Domain Decomposition Methods for Hyperbolic Problems

Proceedings Mathematical Sciences

Pravir Dutt²  Subir Singh Lamba¹ 

[1] $$;Department of Mathematics, Indian Institute of Technology, Kanpur 0 0, India$$

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

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 𝐿2 norms of the residuals and a term which is the sum of the squares of the 𝐿2 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.

【 授权许可】

Unknown