Analysis of multiple inclusion potential problems by the Adaptive Cross Approximation method

Over recent years the rapid evolution of the computational power has motivated the development of new numerical techniques to account for engineering solutions. The Boundary Element Method (BEM) has shown to be a powerful numeric tool for the analysis and solution of many physical and engineering problems. However, BEM fully populated and non-symmetric system matrices implies in higher memory requirements and solution times. This work analyze the application of hierarchical matrices and low rank approximations, applying the Adaptive Cross Approximation - ACA, to multiple inclusion potential problems. The use of hierarchical format is aimed at reducing the storage requirement and the computational complexity arising in the BEM. First, the use of hierarchical matrices and low rank approximation on multidomain potential problems is depicted. Finally, a numerical example is performed to show the applicability of using ACA in largescale multidomain problems. Moreover, the application of ACA to multidomain problems showed to be an important option in future multiscale problem analyses.