2019/05/06 by M. Bauer, Bauer, M., M. Bebendorf +1
Computer Science · Engineering · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1905.01918
openalex publication_date 2019/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.