Realizing Network Parallel Of A Two-grid Discretization Scheme For Eigenvalue Problems

The finite element method of eigenvalue problems is useful widely in aspects of science study, engineering design, structural mechanics and quantum mechanics. With the advance of science and technology, eigenvalue problems of enormous size involved in science study and engineering computation , which can't be realized under a single computer system with the serial algorithm . The problem is solved after the advent of the parallel computer, it is limited the scope of application because of expensive and the dependenee of program on hardware. The network parallel computing base on PVM could be used to solve the problem which can't be solved with PC , in this way, the finite method of eigenvalue problems are solved perfectly.As the first attempt, after analyzing the parallelization in realizing process of two-grid discretization scheme for eigenvalue problems, in which the matrix and vector are stored through row-block , and line assign is adopted for the generation of rigidity matrix, mass matrix and load vector. We could realize the solution of the eigenvalue with corresponding eigenvector because of the computing quality is less on the coarse grid. Firstly, we decompose rigidity matrix with LU method and solve the inverse matrix. Secondly, we use inverse matrix and mass matrix of coarse grid multiply each other. Finally, minimum eigenvalue with corresponding eigenvector are solved with inverse power method. On the fine grid computation quantity and store space are both large,so we use parallel to realize completion of rigidity matrix, mass matrix and load vector.A two-grid discretization scheme for eigenvalue problems need to solve finite element system of equations on the fine grid, the coefficient matrix of the system of equations is a large sparse matrix, aim at conjugate gradient method of adopting pre-process of system of equations is valid. This text makes use of the m-Step Jacobi PCG method to carry on reorganize, which gets parallel algorithm of m—Step Jacobi PCG based on PVM, parallel solution of finite element system of equations is realized by the algorithm, the building of network parallel numerical computing platforms based on VC6.0, according to program computation of exact square district and L type district, all the algorithms are implemented on LAN made of 1-8 personal computers, and we get the right answer, after pre-process itertion convergence speed is quick, and parallel speedup and computing time are both ideal.