Error estimation for quadrature by expansion in layer potential evaluation

DOI10.1007/s10444-016-9484-xzbMath1367.65154arXiv1603.08366OpenAlexW3104692319MaRDI QIDQ2361159

Ludvig af Klinteberg, Anna-Karin Tornberg

Publication date: 29 June 2017

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.08366

zbMATH Keywords

numerical exampleerror estimateHelmholtz equationquadraturecontour integrationlayer potentialboundary integral methodsLapalce equationnearly singular

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (22)

Quadrature error estimates for layer potentials evaluated near curved surfaces in three dimensions ⋮ Close evaluation of layer potentials in three dimensions ⋮ An adaptive kernel-split quadrature method for parameter-dependent layer potentials ⋮ A robust solver for elliptic PDEs in 3D complex geometries ⋮ A highly accurate boundary integral equation method for surfactant-laden drops in 3D ⋮ Ubiquitous evaluation of layer potentials using quadrature by kernel-independent expansion ⋮ A local target specific quadrature by expansion method for evaluation of layer potentials in 3D ⋮ Accurate quadrature of nearly singular line integrals in two and three dimensions by singularity swapping ⋮ Corrected trapezoidal rule for near-singular integrals in axi-symmetric Stokes flow ⋮ Fast algorithms for quadrature by expansion. I: Globally valid expansions ⋮ Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology ⋮ Simulation and validation of surfactant-laden drops in two-dimensional Stokes flow ⋮ A fast algorithm for quadrature by expansion in three dimensions ⋮ Optimization of fast algorithms for global quadrature by expansion using target-specific expansions ⋮ Adaptive Quadrature by Expansion for Layer Potential Evaluation in Two Dimensions ⋮ Partition of unity extension of functions on complex domains ⋮ STABLE IDENTIFICATION OF SOURCES LOCATED ON SEPARATION INTERFACES OF TWO DIFFERENT HOMOGENEOUS MEDIA ⋮ Viscous transport in eroding porous media ⋮ Asymptotic Approximations for the Close Evaluation of Double-Layer Potentials ⋮ Error estimates for the nearly singular momentum-space bound-state equations ⋮ A fast algorithm with error bounds for quadrature by expansion ⋮ A fast integral equation method for the two-dimensional Navier-Stokes equations

Uses Software

• DLMF

Cites Work

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• Quadrature by expansion: a new method for the evaluation of layer potentials
• Fast algorithms for quadrature by expansion. I: Globally valid expansions
• NIST digital library of mathematical functions
• On the evaluation of layer potentials close to their sources
• On the Convergence of Local Expansions of Layer Potentials
• Evaluation of Layer Potentials Close to the Boundary for Laplace and Helmholtz Problems on Analytic Planar Domains
• The Exponentially Convergent Trapezoidal Rule
• Convergence Properties of Gaussian Quadrature Formulae
• Clenshaw–Curtis and Gauss–Legendre Quadrature for Certain Boundary Element Integrals
• Nearly Singular Integrals in 3D Stokes Flow
• A Unified Approach to Quadrature Rules with Asymptotic Estimates of Their Remainders

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