A parallel alternating direction implicit preconditioning method
The fast convergence of the ADI method predestines it to be used as a preconditioner \(M_ k^{-1}\) if a certain number of k iterations are applied to determine an approximate solution of a system of linear equations with the matrix \(A=H+V.\) An algorithm is described to compute the preconditioner \(M_ k^{-1}\) in order to achieve the maximum degree of parallelism. If H and V can be represented in the tensor product form, it is possible to recast the given system of equations into one where the commutativity holds. For this case a highly efficient algorithm, equivalent to the tensor product generalized ADI method, is established. If proper chosen, distinct acceleration parameters are used, it is shown that the sequential computations can completely be avoided, and the desired high parallelism is achieved. Moreover, it is shown that the resulting preconditioner \(M_ k\) is positive definite and thus is applicable in connection with conjugate gradient methods.
parallel alternating direction implicit preconditioning method
scientific article; zbMATH DE number 4215262
scientific article