Multi-core Directly And Parallel Iterative Method And Its Application In Radiation Hydrodynamics

The rapid development and application of massively parallel computers have make it possible for the high resolution numerical simulation of complex physical systems. In these numerical simulations, the solution of sparse linear algebraic equations arising from the implicit discretization of system tends to occupy a high percentage of the total simulation time, and some reach up to80%. In order to effectively shorten the simulation time, the corresponding application programs must have high scalability. Therefore, developing high scalability linear solver based on massively parallel machine is important for achieving high performance, and has important theory significance and application value.This dissertation mainly covers the following five aspects:First, design the parallel GPBiCR (in brief, PGPBiCR) method by reducing the number of global communication of the original (serial) GPBiCR method. The PGP-BiCR method and GPBiCR method have the same convergence and numerical stability. Parallel performance analysis shows that PGPBiCR method has better parallelism and scalability than the original GPBiCR method. In theory, we prove that PGPBiCR method has better parallel communication performance than GPBiCR method. and the parallel communication performance can be improved by a factor of about3. Nu-merical experiments obtain the results which coincide with the theoretical analysis.Second, desing the parallel BiCGSTAB2(PBiCGSTAB2, in brief) method by re-constructing the original (serial) BiCGSTAB2method. The PBiCGSTAB2method and BiCGSTAB2method have the same numerical stability and convergence. In order to keep the reliability of performance analysis, one even step and one odd step are looked as one large iterative step. Parallel performance analysis shows that PBiCGSTAB2method has better parallelism and scalability than BiCGSTAB2method. We show that the percent of the parallel communication performance improvement approach66.7%for different problem size. At the same time, numerical experiments also show that PBiCGSTAB2method and BiCGSTAB2method have the same convergence and numerical stability.Third, based on the current mainstream multi-core architecture of parallel com- puter and the fast and robust structured multifrontal factorization (in brief, RSMF) method, we propose a multi-core parallel RSMF (in brief, MRSMF) method. MRSMF method parallelizes the nested dissection ordering, symbolic decomposition and numer-ical decomposition of RSMF method, which aim is to implement these operations on the multi-core parallel machine. The multi-core parallelization of symbolic decompo-sition and numerical decomposition are based on binary elimination tree. Numerical experiments show that the MRSMF method is effective.Fourth, based on the two dimensional three temperature (2D3T) radiation diffusion equations and its discrete system, using block diagonal structure of three temperature matrix, the reorderong and symbolic decomposition parts of RSMF method are re-placed with corresponding block operation in order to improve the efficiency. At the same time, based on good reorder and block matrix technique, the time efficiency of numerical decomposition is also improved. We call this block form method as block RSMF (in brief, BRSMF) method. Numerical experiments on three temperature matri-ces obtained through the five points discrete stencil verify BRSMF method’s stability and efficiency, and show that the improvement becomes more and more remarkable with the increase of problem size.Fifths, based on the proposed MRSMF method and BRSMF method, we further gain the multi-core parallel block RSMF (MBRSMF,in brief) method. The MRSMF method fully combines the multi-core parallel features and block operation characteris-tics. Numerical experiments based on the five points discrete stencil of2D3T radiation diffusion equations show that the MB RSMF method is more effective than the MRSMF and BRSMF methods.Finally, we use some practical three temperature system models to test the PGP-BiCR method, MRSMF method, BRSMF method and MBRSMF method. The results further verify the efficiency of the proposed methods.