• Domain Decomposition Methods for Hyperbolic Problems

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/119/02/0231-0249

• # Keywords

Domain decomposition method; finite speed of propagation; pulsating boundaries; stability estimates; parallel preconditioners.

• # Abstract

In this paper a method is developed for solving hyperbolic initial boundary value problems in one space dimension using domain decomposition, which can be extended to problems in several space dimensions. We minimize a functional which is the sum of squares of the $L^2$ norms of the residuals and a term which is the sum of the squares of the $L^2$ norms of the jumps in the function across interdomain boundaries. To make the problem well posed the interdomain boundaries are made to move back and forth at alternate time steps with sufficiently high speed. We construct parallel preconditioners and obtain error estimates for the method.

The Schwarz waveform relaxation method is often employed to solve hyperbolic problems using domain decomposition but this technique faces difficulties if the system becomes characteristic at the inter-element boundaries. By making the inter-element boundaries move faster than the fastest wave speed associated with the hyperbolic system we are able to overcome this problem.

• # Author Affiliations

1. Department of Mathematics, Indian Institute of Technology, Kanpur 208 016, India

• # Proceedings – Mathematical Sciences

Volume 132, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019