Computational complexity and memory usage for multi-frontal direct solvers in structured mesh finite elements

The multi-frontal direct solver is the state-of-the-art algorithm for the direct solution of sparse linear systems. This paper provides computational complexity and memory usage estimates for the application of the multifrontal direct solver algorithm on linear systems resulting from B-spline-based isogeometric finite elements, where the mesh is a structured grid. Specifically we provide the estimates for systems resulting from Cp−1 polynomial B-spline spaces and compare them to those obtained using C spaces.