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WAVELET METHODS FOR BOUNDARY INTEGRAL EQUATIONS
Communications in Numerical Methods in Engineering, 1997The author describes a recent application of the wavelet idea to the boundary integral equation of the two-dimensional direct boundary element formulation of the Laplace equation. The results for two simple problems are also included to illustrate the expected accuracy obtained with the procedure.
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Numerical Integration of the Boundary-Layer Equations
2000Numerical solutions of the boundary–layer equations are based on the assumption that the differential expressions in the partial differential equations can be approximated by difference expressions. This approximation, called discretisation can be obtained from a series expansion for the velocity components in the coordinate directions.
Hermann Schlichting, Klaus Gersten
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A Boundary Integral Equation Approach to Oxidation Modeling
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 1985Thermal oxidation of silicon involves the diffusion of oxidant molecules from the gas-oxide interface to the oxide-silicon interface, and the transport of newly formed oxide away from the latter. Under suitable formulations these two processes can be shown to be boundary-value problems of harmonic and biharmonic nature.
Thye-Lai Tung, Dimitri A. Antoniadis
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Boundary Integral Equations and Boundary Elements Methods in Elastodynamics
2007We review the application of boundary integral equation (BIE) methods to elastic wave propagation problems. BIE methods express the wavefield as an integral equation defined over the boundary of the domain studied. They can be grouped into two families.
Bouchon, Michel +1 more
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1984
According to the Dirichlet existence-uniqueness theorem, there exists a unique harmonic function φ in Bi which assumes prescribed continuous boundary values on a Liapunov surface ∂B. To construct φ in Bi, we write $$\phi (\underline {\text{p}} ) = \mathop \smallint \limits_{\partial {\text{B}}} g(\underline {\text{p}} {\text{,}}\underline {\text{q}}
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According to the Dirichlet existence-uniqueness theorem, there exists a unique harmonic function φ in Bi which assumes prescribed continuous boundary values on a Liapunov surface ∂B. To construct φ in Bi, we write $$\phi (\underline {\text{p}} ) = \mathop \smallint \limits_{\partial {\text{B}}} g(\underline {\text{p}} {\text{,}}\underline {\text{q}}
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Boundary Integral Solutions of Laplace's Equation
Bell System Technical Journal, 1978Although Laplace's equation is simple, the region over which it is to be solved is often complicated. Both the shape of the region and the boundary conditions can induce solutions Φ which are singular at isolated points on the boundary of the region. Boundary integral equation methods are well-suited to the problem, reducing a two-dimensional partial ...
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On boundary integral equations in electroelasticity
Journal of Applied Mathematics and Mechanics, 1989zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vatul'yan, A. O., Kublikov, V. L.
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Applied Mathematics and Mechanics, 1983
Based on [1], we have further applied the variational principle of the variable boundary to investigate the discretization analysis of the solid system and derived the generalized Galerkin's equations of the finite element, the boundary variational equations and the boundary integral equations. These equations indicate that the unknown functions of the
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Based on [1], we have further applied the variational principle of the variable boundary to investigate the discretization analysis of the solid system and derived the generalized Galerkin's equations of the finite element, the boundary variational equations and the boundary integral equations. These equations indicate that the unknown functions of the
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An Indirect Boundary Integral Equation Method for the Biharmonic Equation
SIAM Journal on Numerical Analysis, 1994An indirect boundary integral equation method for solving the Dirichlet problem for the biharmonic equation is proposed. For the numerical solution, a discrete Galerkin method is used and a complete numerical analysis in a suitable Sobolev space is given.
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