Elisabeth Linnér
Division of Scientific Computing
Department of Information Technology
Uppsala University
This talk describes a method for constructing sparse approximate inverses (SPAI) of (blocks of) matrices as arising in the numerical solution of partial differential equations, discretized using the finite element method. The matrices have a two-by-two block form, which in this case is obtained via refinement of the discretization mesh and classifying the nodes as "coarse" and "fine". The SPAI matrix is assembled from small matrices, obtained by manipulation of the local stiffness matrices; a procedure that is fully parallelizable. The framework can be used recursively on a sequence of meshes and is suitable for constructing of algebraic multilevel preconditioners of block-multiplicative type. As an illustration, numerical results of using this method to solve the Laplace problem will be presented, both serially and in parallel.