수 학 과

[수학과 강연회]

Title : Multigrid Methods for Vector Field Problems 

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Abstract : We design and analyze V‐cycle multigrid methods for problems posed in H(div) and H(curl). Due to the fact that traditional smoothers do not work well for the vector field problems, a special approach for smoothers in the multigrid methods is essential. We introduce a new smoothing technique which involves non-overlapping domain decomposition preconditioners based on substructuring. We prove uniform convergence of the V‐cycle methods on bounded convex hexahedral domains. Numerical experiments that support the theory are also presented.