In a sparse linear system derived from two-dimensional three-temperature energy equations, the diagonal dominan varies greatly from row to row and so is the magnitude of the elements. We provide a new scaling method to improve the diagonal dominance. As ILUT is used to the derived linear system, it reserves the number of elements in each row and several relatively large elements related to the photon are dropped due to the large difference among elements. To improve the equality of the ILUT, we provide a new method named multiple row ILUT (MRILUT), in which multiple rows are computed before dropping. The provided methods are embedded into a preconditioned Krylov subspace method to solve the actual two-dimensional energy equations with three temperatures. The number of iteration at each time step and the total computation time are both greatly reduced.

A preconditioner of incomplete factorization types and a modified version are provided for the 3-D problems with the help of local block decomposition of a block tridiagonal matrix recursively. Then the existence of both preconditioners is focused on. For the seven point matrix discreted from the 3-D Laplace operator with the seven point difference technique, the actual condition numbers are computed and the results show that for the non-modified preconditioner, the condition number is proportional to N^2／3, where N is the order of the matrix. For the modified version, the condition number is proportional to the cube root of the order of the matrix thereafter. Finally, highly efficient implementation is considered and several effective experiments are done for these preconditioners on personal computers with main frequency of 550MHz and memory of 256M.

With the development of massively parallel processing, it is necessary that the parallel applications would be capable of good scalability. It is described how to use the near optimal scalability analysis method with the two dimensional electromagnetic plasma parallel program using particle in cell method as an example. Having known the performance of small parallel systems, one can obtain the information about how many processors which the larger systems are running on can obtain the more"reasonable" performance when using the near optimal scalability analysis. A suit of practical scalability evaluation method is also proposed to find the reason why the practical scalability is bad, and help to optimize the application programs.

A parallel solver for circulant block tridiagonal systems on distributed memory multicomputers is developed.The algorithm is based on matrix block operations.The implementation of this algorithm invokes BLAS3 subroutines.The complexity of the algorithm is analyzed.A sufficient condition guaranteeing the processes not to break down is given.The numerical experiments on a distributed memory multicomputer YH3E show that this algorithm has a high parallel efficiency.

The LSQ coupled states of l-shell are constructed by (U,D)L-LSQ scheme, where U(D) is the total orbital angular momentum of spin up(down) electrons, the LS and Q are the total orbital angular momentum, spin and quasispin respectively, the (U,D) L-LSQ is unitary transformation. The scalar operators which commute with the total orbital angular momentum, spin and quasispin operators, are constructed from 4 creation-annihilation operators, and the LSQ coupled states are further or complete classified by its eigenvalues. The complete classifications of coupled states for f- and g-shell are obtained, the primary results of complete classifications of coupled states for g-shell are listed.