Test And Study Direct Algorithm For Solving Matrix Eguations

In computational electromagnetics, the moment method is used to producelarge-scale fast solving of dense matrix equation is the key to the problem of momentmethod for calculation, the LU decomposition is an effective way to solve the linearsystem of equations directly. In this thesis, we tested a out-of-core parallel LUdecomposition procedure, the program based on Linux system platform, extensive useof MPI, lapack libraries and scalapack libraries in the library function, and highcomputational efficiency. The influencing factors of out-of-core parallel LUdecomposition has four, respectively is the size of the matrix, the matrix blocking,processes, and load balancing and the distribution of the grid. By testing found that thedistributed block size of the matrix in the program it is advisable to take90or so; Try toget as close to the square grid process; As the size of the matrix increasing thecomputational time is longer with the speed of O(N3). In addition, this thesis hascompared the in-core parallel LU decomposition, out-of-cor parallel LU decompositionand parallel in-core CGNR within three methods of calculation efficiency. Foundlarge-scale dense matrix equation when the out-of-core parallel LU algorithm has manyadvantages compared with iterative algorithm. First of all, the speed of the iterativealgorithm to transcend LU decomposition method is the premise of condition number ofmatrix equation is very low, but in most cases the condition number of matrix equationis very high; Second, the rate of out-of-core LU decomposition is slower than in-coreLU decomposition, so large-scale matrix equation using disk space instead of memoryspace does not lead to the rapid increase of computing time.