Grouping variables in Frontal Matrices to improve Low-Rank Approximations in a Multifrontal Solver

Session 3International audienc

Algebraic acceleration and regularization of the source reconstruction method with the recompressed adaptive cross approximation

We present a compression algorithm to accelerate the solution of source reconstruction problems that are formulated with integral equations and defined on arbitrary three-dimensional surfaces. This compression technique benefits from the adaptive cross approximation (ACA) algorithm in the first step. A further error-controllable recompression is applied after the ACA. The numerical results illustrate the efficiency and accuracy of the proposed method. © 2014 IEEE

Block-adaptive Cross Approximation of Discrete Integral Operators

In this article we extend the adaptive cross approximation (ACA) method known for the efficient approximation of discretisations of integral operators to a block-adaptive version. While ACA is usually employed to assemble hierarchical matrix approximations having the same prescribed accuracy on all blocks of the partition, for the solution of linear systems it may be more efficient to adapt the accuracy of each block to the actual error of the solution as some blocks may be more important for the solution error than others. To this end, error estimation techniques known from adaptive mesh refinement are applied to automatically improve the block-wise matrix approximation. This allows to interlace the assembling of the coefficient matrix with the iterative solution