AN EFFICIENT GALERKIN BOUNDARY ELEMENT METHOD FOR THE TRANSIENT HEAT EQUATION

被引：19

作者：

Messner, Michael ^{[1
]}

Schanz, Martin ^{[1
]}

Tausch, Johannes ^{[2
]}

机构：

[1] Graz Univ Technol, Inst Appl Mech, A-8010 Graz, Austria

[2] So Methodist Univ, Dept Math, Dallas, TX 75275 USA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2015年 / 37卷 / 03期

基金：

美国国家科学基金会;

关键词：

heat equation; boundary element method; Galerkin discretization; multipole method;

D O I：

10.1137/151004422

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present boundary integral representations of several initial boundary value problems related to the heat equation. A Galerkin discretization with piecewise constant functions in time and piecewise linear functions in space leads to optimal a priori error estimates, provided that the meshwidths in space and time satisfy h(t) = O(h(x)(2)). Each time step involves the solution of a linear system, whose spectral condition number is independent of the refinement under the same assumption on the mesh. We show that if the parabolic multipole method is used to apply parabolic boundary integral operators, the overall complexity of the scheme is log-linear while preserving the convergence of the Galerkin discretization method. The theoretical estimates are confirmed numerically at the end of the paper.

引用

页码：A1554 / A1576

页数：23