A modified domain decomposition spectral collocation method for parabolic partial differential equations

被引：0

作者：

Luo, Wei-Hua ^{[1
,2
]}

Yin, Liang ^{[3
]}

Guo, Jun ^{[4
]}

机构：

[1] Hunan Univ Arts & Sci, Sch Math & Phys, Changde 415000, Hunan, Peoples R China

[2] Neijiang Normal Univ, Lab Numer Simulat Sichuan Prov Univ, Neijiang 641000, Sichuan, Peoples R China

[3] Hunan Univ Arts & Sci, Coll Mech Engn, Changde 415000, Hunan, Peoples R China

[4] Chengdu Univ Informat Technol, Coll Appl Math, Chengdu 610225, Sichuan, Peoples R China

来源：

NETWORKS AND HETEROGENEOUS MEDIA | 2024年 / 19卷 / 03期

关键词：

domain decomposition; spectral collocation method; preconditioner; parabolic PDE; FINITE-ELEMENT-METHOD; ALLEN-CAHN EQUATION; SCHEMES; SPACE; TIME;

D O I：

10.3934/nhm.2024041

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, utilizing Legendre polynomials as the basis functions in both space and time, we present a modified domain decomposition spectral method for 2-dimensional parabolic partial differential ff erential equations. For solving the obtained linear/nonlinear / nonlinear algebraic equations, a dimension expanding preconditioner is applied employing the obtained saddle construction of the coefficient ffi cient matrix. Numerical examples are given to show the performance of the presented method and the efficiency ffi ciency of the preconditioner.

引用

页码：923 / 939

页数：17

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