COMPARISON OF LINEAR AND QUADRATIC DISCONTINUOUS SPATIAL FINITE ELEMENT METHODS FOR PARALLEL SN TRANSPORT ON TRIANGLES

摘要

We compare the performance of linear and quadratic discontinuous finite elements methods spatial discretizations (LDFEM and QDFEM) of the SN transport equation on triangles in two-dimensional, axisymmetric coordinate system (r-z). Numerical results reveal that both unlumped and fully lumped LDFEM are second order accurate as expected. The QDFEM exhibits third order accuracy. Because the QDFEM is third order accurate, it obtains same level of error reduction as LDFEM with a smaller mesh, i.e., coarser mesh cells. Therefore, QDFEM requires less memory and solves the problem faster than LDFEM. Numerical results show that, for optically thick problems, parallel block-Jacobi algorithm reduces CPU times when compared to full parallel sweeps for both LDFEM and QDFEM.