In this contribution, the numerical solution of the spectral fractional elliptic equation with power α ∈ (1, 2) is studied.After discretization, the problem is reduced to solving a system of linear algebraic equations.We apply the Best Uniform Rational Approximation (BURA) method and focus on the numerical aspects, related to its implementation.An extensive experimental study is conducted to evaluate the accuracy of the proposed approach.The numerical results confirm the theoretical analysis and demonstrate the effectiveness of using the BURA method for the fractional super-diffusion problems.

It was shown that block-circulant preconditioners, applied to a conjugate gradient method, used to solve structured sparse linear systems, arising from 2D or 3D elliptic problems, have very good numerical properties and a potential for good parallel efficiency.In this contribution, hybrid parallelization based on MPI and OpenMP standards is experimentally investigated.Specifically, the aim of this work is to analyze parallel performance of the implemented algorithms on a supercomputer consisting of Intel Xeon processors and Intel Xeon Phi coprocessors.While obtained results confirm the positive outlook of the proposed approach, important open issues are also identified.

Summary In this article, we present an experimental performance study of a parallel implementation of two Poissonian image restoration algorithms. Hybrid parallelization, based on MPI and OpenMP standards, is investigated. The implementation is tested for high‐resolution radiographic images, on a supercomputer based on Intel Xeon processors, combined with Intel Xeon Phi coprocessors. The experimental results show an essential improvement in the execution times, when running experiments for a variety of problem sizes, and number of threads.

Currently, we are developing an agent-team based infrastructure for resource brokering and management in Grids. In this note we consider how team is supervised and how mirroring can be applied to improve chances of its long-term persistence.