Fast parallel textured algorithms for parabolic equations

Fast linear equation solvers based on recursive multiplicative, additive textured decompositions and corresponding recursive block Jacobi methods are introduced. The basic difference between this approach and classical iterative algorithms is that different approximations of the system matrix are used in the classical approach. It is shown that, with proper composition of approximation matrices, the spectral radius of error dynamic is greatly reduced, and with proper decomposition size the spectral radius will approach a constant strictly less than one, even if the dimension of the problem tends to infinity. This enables the authors to devise a parallel algorithm with better time complexity. The associated recursive block Jacobi methods are developed and investigated, and their performance is compared with that of the textured decomposition methods. These algorithms are applied to dynamic simulation of parabolic equations.<>