Self-adaptive hphp finite element method with iterative mesh truncation technique accelerated with Adaptive Cross Approximation

To alleviate the computational bottleneck of a powerful two-dimensional self-adaptive hphp finite element method (FEM) for the analysis of open region problems, which uses an iterative computation of the Integral Equation over a fictitious boundary for truncating the FEM domain, we propose the use of Adaptive Cross Approximation (ACA) to effectively accelerate the computation of the Integral Equation. It will be shown that in this context ACA exhibits a robust behavior, yields good accuracy and compression levels up to 90%, and provides a good fair control of the approximants, which is a crucial advantage for hphp adaptivity. Theoretical and empirical results of performance (computational complexity) comparing the accelerated and non-accelerated versions of the method are presented. Several canonical scenarios are addressed to resemble the behavior of ACA with hh, pp and hphp adaptive strategies, and higher order methods in general.