Memory Saving Direct Method for the Solution of Large Linear Equations in Structure Analysis.
Yuji Aoyama, Genki YAGAWA, Koichi Hirama · TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C · 1998
Linear simultaneous equations to be solved in structure analyses are becoming larger, thus require larger amount of memory in the solution accordingly. In this paper, we propose a memory saving strategy for the solution of linear equations by the direct method; LU factorization combined with forward and backward substitutions. This strategy is effective if the matrix is symmetric, banded and sparse. The strategy was applied to the solution of one million linear equations with a matrix half bandwidth of 3372 and the memory size was improved from 27 to 2.3 Gbytes. The memory saving direct method was also parallelysed. The computation time for the above solution was about four hours using 32 processors of Hitachi SR 2201.