1995
DOI: 10.1137/0916040
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Piecewise Polynomial Collocation for Boundary Integral Equations

Abstract: This paper considers the numerical solution of boundary integral equations of the second kind for Laplace's equation Au 0 on connected regions D in R with boundary S. The bounda S is allowed to be smooth or piecewisc smooth, and we let {AK _< K _< N} be a triangulation of S. The numerical method is collocation with approximations which arc pieccwise quadratic in the parametrization variables, leading to a numerical solution UN. Superconvergence results for UN are given for S a smooth surface and for a special … Show more

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Cited by 43 publications
(32 citation statements)
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“…This constitutes a Cauchy problem for Laplace's equation: 42 (1) with the following boundary conditions:…”
Section: Formulating the Methods Of Fundamental Solutions For Ecgimentioning
confidence: 99%
See 1 more Smart Citation
“…This constitutes a Cauchy problem for Laplace's equation: 42 (1) with the following boundary conditions:…”
Section: Formulating the Methods Of Fundamental Solutions For Ecgimentioning
confidence: 99%
“…Importantly, this formulation requires computation of complicated singular integrals that require careful handling. 1,36,73 In addition, BEM often suffers from slow convergence due to the use of low order polynomial approximations. 36,63 These difficulties with the efficient implementation of BEM led us to explore the possibility of applying a meshless method to inverse electrocardiography, in the hope of overcoming such mesh-related problems.…”
Section: Introductionmentioning
confidence: 99%
“…For a not necessarily convex domain Ω with Γ a Lyapunov surface in C 1,α , 0 < α ≤ 1, the kernel n(y)·(y−x) / |x−y| 3 …”
Section: Continuous Boundary Datamentioning
confidence: 99%
“…Moreover, the approximate solutions of (2.3) with piecewise linear or piecewise constant boundary elements μ h ∈ S h and point collocation converge in C 0 (Γ) with meshwidth h → 0 (see [2,3,27,74]). …”
Section: Continuous Boundary Datamentioning
confidence: 99%
See 1 more Smart Citation