Computational Complexity Analysis for Multifrontal Method With Limited-Depth of Assembly Tree

The computational complexity and memory requirement of multifrontal method is analyzed for solving finite element system of equations defined on 2- and 3-D regular meshes with respect to the number of fronts and the depth of assembly tree. Accurate estimation of operation counts obtained along with the relevant parameters for both local and multilevel global condensation phases is more suitable to practical applications than previous estimation. It, moreover, enables us to illustrate how the number of fronts, the depth of assembly tree, and the performance of the method are related, and how the multilevel multifrontal scheme reduces the total numerical operations intrinsically. The operation count, memory usage, and execution time of the method are experimentally measured by running a sequence of 2- and 3-D examples, the obtained results consistently follow the theoretical estimations.