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by Jari Toivanen, Jari Toivanen
http://www.mit.jyu.fi/~tene/papers/report96-14.ps.gz
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Abstract:
The two--dimensional Helmholtz equation with the Sommerfeld radiation condition at the infinity is approximated inside a rectangle with a second--order absorbing boundary conditions on the artificial boundary. The discretization is done using linear finite elements. The mesh is rectangular with refinement in the layer and local fitting to the boundaries. In the solution procedure, the domain is decomposed into two parts, namely to slightly extended layer and its complement without the obstacle. For the outer domain, a separable preconditioner is obtained by applying a fictitious domain method. The preconditioner for the whole domain is coupled from domain decomposition and fictitious domain preconditioners. The system of linear equations is solved by the preconditioned GMRES method in a subspace. The partial solution technique is used to solve the separable part of preconditioner during the iterations in the subspace. The other part corresponding to the extended layer is solved by LU decomposition. In the problems without layer, the preconditioning is done using a fictitious domain method without domain decomposition.
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