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A parallel direct solver for the selfadaptive hp
 J. PARALLEL DISTRIB COMPUT
, 2010
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A Multi Level Direct Substructuring Multifrontal Parallel Solver for the hpFinite Element Method
"... We describe a new parallel direct solver for hp refined meshes, embedded into a 3D selfadaptive hp finiteelement method. The solver utilizes a substructuring method with multifrontal processing of subdomain internal nodes over each subdomain. This method of solution includes a new approach to so ..."
Abstract

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We describe a new parallel direct solver for hp refined meshes, embedded into a 3D selfadaptive hp finiteelement method. The solver utilizes a substructuring method with multifrontal processing of subdomain internal nodes over each subdomain. This method of solution includes a new approach to solve the interface problem. Specifically, the solver utilizes multifrontal processing of the top of the tree of separators associated with the subdomains on which we apply the Schur complement strategy. The relative efficiency of the solver is both analyzed theoretically and measured on a sequence of meshes generated for a 3D borehole resistivity logging problem in a deviated well. Execution time and memory usage of the solver are compared against the parallel MUMPS solver executed over the entire problem, and the MUMPSbased direct substructuring method with the sequential or parallel MUMPS solvers utilized to approach the interface problem. We show that the relative efficiency of the new solver tends to infinity as the polynomial orders of approximation utilized on the hp meshes approaches infinity. This result is achieved under the assumption that the domain decomposition is performed on the level of finiteelement faces. Such a behavior comes as a consequence of the fact that the computational cost in the interior of highorder elements is several orders of magnitude higher then the computational cost over highorder elements faces. Based on the performed experiments, it follows that our new solver is up to five times faster than the MUMPS parallel solver when implemented on on 16 processors and if executed on computational meshes with high polynomial orders of approximation. Key words: Parallel direct solvers, Finite Element Method, hp adaptivity, 3D resistivity logging simulations.