Parallel multi-frontal solver for p adaptive finite element modeling of multi-physics computational problems

The paper presents a parallel direct solver for multi-physics problems. The solver is dedicated for solving problems resulting from adaptive finite element method computations. The concept of finite element is actually replaced by the concept of the node. The computational mesh consists of several nodes, related to element vertices, edges, faces and interiors. The ordering of unknowns in the solver is performed on the level of nodes. The concept of the node can be efficiently utilized in order to recognize unknowns that can be eliminated at a given node of the elimination tree. The solver is tested on the exemplary three-dimensional multi-physics problem involving the computations of the linear acoustics coupled with linear elasticity. The three-dimensional tetrahedral mesh generation and the solver algorithm are modeled by using graph grammar formalism. The execution time and the memory usage of the solver are compared with the MUMPS solver.