| Summary: | 碩士 === 國立清華大學 === 資訊工程學系 === 104 === 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.
|
|---|
