A fast numerical solution for the first kind boundary integral equation for the Helmholtz equation

DOI10.1007/s10543-012-0380-6zbMath1262.65189OpenAlexW2051533681MaRDI QIDQ695065

Haotao Cai

Publication date: 20 December 2012

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-012-0380-6

zbMATH Keywords

convergencenumerical exampleHelmholtz equationboundary integral equation methodnumerical integration schemematrix truncation strategyfast numerical solution

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38)

Cites Work

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• Hyperbolic cross and the complexity of the approximate solution of Fredholm integral equations of the second kind with differentiable kernels
• Fast Fourier-Galerkin methods for solving singular boundary integral equations: Numerical integration and precondition
• A quadrature-based approach to improving the collocation method
• The modified quadrature method for logarithmic-kernel integral equations on closed curves
• An unconventional quadrature method for logarithmic-kernel integral equations on closed curves
• On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation
• Optimized tensor-product approximation spaces
• High dimensional polynomial interpolation on sparse grids
• Fast Fourier-Galerkin methods for first-kind logarithmic-kernel integral equations on open arcs
• On quadrature methods for highly oscillatory integrals and their implementation
• Fast discrete algorithms for sparse Fourier expansions of high dimensional functions
• The Numerical Solution of First-Kind Logarithmic-Kernel Integral Equations on Smooth Open Arcs
• A Fast Fourier–Galerkin Method for Solving Singular Boundary Integral Equations
• Boolean Methods for Double Integration
• Procedures for Computing One- and Two-Dimensional Integrals of Functions with Rapid Irregular Oscillations
• Quadrature methods for logarithmic-kernel integral equations on closed curves
• The Numerical Solution of Integral Equations of the Second Kind
• On the numerical quadrature of highly-oscillating integrals II: Irregular oscillators
• On the numerical quadrature of highly-oscillating integrals I: Fourier transforms
• Linear integral equations