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 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.