The fast Fourier transform and the numerical solution of one-dimensional boundary integral equations

DOI10.1007/BF01389873zbMath0579.65148MaRDI QIDQ1067406

K.-T. Schleicher, U. Lamp, Wolfgang L. Wendland

Publication date: 1985

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

Full work available at URL: https://eudml.org/doc/133020

zbMATH Keywords

boundary element methodfast Fourier transformprojection methodboundary integral equationsFourier seriesSystemsCauchy kernelquadrature errorsGaussian quadraturesasymptotic error estimatesclamped plateelliptic pseudodifferential equations

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Boundary value problems for PDEs with pseudodifferential operators (35S15)

Related Items (12)

Fast solution of a class of periodic pseudodifferential equations ⋮ A note on the sparse representation of discrete integral operators ⋮ Reduction of an infinite system of integrodifferential equations for electric currents on a lattice of closed curves to a finite system of independent pseudodifferential equations on a circle ⋮ Unnamed Item ⋮ A Nyström method for the two dimensional Helmholtz hypersingular equation ⋮ A fully-discrete trigonometric collocation method ⋮ Efficient MFS algorithms in regular polygonal domains ⋮ Unnamed Item ⋮ Qualocation ⋮ First kind integral equations for the numerical solution of the plane Dirichlet problem ⋮ Quadrature by Parity Asymptotic eXpansions (QPAX) for Scattering by High Aspect Ratio Particles ⋮ Boundary integral equations in time-harmonic acoustic scattering

Cites Work

• The convergence of Galerkin and collocation methods with splines for pseudodifferential equations on closed curves
• Spectral properties of elliptic pseudodifferential operators on a closed curve
• A boundary integral equation method for a Neumann boundary problem for force-free fields
• A finite element method for some integral equations of the first kind
• Ein numerisches Verfahren zur Lösung des Neumannschen Außenraumproblems für die Helmholtzsche Schwingungsgleichung
• Fast Fourier Methods in Computational Complex Analysis
• On the Asymptotic Convergence of Collocation Methods
• A Spline-Trigonometric Galerkin Method and an Exponentially Convergent Boundary Integral Method
• A Finite Element Collocation Method for Singular Integral Equations
• Some applications of a galerkin‐collocation method for boundary integral equations of the first kind
• On the Asymptotic Convergence of Collocation Methods With Spline Functions of Even Degree
• On the Two-Dimensional Exterior Boundary-Value Problems of Elasticity
• An Algorithm for the Machine Calculation of Complex Fourier Series
• An integral equation approach to boundary value problems of classical elastostatics
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