Performance Analysis of a Multicore Implementation for Solving a Two-Dimensional Inverse Anomalous Diffusion Problem

In this work we deal with the solution of a two-dimensional inverse time fractional diffusion equation, involving a Caputo fractional derivative in his expression. Since we deal with a huge practical problem with a large domain, by starting from an accurate meshless localized collocation method using RBFs, here we propose a fast algorithm, implemented in a multicore architecture, which exploits suitable parallel computational kernels. More in detail, we firstly developed, a C code based on the numerical library LAPACK to perform the basic linear algebra operations and to solve linear systems, then, due to the high computational complexity and the large size of the problem, we propose a parallel algorithm specifically designed for multicore architectures and based on the Pthreads library. Performance analysis will show accuracy and reliability of our parallel implementation.