Block-adaptive Cross Approximation of Discrete Integral Operators
For researchers solving linear systems from integral equations, this method improves efficiency by focusing computational resources on blocks that matter most for solution accuracy.
The paper extends adaptive cross approximation (ACA) to a block-adaptive version that adjusts accuracy per block based on solution error, enabling interleaved matrix assembly and iterative solution.
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.