische Mathematik 58, no. 1 (December 1990): 537–67. http://dx.doi.org/10.1007/bf01385639.

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45

Lubich, Ch, and R. Schneider. "Time discretization of parabolic boundary integral equations." Numerische Mathematik 63, no. 1 (December 1992): 455–81. http://dx.doi.org/10.1007/bf01385870.

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46

Chen, J. T., M. T. Liang, and S. S. Yang. "Dual boundary integral equations for exterior problems." Engineering Analysis with Boundary Elements 16, no. 4 (December 1995): 333–40. http://dx.doi.org/10.1016/0955-7997(95)00078-x.

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47

Sloan, Ian H., and W. L. Wendland. "Qualocation methods for elliptic boundary integral equations." Numerische Mathematik 79, no. 3 (May 1, 1998): 451–83. http://dx.doi.org/10.1007/s002110050347.

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48

Gray, L. J., S. Nintcheu Fata, and D. Ma. "Iterative solution of Hermite boundary integral equations." International Journal for Numerical Methods in Engineering 74, no. 2 (2008): 337–46. http://dx.doi.org/10.1002/nme.2173.

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49

ou Han, Yaz. "Integral equations on compact manifold with boundary." Mathematical Inequalities & Applications, no. 1 (2023): 161–82. http://dx.doi.org/10.7153/mia-2023-26-13.

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50

Petrov, Andrey, Sergey Aizikovich, and Leonid A. Igumnov. "Modeling of Wave Propagation in the Unsaturated Soils Using Boundary Element Method." Key Engineering Materials 743 (July 2017): 158–61. http://dx.doi.org/10.4028/www.scientific.net/kem.743.158.

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Problems of wave propagation in poroelastic bodies and media are considered. The behavior of the poroelastic medium is described by Biot theory for partially saturated material. Mathematical model is written in term of five basic functions – elastic skeleton displacements, pore water pressure and pore air pressure. Boundary element method (BEM) is used with step method of numerical inversion of Laplace transform to obtain the solution. Research is based on direct boundary integral equation of three-dimensional isotropic linear theory of poroelasticity. Green’s matrices and, based on it, boundary integral equations are written for basic differential equations in partial derivatives. Discrete analogue are obtained by applying the collocation method to a regularized boundary integral equation. To approximate the boundary consider its decomposition to a set of quadrangular and triangular 8-node biquadratic elements, where triangular elements are treated as singular quadrangular. Every element is mapped to a reference one. Interpolation nodes for boundary unknowns are a subset of geometrical boundary-element grid nodes. Local approximation follows the Goldshteyn’s generalized displacement-stress matched model: generalized boundary displacements are approximated by bilinear elements whereas generalized tractions are approximated by constant. Integrals in discretized boundary integral equations are calculated using Gaussian quadrature in combination with singularity decreasing and eliminating algorithms.

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Journal articles on the topic 'Boundary integral equations'

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