A domain renumbering algorithm for multi-domain boundary face method

In this paper, a domain number optimization algorithm for the multi-domain boundary face method is proposed. The advantage of the algorithm is to make nonzero blocks of the overall assembled matrix are as close to the main diagonal as possible. This will minimize the block fill-in effect that occurs during the solution process. Consequently, the time used for LU-decomposition and the memory requirement of the matrix will be reduced significantly. In this algorithm, one or more level structures are generated by considering the freedom degrees and the connectivity of the domains. Then we renumber the domains according to the level structure of the smallest bandwidth. Four steady-state heat conduction problems of multi-domain are solved to test the algorithm, and high efficiency is observed.