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Journal articles on the topic 'Localised boundary-domain integral equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Chkadua, Otar, Sergey E. Mikhailov, and David Natroshvili. "Localized boundary-domain integral equation formulation for mixed type problems." Georgian Mathematical Journal 17, no. 3 (2010): 469–94. http://dx.doi.org/10.1515/gmj.2010.025.

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Abstract Some modifed direct localized boundary-domain integral equations (LBDIEs) systems associated with the mixed boundary value problem (BVP) for a scalar “Laplace” PDE with variable coefficient are formulated and analyzed. The main results established in the paper are the LBDIEs equivalence to the original variable-coefficient BVPs and the invertibility of the corresponding localized boundary-domain integral operators in appropriately chosen function spaces.

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2

Chkadua, Otar, Sergey E. Mikhailov, and David Natroshvili. "Singular localised boundary‐domain integral equations of acoustic scattering by inhomogeneous anisotropic obstacle." Mathematical Methods in the Applied Sciences 41, no. 17 (2018): 8033–58. http://dx.doi.org/10.1002/mma.5268.

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3

Rungamornrat, Jaroon, and Sakravee Sripirom. "Stress Analysis of Three-Dimensional Media Containing Localized Zone by FEM-SGBEM Coupling." Mathematical Problems in Engineering 2011 (2011): 1–27. http://dx.doi.org/10.1155/2011/702082.

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This paper presents an efficient numerical technique for stress analysis of three-dimensional infinite media containing cracks and localized complex regions. To enhance the computational efficiency of the boundary element methods generally found inefficient to treat nonlinearities and non-homogeneous data present within a domain and the finite element method (FEM) potentially demanding substantial computational cost in the modeling of an unbounded medium containing cracks, a coupling procedure exploiting positive features of both the FEM and a symmetric Galerkin boundary element method (SGBEM)

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4

Mikhailov, S. E., and I. S. Nakhova. "Mesh-based numerical implementation of the localized boundary-domain integral-equation method to a variable-coefficient Neumann problem." Journal of Engineering Mathematics 51, no. 3 (2005): 251–59. http://dx.doi.org/10.1007/s10665-004-6452-0.

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5

Keeler, J. S., B. J. Binder, and M. G. Blyth. "On the critical free-surface flow over localised topography." Journal of Fluid Mechanics 832 (October 26, 2017): 73–96. http://dx.doi.org/10.1017/jfm.2017.639.

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Flow over bottom topography at critical Froude number is examined with a focus on steady, forced solitary wave solutions with algebraic decay in the far field, and their stability. Using the forced Korteweg–de Vries (fKdV) equation the weakly nonlinear steady solution space is examined in detail for the particular case of a Gaussian dip using a combination of asymptotic analysis and numerical computations. Non-uniqueness is established and a seemingly infinite set of steady solutions is uncovered. Non-uniqueness is also demonstrated for the fully nonlinear problem via boundary-integral calcula

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6

Münch, Arnaud. "Optimal Internal Dissipation of a Damped Wave Equation Using a Topological Approach." International Journal of Applied Mathematics and Computer Science 19, no. 1 (2009): 15–38. http://dx.doi.org/10.2478/v10006-009-0002-x.

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Optimal Internal Dissipation of a Damped Wave Equation Using a Topological ApproachWe consider a linear damped wave equation defined on a two-dimensional domain Ω, with a dissipative term localized in a subset ω. We address the shape design problem which consists in optimizing the shape of ω in order to minimize the energy of the system at a given timeT. By introducing an adjoint problem, we first obtain explicitly the (shape) derivative of the energy at timeTwith respect to the variation in ω. Expressed as a boundary integral on ∂ω, this derivative is then used as an advection velocity in a H

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7

Klettner, Christian A., and Ian Eames. "Momentum and energy of a solitary wave interacting with a submerged semi-circular cylinder." Journal of Fluid Mechanics 708 (August 10, 2012): 576–95. http://dx.doi.org/10.1017/jfm.2012.333.

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AbstractThe interaction of a weakly viscous solitary wave with a submerged semi-circular cylinder was examined using high-resolution two-dimensional numerical calculations. Two simulations were carried out: (a) as a baseline calculation, the propagation of a solitary wave over uniform depth; and (b) a solitary wave interacting with a submerged semi-circular cylinder. Large-scale simulations were performed to resolve the viscous boundary layers on the free surface, bottom and around the obstacle. Integral measures such as momentum and energy are analysed and compared against analytical approxim

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8

Vellingiri, Rajagopal, Dmitri Tseluiko, and Serafim Kalliadasis. "Absolute and convective instabilities in counter-current gas–liquid film flows." Journal of Fluid Mechanics 763 (December 11, 2014): 166–201. http://dx.doi.org/10.1017/jfm.2014.667.

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AbstractWe consider a thin liquid film flowing down an inclined plate in the presence of a counter-current turbulent gas. By making appropriate assumptions, Tseluiko & Kalliadasis (J. Fluid Mech., vol. 673, 2011, pp. 19–59) developed low-dimensional non-local models for the liquid problem, namely a long-wave (LW) model and a weighted integral-boundary-layer (WIBL) model, which incorporate the effect of the turbulent gas. By utilising these models, along with the Orr–Sommerfeld problem formulated using the full governing equations for the liquid phase and associated boundary conditions, we

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9

Chang, Chia-Hao, Ching-Sheng Huang, and Hund-Der Yeh. "Technical Note: Three-dimensional transient groundwater flow due to localized recharge with an arbitrary transient rate in unconfined aquifers." Hydrology and Earth System Sciences 20, no. 3 (2016): 1225–39. http://dx.doi.org/10.5194/hess-20-1225-2016.

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Abstract. Most previous solutions for groundwater flow induced by localized recharge assumed either aquifer incompressibility or two-dimensional flow in the absence of the vertical flow. This paper develops a new three-dimensional flow model for hydraulic head variation due to localized recharge in a rectangular unconfined aquifer with four boundaries under the Robin condition. A governing equation describing spatiotemporal head distributions is employed. The first-order free-surface equation with a source term defining a constant recharge rate over a rectangular area is used to depict water t

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10

Chang, C. H., C. S. Huang, and H. D. Yeh. "Technical Note: Three-dimensional transient groundwater flow due to localized recharge with an arbitrary transient rate in unconfined aquifers." Hydrology and Earth System Sciences Discussions 12, no. 11 (2015): 12247–80. http://dx.doi.org/10.5194/hessd-12-12247-2015.

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Abstract. Most previous solutions for groundwater flow induced by localized recharge assumed either aquifer incompressibility or two-dimensional flow in the absence of the vertical flow. This paper develops a new three-dimensional flow model for hydraulic head variation due to localized recharge in a rectangular unconfined aquifer with four boundaries under the Robin condition. A governing equation for describing the head distribution is employed. The first-order free surface equation with a source term defining a constant recharge rate over a rectangular area is used to depict water table mov

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11

Chkadua, O., S. E. Mikhailov, and D. Natroshvilli. "Analysis of some localized boundary-domian integral equations." Journal of Integral Equations and Applications 21, no. 3 (2009): 407–47. http://dx.doi.org/10.1216/jie-2009-21-3-407.

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12

Mikhailov, S. E. "Will the boundary(-domain) integral-equation methods survive? Preface to the special issue on non-traditional boundary (-domain) integral-equation methods." Journal of Engineering Mathematics 51, no. 3 (2005): 197–98. http://dx.doi.org/10.1007/s10665-004-6453-z.

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13

Guo, Shuaiping, Qiqiang Wu, Hongguang Li, and Kuidong Gao. "Triple reciprocity method for unknown function's domain integral in boundary integral equation." Engineering Analysis with Boundary Elements 113 (April 2020): 170–80. http://dx.doi.org/10.1016/j.enganabound.2019.12.014.

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14

Perez, M. M., and L. C. Wrobel. "An Integral-Equation Formulation for Anisotropic Elastostatics." Journal of Applied Mechanics 63, no. 4 (1996): 891–902. http://dx.doi.org/10.1115/1.2787244.

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In this paper a conceptually simple integral-equation formulation for homogeneous anisotropic linear elastostatics is presented. The basic idea of the approach proposed here is to rewrite the system of differential equations of the anisotropic problem to enable the use of the isotropic fundamental solution. This procedure leads to an extended form of Somigliana’s identity where a domain term occurs as a result of the anisotropy of the material. A supplementary integral equation is then established to cope with the resulting domain unknowns. Although the solution of these integral equations req

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15

Gupta, P. K., L. A. Bennett, and A. P. Raiche. "Hybrid calculations of the three‐dimensional electromagnetic response of buried conductors." GEOPHYSICS 52, no. 3 (1987): 301–6. http://dx.doi.org/10.1190/1.1442304.

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The hybrid method for computing the electromagnetic response of a three‐dimensional conductor in a layered, conducting half‐space consists of solving a finite‐element problem in a localized region containing the conductor, and using integral‐equation methods to obtain the fields outside that region. The original scheme obtains the boundary values by iterating between the integral‐equation solution and the finite‐element solution, after making an initial guess based on primary values from the field. A two‐dimensional interpolation scheme is then used to speed the evaluation of the [Formula: see

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16

CHKADUA, O., S. E. MIKHAILOV, and D. NATROSHVILI. "ANALYSIS OF DIRECT SEGREGATED BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR VARIABLE-COEFFICIENT MIXED BVPs IN EXTERIOR DOMAINS." Analysis and Applications 11, no. 04 (2013): 1350006. http://dx.doi.org/10.1142/s0219530513500061.

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Direct segregated systems of boundary-domain integral equations are formulated for the mixed (Dirichlet–Neumann) boundary value problems for a scalar second-order divergent elliptic partial differential equation with a variable coefficient in an exterior three-dimensional domain. The boundary-domain integral equation system equivalence to the original boundary value problems and the Fredholm properties and invertibility of the corresponding boundary-domain integral operators are analyzed in weighted Sobolev spaces suitable for infinite domains. This analysis is based on the corresponding prope

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17

Dong, C. Y., and C. J. de Pater. "A boundary-domain integral equation for a coated plane problem." Mechanics Research Communications 27, no. 6 (2000): 643–52. http://dx.doi.org/10.1016/s0093-6413(00)00141-5.

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18

Gao, Xiao-Wei. "A boundary-domain integral equation method in viscous fluid flow." International Journal for Numerical Methods in Fluids 45, no. 5 (2004): 463–84. http://dx.doi.org/10.1002/fld.705.

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19

Qiu, Tianyu, Alexander Rieder, Francisco-Javier Sayas, and Shougui Zhang. "Time-domain boundary integral equation modeling of heat transmission problems." Numerische Mathematik 143, no. 1 (2019): 223–59. http://dx.doi.org/10.1007/s00211-019-01040-y.

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20

Adolfsson, V., M. Goldberg, B. Jawerth, and H. Lennerstad. "Localized Galerkin Estimates for Boundary Integral Equations on Lipschitz Domains." SIAM Journal on Mathematical Analysis 23, no. 5 (1992): 1356–74. http://dx.doi.org/10.1137/0523078.

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21

Palupi, Irma. "Implicit Boundary Integral Method for Homogeneous Hele-Shaw Problem with multi-connected Domain." Indonesian Journal on Computing (Indo-JC) 4, no. 1 (2019): 93. http://dx.doi.org/10.21108/indojc.2019.4.1.279.

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In this work, we implement the implicit boundary integral method for a homogeneous Hele-Shaw problem with a multi-connected domain. This method base on the solution of layer potential integral for the Laplace equation. The numerical technique is easy to implement, base on the idea of averaging the parameterization near the boundary and applying the Coarea formula. This technique changes the boundary integral into the Riemann integral that numerically easy to compute. The difficulty in the computation of hypersingular integral occurs to compute the normal velocity of free boundary. We use a col

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22

Dong, C. Y., S. H. Lo, and Y. K. Cheung. "Application of the boundary-domain integral equation in elastic inclusion problems." Engineering Analysis with Boundary Elements 26, no. 6 (2002): 471–77. http://dx.doi.org/10.1016/s0955-7997(02)00012-7.

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23

Ravnik, J., and J. Tibaut. "Boundary-domain integral method for vorticity transport equation with variable viscosity." International Journal of Computational Methods and Experimental Measurements 6, no. 6 (2018): 1087–96. http://dx.doi.org/10.2495/cmem-v6-n6-1087-1096.

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24

El-shenawy, Atallah, and Elena A. Shirokova. "The Approximate Solution of 2D Dirichlet Problem in Doubly Connected Domains." Advances in Mathematical Physics 2018 (July 9, 2018): 1–6. http://dx.doi.org/10.1155/2018/6951513.

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We propose a new method for constructing an approximate solution of the two-dimensional Laplace equation in an arbitrary doubly connected domain with smooth boundaries for Dirichlet boundary conditions. Using the fact that the solution of the Dirichlet problem in a doubly connected domain is represented as the sum of a solution of the Schwarz problem and a logarithmic function, we reduce the solution of the Schwartz problem to the Fredholm integral equation with respect to the boundary value of the conjugate harmonic function. The solution of the integral equation in its turn is reduced to sol

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25

Zahroh, Millatuz. "PENENTUAN JENIS FUNGSI BASIS RADIAL DALAM DUAL RECIPROCITY BOUNDARY ELEMENT METHOD." Majalah Ilmiah Matematika dan Statistika 21, no. 1 (2021): 53. http://dx.doi.org/10.19184/mims.v21i1.23650.

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Problems involving modified Helmholtz equation are considered in this paper. To solve the problem numerically, dual reciprocity boundary element method (DRBEM) is employed. Some stage have been passed, using reciprocal relation to approximate boundary integral and domain integral in modified Helmholtz equation . Until, linear equation system are obtained in matrix form. MATLAB is used to calculate the solutions of Solutions of are compared between the exact solution and the numerical solution of modified Helmholtz equation. The numerical results are based on the using of three types of radial

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26

Kress, Rainer. "Integral equation methods in inverse obstacle scattering." ANZIAM Journal 42, no. 1 (2000): 65–78. http://dx.doi.org/10.1017/s1446181100011603.

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AbstractIn this survey we consider a regularized Newton method for the approximate solution of the inverse problem to determine the shape of an obstacle from a knowledge of the far field pattern for the scattering of time-harmonic acoustic or electromagnetic plane waves. Our analysis is in two dimensions and the numerical scheme is based on the solution of boundary integral equations by a Nyström method. We include an example of the reconstruction of a planar domain with a corner both to illustrate the feasibility of the use of radial basis functions for the reconstruction of boundary curves w

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27

Litynskyy, Svyatoslav, Yuriy Muzychuk, and Anatoliy Muzychuk. "On the Numerical Solution of the Initial-Boundary Value Problem with Neumann Condition for the Wave Equation by the Use of the Laguerre Transform and Boundary Elements Method." Acta Mechanica et Automatica 10, no. 4 (2016): 285–90. http://dx.doi.org/10.1515/ama-2016-0044.

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Abstract We consider a numerical solution of the initial-boundary value problem for the homogeneous wave equation with the Neumann condition using the retarded double layer potential. For solving an equivalent time-dependent integral equation we combine the Laguerre transform (LT) in the time domain with the boundary elements method. After LT we obtain a sequence of boundary integral equations with the same integral operator and functions in right-hand side which are determined recurrently. An error analysis for the numerical solution in accordance with the parameter of boundary discretization

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28

Uecker, Hannes. "Self-similar decay of localized perturbations in the integral boundary layer equation." Journal of Differential Equations 207, no. 2 (2004): 407–22. http://dx.doi.org/10.1016/j.jde.2004.07.029.

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29

PĂRĂU, E. I., J. M. VANDEN-BROECK, and M. J. COOKER. "Nonlinear three-dimensional interfacial flows with a free surface." Journal of Fluid Mechanics 591 (October 30, 2007): 481–94. http://dx.doi.org/10.1017/s0022112007008452.

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A configuration consisting of two superposed fluids bounded above by a free surface is considered. Steady three-dimensional potential solutions generated by a moving pressure distribution are computed. The pressure can be applied either on the interface or on the free surface. Solutions of the fully nonlinear equations are calculated by boundary-integral equation methods. The results generalize previous linear and weakly nonlinear results. Fully localized gravity–capillary interfacial solitary waves are also computed, when the free surface is replaced by a rigid lid.

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30

Shevchuk, R. V., I. Ya Savka, and Z. M. Nytrebych. "The nonlocal boundary value problem for one-dimensional backward Kolmogorov equation and associated semigroup." Carpathian Mathematical Publications 11, no. 2 (2019): 463–74. http://dx.doi.org/10.15330/cmp.11.2.463-474.

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This paper is devoted to a partial differential equation approach to the problem of construction of Feller semigroups associated with one-dimensional diffusion processes with boundary conditions in theory of stochastic processes. In this paper we investigate the boundary-value problem for a one-dimensional linear parabolic equation of the second order (backward Kolmogorov equation) in curvilinear bounded domain with one of the variants of nonlocal Feller-Wentzell boundary condition. We restrict our attention to the case when the boundary condition has only one term and it is of the integral ty

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31

Levinski, Vladimir, and Jacob Cohen. "The evolution of a localized vortex disturbance in external shear flows. Part 1. Theoretical considerations and preliminary experimental results." Journal of Fluid Mechanics 289 (April 25, 1995): 159–77. http://dx.doi.org/10.1017/s0022112095001285.

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The evolution of a finite-amplitude three-dimensional localized disturbance embedded in external shear flows is addressed. Using the fluid impulse integral as a characteristic of such a disturbance, the Euler vorticity equation is integrated analytically, and a system of linear equations describing the temporal evolution of the three components of the fluid impulse is obtained. Analysis of this system of equations shows that inviscid plane parallel flows as well as high Reynolds number two-dimensional boundary layers are always unstable to small localized disturbances, a typical dimension of w

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32

Kawaguchi, H. "Time-domain analysis of electromagnetic wave fields by boundary integral equation method." Engineering Analysis with Boundary Elements 27, no. 4 (2003): 291–304. http://dx.doi.org/10.1016/s0955-7997(02)00117-0.

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33

Anwar, M. N., and H. H. Sherief. "Boundary integral equation formulation of generalized thermoelasticity in a Laplace-transform domain." Applied Mathematical Modelling 12, no. 2 (1988): 161–66. http://dx.doi.org/10.1016/0307-904x(88)90007-8.

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34

Gao, Xiao-Wei, Hai-Feng Peng, and Jian Liu. "A boundary-domain integral equation method for solving convective heat transfer problems." International Journal of Heat and Mass Transfer 63 (August 2013): 183–90. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.03.071.

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35

Ramazanov, M. I., and N. K. Gulmanov. "On the singular Volterra integral equation of the boundary value problem for heat conduction in a degenerating domain." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 31, no. 2 (2021): 241–52. http://dx.doi.org/10.35634/vm210206.

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In this paper, we consider a singular Volterra type integral equation of the second kind, to which some boundary value problems of heat conduction in domains with a boundary varying with time are reduced by the method of thermal potentials. The peculiarity of such problems is that the domain degenerates into a point at the initial moment of time. Accordingly, a distinctive feature of the integral equation under study is that the integral of the kernel, as the upper limit of integration tends to the lower one, is not equal to zero. This circumstance does not allow solving this equation by the m

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36

Hacene, Saker. "On the Harmonic Problem with Nonlinear Boundary Integral Conditions." International Journal of Analysis 2014 (February 23, 2014): 1–5. http://dx.doi.org/10.1155/2014/976520.

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In the present work, we deal with the harmonic problems in a bounded domain of ℝ2 with the nonlinear boundary integral conditions. After applying the Boundary integral method, a nonlinear boundary integral equation is obtained; the existence and uniqueness of the solution will be a consequence of applying theory of monotone operators.

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37

Gao, Xiao Wei, and Chuan Zeng Zhang. "Isotropic Damage Analysis of Elastic Solids Using Meshless BEM." Key Engineering Materials 324-325 (November 2006): 1261–64. http://dx.doi.org/10.4028/www.scientific.net/kem.324-325.1261.

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In this paper, an isotropic elastic damage analysis is presented by using a meshless boundary element method (BEM) without internal cells. First, nonlinear boundary-domain integral equations are derived by using the fundamental solutions for undamaged, homogeneous, isotropic and linear elastic solids and the concept of normalized displacements, which results in boundary-domain integral equations without an involvement of the displacement gradients in the domain-integral. Then, the arising domain-integral due to the damage effects is converted into a boundary integral by approximating the norma

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38

Syngellakis, Stavros, and Jiang Wei Wu. "Nonlinear Viscoelastic Fracture Mechanics Using Boundary Elements." Key Engineering Materials 454 (December 2010): 137–48. http://dx.doi.org/10.4028/www.scientific.net/kem.454.137.

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The boundary element methodology is applied to the fracture mechanics of non-linear viscoelastic solids. The adopted non-linear model is based on the ‘free volume’ concept, which is introduced into the relaxation moduli entering the linear viscoelastic relations through a time shift depending on the volumetric strain. Nonlinearity generates an irreducible domain integral into the original boundary integral equation governing the behaviour of linear viscoelastic solids. This necessitates the evaluation of domain strains, which relies on a non-standard differentiation of an integral with a stron

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39

Falletta, Silvia, and Giovanni Monegato. "Exact nonreflecting boundary conditions for exterior wave equation problems." Publications de l'Institut Math?matique (Belgrade) 96, no. 110 (2014): 103–23. http://dx.doi.org/10.2298/pim1410103f.

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We consider the classical wave equation problem defined on the exterior of a bounded 2D space domain, possibly having far field sources. We consider this problem in the time domain, but also in the frequency domain. For its solution we propose to associate with it a boundary integral equation (BIE) defined on an artificial boundary surrounding the region of interest. This boundary condition is nonreflecting (or transparent) for both outgoing and incoming waves and it does not have to include necessarily the problem datum supports. The problem physical domain can even be a multi-domain, defined

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40

Guo, Li, Tang Chen, Jun Hong, Ling Qiao, and Xiao Ming Guo. "Study on Chloride Diffusion in Concrete with Non-Homogenous Coefficient Using Meshless Boundary Element Method." Materials Science Forum 650 (May 2010): 38–46. http://dx.doi.org/10.4028/www.scientific.net/msf.650.38.

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A new robust numerical technique was proposed for analyzing chloride transient diffusion in concrete with non-homogenous coefficient. The method was based on a meshless boundary element method which results in an integral equation for explicitly evaluating field chloride quantities. Weighted residual method and Green’s function were adopted to derive domain and boundary integral equations. A radial integration method coupling with radial basis function approximation technology was used to convert domain integral into equivalent boundary integral. With central finite difference method, an expli

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41

Chkadua, O., S. E. Mikhailov, and D. Natroshvili. "Localized Boundary-Domain Singular Integral Equations Based on Harmonic Parametrix for Divergence-Form Elliptic PDEs with Variable Matrix Coefficients." Integral Equations and Operator Theory 76, no. 4 (2013): 509–47. http://dx.doi.org/10.1007/s00020-013-2054-4.

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42

Nanni, Luca. "Theoretical Investigation of Subluminal Particles Endowed with Imaginary Mass." Particles 4, no. 2 (2021): 325–32. http://dx.doi.org/10.3390/particles4020027.

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In this article, the general solution of the tachyonic Klein–Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex ω-plane. In particular, it is proved that this solution does not contain any superluminal components under the given boundary conditions. On the basis of this result, we infer that all possible spacelike wave equations describe the dynamics of subluminal particles endowed with imaginary mass. This result is validated for the Chodos equation, used to describe the hypothetical superluminal behaviour of the neutrino. In this specific framework,

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43

Zakerdoost, Hassan, Hassan Ghassemi, and Mehdi Iranmanesh. "Solution of Boundary Value Problems Using Dual Reciprocity Boundary Element Method." Advances in Applied Mathematics and Mechanics 9, no. 3 (2017): 680–97. http://dx.doi.org/10.4208/aamm.2014.m783.

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AbstractIn this work we utilize the boundary integral equation and the Dual Reciprocity Boundary Element Method (DRBEM) for the solution of the steady state convection-diffusion-reaction equations with variable convective coefficients in two-dimension. The DRBEM is a numerical method to transform the domain integrals into the boundary only integrals by using the fundamental solution of Helmholtz equation. Some examples are calculated to confirm the accuracy of the approach. The results obtained by the analytic solutions are in good agreement with ones provided by the DRBEM technique.

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44

Zrazhevsky, Grigoriy, and Vera Zrazhevska. "OBTAINING AND INVESTIGATION OF THE INTEGRAL REPRESENTATION OF SOLUTION AND BOUNDARY INTEGRAL EQUATION FOR THE NON-STATIONARY PROBLEM OF THERMAL CONDUCTIVITY." EUREKA: Physics and Engineering 6 (November 30, 2016): 53–58. http://dx.doi.org/10.21303/2461-4262.2016.00216.

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Technological processes in the energy sector and engineering require the calculation of temperature regime of functioning of different constructions. Mathematical model of thermal loading of constructions is reduced to a non-stationary initial-boundary value problem of thermal conductivity. The article examines the formulation of the non-stationary initial-boundary value problem of thermal conductivity in the form of a boundary integral equation, analyzes the singular equation and builds the fundamental solution. To build the integral representation of the solution the method of weighted resid

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45

Zhou, Hong, Xiaofei Chen, and Ying Chang. "Review on localized boundary integral equation: Discrete wavenumber method for 2D irregular layers." Earthquake Science 23, no. 2 (2010): 129–37. http://dx.doi.org/10.1007/s11589-009-0070-x.

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Jenaliyev, M. T., M. I. Ramazanov та A. O. Tanin. "To the solution of the Solonnikov-Fasano problem with boundary moving on arbitrary law x = γ(t)." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 101, № 1 (2021): 37–49. http://dx.doi.org/10.31489/2021m1/37-49.

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In this paper we study the solvability of the boundary value problem for the heat equation in a domain that degenerates into a point at the initial moment of time. In this case, the boundary changing with time moves according to an arbitrary law x = γ(t). Using the generalized heat potentials, the problem under study is reduced to a pseudo-Volterra integral equation such that the norm of the integral operator is equal to one and it is shown that the corresponding homogeneous integral equation has a nonzero solution.

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Hagedorn, P., and W. Schramm. "On the Dynamics of Large Systems With Localized Nonlinearities." Journal of Applied Mechanics 55, no. 4 (1988): 946–51. http://dx.doi.org/10.1115/1.3173746.

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In this paper, a certain class of dynamical systems is discussed, which can be decomposed into a large linear subsystem and one or more nonlinear subsystems. For this class of nonlinear systems the dynamic behavior is represented in the time domain by means of an integral equation. A simple numerical procedure for the solution of this integral equation is given. It is also shown how the decomposition of the system can be used in measuring the frequency response of the large linear subsystem, without actually separating it from the nonlinear subsystems. An elastostatic analogy is used to illust

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Tynda, Aleksandr N., and Konstantin A. Timoshenkov. "Application of boundary integral equation method to numerical solution of elliptic boundary-value problems in R3." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 22, no. 3 (2020): 319–32. http://dx.doi.org/10.15507/2079-6900.22.202003.319-332.

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In this paper we propose numerical methods for solving interior and exterior boundary-value problems for the Helmholtz and Laplace equations in complex three-dimensional domains. The method is based on their reduction to boundary integral equations in R2. Using the potentials of the simple and double layers, we obtain boundary integral equations of the Fredholm type with respect to unknown density for Dirichlet and Neumann boundary value problems. As a result of applying integral equations along the boundary of the domain, the dimension of problems is reduced by one. In order to approximate so

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Fichte, L. O., S. Lange, Th Steinmetz, and M. Clemens. "Shielding properties of a conducting bar calculated with a boundary integral method." Advances in Radio Science 3 (May 12, 2005): 119–23. http://dx.doi.org/10.5194/ars-3-119-2005.

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Abstract. A plane rectangular bar of conducting and permeable material is placed in an external low-frequency magnetic field. The shielding properties of this object are investigated by solving the given plane eddy current problem for the vector potential with the boundary integral equation method. The vector potential inside the rectangle is governed by Helmholtz' equation, which in our case is solved by separation. The solution is inserted into the remaining boundary integral equation for the exterior vector potential in the domain surrounding the bar. By expressing its logarithmic kernel as

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Hackbusch, W., W. Kress, and S. A. Sauter. "Sparse convolution quadrature for time domain boundary integral formulations of the wave equation." IMA Journal of Numerical Analysis 29, no. 1 (2008): 158–79. http://dx.doi.org/10.1093/imanum/drm044.

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