Spline qualocation methods for boundary integral equations

DOI10.1007/BF01385639zbMath0694.65068MaRDI QIDQ909427

Graeme Chandler, Ian H. Sloan

Publication date: 1990

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133515

zbMATH Keywords

stabilityconvergenceboundary element methodnumerical experimentsboundary integral equationsrates of convergencePetrov-Galerkin methodqualocation methodlogarithmic kernelquadrature rulespseudo-differential operatorspiecewise-linear splines

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical methods for integral equations (65R20) Integral representations of solutions to PDEs (35C15) Boundary value problems for PDEs with pseudodifferential operators (35S15) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (29)

On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation ⋮ Stability of spline approximation methods for multidimensional pseudodifferential operators ⋮ Convergence analysis of oversampled collocation boundary element methods in 2D ⋮ A Nyström flavored Calderón calculus of order three for two dimensional waves, time-harmonic and transient ⋮ Fully-discrete collocation methods for an integral equation of the first kind ⋮ An analysis of least-squares oversampled collocation methods for compactly perturbed boundary integral equations in two dimensions ⋮ Semi-discrete Galerkin approximations for the single-layer equation on Lipschitz curves ⋮ Ian Sloan’s Legacy in Integral Equation Methods ⋮ The fast solution of periodic pseudodifferential equations ⋮ An asymptotic series approach to qualocation methods ⋮ Stability of qualocation methods for elliptic boundary integral equations ⋮ An a posteriori error estimate for a first-kind integral equation ⋮ An unconventional quadrature method for logarithmic-kernel integral equations on closed curves ⋮ Properties of certain trigonometric series arising in numerical analysis ⋮ Spline approximation methods for multidimensional periodic pseudodifferential equations ⋮ Qualocation for boundary integral equations using splines with multiple knots ⋮ Dirac delta methods for Helmholtz transmission problems ⋮ Boundary element simulation of thermal waves ⋮ Superapproximation and commutator properties of discrete orthogonal projections for continuous splines ⋮ Numerical solution of linear Volterra integral equations of the second kind with sharp gradients ⋮ The tolerant qualocation method for variable-coefficient elliptic equations on curves ⋮ Boundary element simulation of thermal waves ⋮ Numerical Evaluation of Some Trigonometric Series ⋮ Tolerant qualocation -- a qualocation method for boundary integral equations with reduced regularity requirement ⋮ Commutator properties for periodic splines ⋮ Qualocation ⋮ Discrete orthogonal projections on multiple knot periodic splines ⋮ The use of discrete orthogonal projections in boundary element methods ⋮ The \(K\)-operator and the qualocation method for strongly elliptic equations on smooth curves

Cites Work

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