Dynamical low-rank integrators for second-order matrix differential equations

被引：3

作者：

Hochbruck, Marlis ^{[1
]}

Neher, Markus ^{[1
]}

Schrammer, Stefan ^{[1
]}

机构：

[1] Karlsruhe Inst Technol, Inst Appl & Numer Math, Karlsruhe, Germany

来源：

BIT NUMERICAL MATHEMATICS | 2023年 / 63卷 / 01期

关键词：

Dynamical low-rank approximation; Matrix differential equations; PROJECTOR-SPLITTING INTEGRATOR; TIME INTEGRATION;

D O I：

10.1007/s10543-023-00941-7

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this paper, we construct and analyze a new dynamical low-rank integrator for second-order matrix differential equations. The method is based on a combination of the projector-splitting integrator introduced in Lubich and Oseledets (BIT 54(1):171-188, 2014. ) and a Strang splitting. We also present a variant of the new integrator which is tailored to semilinear second-order problems.

引用

页数：21

共 16 条

[1] ON LEAPFROG-CHEBYSHEV SCHEMES [J].

Carle, Constantin ;

Hochbruck, Marlis ;

Sturm, Andreas .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2020, 58 (04) :2404-2433

[2] An unconventional robust integrator for dynamical low-rank approximation [J].

Ceruti, Gianluca ;

Lubich, Christian .

BIT NUMERICAL MATHEMATICS, 2022, 62 (01) :23-44

[3] TIME INTEGRATION OF TREE TENSOR NETWORKS [J].

Ceruti, Gianluca ;

Lubich, Christian ;

Walach, Hanna .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2021, 59 (01) :289-313

[4] A low-rank projector-splitting integrator for the Vlasov-Maxwell equations with divergence correction [J].

Einkemmer, Lukas ;

Ostermann, Alexander ;

Piazzola, Chiara .

JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 403

[5] A LOW-RANK PROJECTOR-SPLITTING INTEGRATOR FOR THE VLASOV-POISSON EQUATION [J].

Einkemmer, Lukas ;

Lubich, Christian .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2018, 40 (05) :B1330-B1360

[6]

Hairer E., 2003, Acta Numerica, V12, P399, DOI 10.1017/S0962492902000144

[7]

Hochbruck M., 2022, PREPRINT, DOI [/10.5445/IR/1000143198, DOI 10.5445/IR/1000143198]

[8] Optimized higher order time discretization of second order hyperbolic problems: Construction and numerical study [J].

Joly, P. ;

Rodriguez, J. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (06) :1953-1961

[9] DISCRETIZED DYNAMICAL LOW-RANK APPROXIMATION IN THE PRESENCE OF SMALL SINGULAR VALUES [J].

Kieri, Emil ;

Lubich, Christian ;

Walach, Hanna .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2016, 54 (02) :1020-1038

[10] Dynamical low-rank approximation [J].

Koch, Othmar ;

Lubich, Christian .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2007, 29 (02) :434-454

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