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Preconditioning Discrete Biharmonic Operators by Discrete Laplacians

Tuesday, January 24, 3:30PM – 5PM
POB 6.304

Jinchao Xu Dept. of Math., Penn State

For biharmonic equations (on concave domains), some "natural" mixed finite element methods may be non-optimal or simply divergent. But this type of elements, as demonstrated in this talk based on a joint work with Shuo Zhang, can be used for constructing (nearly) optimal preconditioner for both conforming (such as Agyris) and nonconforming (such as Morley) finite elements for biharmonic equations discretized on unstructured grids. The resulting preconditioner reduces the solution of a discrete biharmonic equation to the solution of several discrete Laplacian equations together with some local relaxation methods (such as Gauss-Seidel).

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