Quadrature algorithms for high dimensional singular integrands on simplices

DOI10.1007/s11075-015-9977-6zbMath1332.65035OpenAlexW1972152164MaRDI QIDQ907587

Tobias von Petersdorff, Alexey Chernov, Christoph Schwab

Publication date: 25 January 2016

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-015-9977-6

zbMATH Keywords

algorithmnumerical integrationnumerical examplesintegral equationsexponential convergenceGevrey regularityhypersingular integralsGauss-Jacobi quadraturehigh-dimensional integrandsGauss-Jacobi quadrature rulesGauss-Legendre quadrature ruleshypersingular kernelsSmolyak-type quadrature rules

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items

Fractional Laplacian -- quadrature rules for singular double integrals in 3D ⋮ Transformation methods for the numerical integration of three-dimensional singular functions ⋮ Nonlocal Control in the Conduction Coefficients: Well-Posedness and Convergence to the Local Limit ⋮ Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver

Uses Software

• Matlab
• Netlib
• numeralgo
• nwSpGr

Cites Work

• Likelihood approximation by numerical integration on sparse grids
• Numerical quadrature for high-dimensional singular integrals over parallelotopes
• Boundary integral equations
• Integral equations with non integrable kernels
• On numerical cubatures of singular surface integrals in boundary element methods
• Numerical integration using sparse grids
• Variable order composite quadrature of singular and nearly singular integrals
• Smolyak cubature of given polynomial degree with few nodes for increasing dimension
• Pseudo-differential operators and Gevrey classes
• Exponential convergence ofhpquadrature for integral operators with Gevrey kernels
• Exponential Convergence of Gauss--Jacobi Quadratures for Singular Integrals over Simplices in Arbitrary Dimension
• Is Gauss Quadrature Better than Clenshaw–Curtis?
• Boundary Element Methods
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