On the existence of mosaic-skeleton approximations for discrete analogues of integral operators
type: Item
instance of: scholarly article
title: On the existence of mosaic-skeleton approximations for discrete analogues of integral operators
zbMATH Open document ID: 1381.65095
DOI: 10.1134/S096554251709007X
author: A. A. Kashirin
author: M. Yu. Taltykina
published in: Computational Mathematics and Mathematical Physics
publication date: 2018-01-04T00:00:00Z
review text: The authors are concerned with the 3D exterior Dirichlet boundary value problem attached to the Laplace and Helmholtz equations. The problems are reduced to some Fredholm integral equations of the first kind. It seems that the integral equations are discretized by a Galerkin-type method. The linear algebraic system provided is solved using the mosaic-skeleton algorithm. This algorithm reduces the computational cost and the complexity of iterative methods for solving dense linear algebraic systems, mainly the matrix-vector multiplication effort. Two numerical examples are carried out in order to illustrate the capabilities of the algorithm.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 6821895
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: Laplace equation
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: boundary integral equation method
zbMATH Keywords: system of linear algebraic equations
zbMATH Keywords: mosaic-skeleton method
zbMATH Keywords: Fredholm integral equations of the first kind
zbMATH Keywords: algorithm
zbMATH Keywords: numerical example
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
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full work available at URL: s096554251709007x
OpenAlex ID: W2759979675
description: scientific article; zbMATH DE number 6821895