On the fast computation of high dimensional volume potentials

DOI10.1090/S0025-5718-2010-02425-1zbMath1213.65046arXiv0911.0443MaRDI QIDQ3168727

Vladimir Gilelevich Maz'ya, Gunther Schmidt, Flavia Lanzara

Publication date: 19 April 2011

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.0443

zbMATH Keywords

numerical experimentsPoisson equationadvection-diffusion equationheat equationsNewton potentialvolume potentialshigh dimensional cases

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Heat equation (35K05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

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Cites Work

• Unnamed Item
• Approximate approximations from scattered data
• Efficient convolution with the Newton potential in \(d\) dimensions
• Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems
• ``Approximate approximations and the cubature of potentials
• Multiresolution separated representations of singular and weakly singular operators
• Potentials of Gaussians and approximate wavelets
• Numerical operator calculus in higher dimensions
• Tensor-Product Approximation to Multidimensional Integral Operators and Green's Functions
• Algorithms for Numerical Analysis in High Dimensions