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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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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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On Boundary Integral Equations of the First Kind
Journal of Computational Mathematics, 1989A large class of elliptic boundary value problems in elasticity and fluid mechanics can be reduced to systems of boundary integral equations of the first kind. This paper summarizes some of the basic concepts and results concerning the mathematical foundation of boundary element methods for treating such a class of boundary integral equations.
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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 integral equation method for the Dirichlet problem for the biharmonic equation is proposed. It leads to a $2 \times 2$ matrix integral equation system. By taking suitable norms on the spaces of density functions, the Fredholm operator theory can be used to prove the solvability. The kernels in this system are relatively complicated.
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