We study the performance of a hierarchical solver for systems of linear algebraic equations arising from finite elements (FEM) discretization of fractional diffusion problems. We assume the integral definition of fractional Lapla-cian in a bounded domain introduced through the Ritz potential. The problem is non-local and the related FEM system has a dense matrix. The Structured Matrix Package (STRUMPACK) and its implementation of a Hierarchical Semi-Separable (HSS) compression is utilized. Our main aim is to evaluate the performance and accuracy of the method by analyzing the required time to solve the problem and the attained accuracy with respect to reference solutions obtained from the original MATLAB® code. We propose a scheme for reordering of the unknowns that significantly improves the execution time. The numerical tests were ran on the high performance cluster AVITOHOL at IICT-BAS.
展开▼
