Out-of-core multi-frontal solver for multi-physics hp adaptive problems
Maciej R. Paszyński, David Pardo, Anna Paszyńska, Leszek Demkowicz · Procedia Computer Science · 2011
In this paper we present the out-of-core solver algorithm for three dimensional (3D) multi-physics problems solved by the Finite Element Method (FEM). The solver is able to solve problems where 3D meshes contain finite elements of different kind (tetrahedral, prism and pyramid elements) with the number of equations and polynomial orders of approximation varying locally on finite element edges, faces, and interiors. The solver works at the level of nodes, representing blocks of the global matrix associated with different vertices, edges, faces, and interiors of different elements. The solver minimizes the memory usage by dumping out all local systems from all nodes of the entire elimination tree during the elimination phase. The systems are going to be reutilized later during the backward substitution stage. The solver is tested on a challenging computational problem: acoustics of the human head. The memory usage of the solver is compared against that of the MUMPS solver.