A Comparison of Accuracy and Efficiency of Parallel Solvers for Fractional Power Diffusion Problems
In this paper, we construct and investigate parallel solvers for three dimensional problems described by fractional powers of elliptic operators. The main aim is to make a scalability analysis of parallel versions of several state of the art solvers. The originality of this work is that we also consider the accuracy of the selected numerical algorithms. For comparison of accuracy, we use solutions obtained solving the test problem by the Fourier algorithm. Such analysis enables to compare the efficiency of the proposed parallel algorithms depending on the required accuracy of solution and on a number of processes used in computations.
KeywordsFractional diffusion Finite volume method Parallel numerical algorithms MPI Scalability Multigrid
The work of authors was supported by EU under the COST programme Action IC1305, “Network for Sustainable Ultrascale Computing (NESUS)”. The third author has been partially supported by the Bulgarian National Science Fund under Grant BNSF-DN12/1.
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