H-matrix approximability of inverses of discretizations of the fractional Laplacian

被引：0

作者：

Karkulik, Michael ^{[1
]}

Melenk, Jens Markus ^{[2
]}

机构：

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Ave Espana 1680, Valparaiso, Chile

[2] Tech Univ Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, Vienna, Austria

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2019年 / 45卷 / 5-6期

基金：

奥地利科学基金会;

关键词：

Hierarchical matrices; Fractional Laplacian; 65N30; 65F05; 65F30; 65F50; FAST DIRECT SOLVER; STRUCTURED LINEAR-SYSTEMS; FINITE-ELEMENT-METHOD; INTEGRAL-EQUATIONS; DIFFERENTIAL-EQUATIONS; EXTENSION PROBLEM; BEM MATRICES; APPROXIMATION; REGULARITY; FACTORIZATION;

D O I：

10.1007/s10444-019-09718-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The integral version of the fractional Laplacian on a bounded domain is discretized by a Galerkin approximation based on piecewise linear functions on a quasiuniform mesh. We show that the inverse of the associated stiffness matrix can be approximated by blockwise low-rank matrices at an exponential rate in the block rank.

引用

页码：2893 / 2919

页数：27

共 63 条

[1] A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian [J].

Acosta, Gabriel ;

Bersetche, Francisco M. ;

Pablo Borthagaray, Juan .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (04) :784-816

[2] A FRACTIONAL LAPLACE EQUATION: REGULARITY OF SOLUTIONS AND FINITE ELEMENT APPROXIMATIONS [J].

Acosta, Gabriel ;

Pablo Borthagaray, Juan .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2017, 55 (02) :472-495

[3]

Adams R. A., 1975, SOBOLEV SPACES

[4] Aspects of an adaptive finite element method for the fractional Laplacian: A priori and a posteriori error estimates, efficient implementation and multigrid solver [J].

Ainsworth, Mark ;

Glusa, Christian .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2017, 327 :4-35

[5]

[Anonymous], THESIS

[6]

[Anonymous], 1955, Ann. Inst. Fourier (Grenoble)

[7]

Bebendorf M, 2000, NUMER MATH, V86, P565, DOI 10.1007/s002110000192

[8] Hierarchical LU decomposition-based preconditioners for BEM [J].

Bebendorf, M .

COMPUTING, 2005, 74 (03) :225-247

[9] Why finite element discretizations can be factored by triangular hierarchical matrices [J].

Bebendorf, Mario .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (04) :1472-1494

[10]

Börm S, 2010, EMS TRACTS MATH, V14, P1, DOI 10.4171/091

← 1 2 3 4 5 6 7 →