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

TL;DR

This paper analyzes the computational complexity and memory requirements of multi-frontal direct solvers applied to structured mesh finite element systems, focusing on B-spline-based isogeometric analysis.

Contribution

It provides detailed estimates of complexity and memory usage for multi-frontal solvers on B-spline finite element systems, comparing different continuity levels.

Findings

Complexity estimates for B-spline systems with various continuity levels.

Memory usage comparisons between $C^{p-1}$ and $C^0$ B-spline spaces.

Insights into solver efficiency for structured mesh finite element problems.

Abstract

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 multi-frontal 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 $C^{p-1}$ polynomial B-spline spaces and compare them to those obtained using $C^0$ spaces.