Block Generalized Locally Toeplitz Sequences: From the Theory to the Applications

被引：27

作者：

Garoni, Carlo ^{[1
,2
]}

Mazza, Mariarosa ^{[3
]}

Serra-Capizzano, Stefano ^{[2
,4
]}

机构：

[1] Univ Italian Switzerland, Inst Computat Sci, CH-6900 Lugano, Switzerland

[2] Univ Insubria, Dept Sci & High Technol, I-22100 Como, Italy

[3] Max Planck Inst Plasma Phys, Div Numer Methods Plasma Phys, D-85748 Garching, Germany

[4] Uppsala Univ, Dept Informat Technol, POB 337, SE-75105 Uppsala, Sweden

来源：

AXIOMS | 2018年 / 7卷 / 03期

关键词：

spectral (eigenvalue) and singular value distributions; generalized locally Toeplitz sequences; discretization of systems of differential equations; higher-order finite element methods; discontinuous Galerkin methods; finite difference methods; isogeometric analysis; B-splines; curl-curl operator; time harmonic Maxwell's equations and magnetostatic problems;

D O I：

10.3390/axioms7030049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The theory of generalized locally Toeplitz ( GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of matrices An arising from virtually any kind of numerical discretization of differential equations ( DEs). Indeed, when the mesh fineness parameter n tends to infinity, these matrices An give rise to a sequence f An g n, which often turns out to be a GLT sequence or one of its " relatives", i. e., a block GLT sequence or a reduced GLT sequence. In particular, block GLT sequences are encountered in the discretization of systems of DEs as well as in the higher- order finite element or discontinuous Galerkin approximation of scalar DEs. Despite the applicative interest, a solid theory of block GLT sequences has been developed only recently, in 2018. The purpose of the present paper is to illustrate the potential of this theory by presenting a few noteworthy examples of applications in the context of DE discretizations.

引用

页数：29

共 43 条

[41] Tyrtyshnikov EE, 1998, LINEAR ALGEBRA APPL, V270, P15
[42] A unifying approach to some old and new theorems on distribution and clustering
Tyrtyshnikov, EE
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1996, 232 : 1 - 43
[43] Distribution of eigenvalues and singular values of Toeplitz matrices under weakened conditions on the generating function
Zamarashkin, NL
Tyrtyshnikov, EE
[J]. SBORNIK MATHEMATICS, 1997, 188 (7-8) : 1191 - 1201

← 1 2 3 4 5 →