Abstract
Poisson’s equation is an important partial differential equation appearing in many physical or engineering simulations. The matrix in the linear system of Poisson’s equation is very sparse, so many solvers utilize iterative methods to take the computational advantage of the sparsity. In this thesis, we present a direct parallel Poisson solver, which hybrids different types of sparse matrix format in different steps to minimize the memory usage and execution time of dissection solver based on domain decomposition method (DDM). It consists of two stages. In the first stage, the reordering techniques are used to create dense submatrices blocks. In the second stage, the submatrices are solved directly by dense matrix solvers. Experiments show that our method is 1.2 times faster than Intel MKL Pardiso solver and only takes its 60% memory usage for the Poisson’s equation of order 4096 . We also tries to generalize the method for symmetric or unsymmetric matrices. Although the result is slower than Intel MKL Pardiso, it still saves 30% memory usage.