Linear-complexity direct finite element solver for irregular meshes and matrices without mesh

In this paper, we develop a linear-complexity direct finite element solver to handle problems discretized into irregular meshes, and further to problems without mesh information. The new capabilities are validated by the simulation of an industry large-scale package structure with a highly irregular mesh and examples that have only matrices without mesh information. We also report simulation results of an IBM full package, where the resulting frequency-domain finite-element matrix of over 22.8488 million unknowns is directly factorized and solved in approximately 16 hours on a single core running at 3 GHz.