Domain decomposition methods for hyperbolic problems |
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Authors: | Pravir Dutt Subir Singh Lamba |
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Institution: | (1) Department of Mathematics, Indian Institute of Technology, Kanpur, 208 016, India |
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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. |
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Keywords: | Domain decomposition method finite speed of propagation pulsating boundaries stability estimates parallel preconditioners |
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