Improving the finite element ordering for the frontal solver (Q2711234)

The context is a domain decomposition method and the linear systems in each subdomain have medium size. The optimization of the numbering of nodes in each subdomain can have different goals: NEWLINENEWLINENEWLINE1. When a direct method (Cholesky, Gauss) is chosen along with skyline structure of the matrix, one has to minimize the bandwidth of the overall system. NEWLINENEWLINENEWLINE2. A direct method with sparse data structure needs to maximize the number of zero terms after triangulation. The sequence of nodes optimal for this pattern is usually different from that obtained for the skyline (band) storage. NEWLINENEWLINENEWLINE3. When a frontal solver is used, the optimization concerning the sequence of elements is sought in the way to minimize the frontwidth. NEWLINENEWLINENEWLINEThe paper is concerned with the proposition of two improvements of greedy methods. A wave reordering method adapts the reordering strategy during the process, and the tabu search optimization technique is adapted for finite element reordering. The well-known benchmark problems from 1979 are considered as small for actual purposes, and so numerical tests are not restricted to them.