Load and Memory Balanced Mesh Partitioning for a Parallel Envelope Method

We use a parallel direct solver based on the Schur complement method for solving large sparse linear systems arising from the finite element method. A domain decomposition of a problem is performed using a graph partitioning. It results in sparse submatrices with balanced sizes. An envelope method is used to factorize these submatrices. However, the memory requirements to store them and the computational cost to factorize them depends heavily on their structure. We propose a technique that modifies the multilevel graph partitioning schema to balance real computational load or memory requirements of the solver.