A parallel sparse direct finite element solver for desktop computers

The parallel finite element solver, which is based on block L·S·L factoring, where S is a sign diagonal, is presented. The sparse symmetric positive definite and indefinite matrices are considered. Unlike the methods presented in the libraries of high-performance procedures, including PARDISO solver, the proposed approach uses the disk storage, if the dimension of the problem exceeds the capacity of random access memory RAM. Two out of core modes OOC and OOC1 are developed. The OOC mode produces the minimal I/O operations, ensures the stable speed-up when the number of processors increases, but requires respectively larger amount of RAM. The OOC1 mode demands the smaller amount of RAM, but the number of I/O operations is significantly greater than in OOC mode and speed up is much poorer. The presented method is essentially faster than multi-frontal solver, especially on multiple processors, because it is not using redundant data transfer from one memory buffer to another.