# On the Impact of Reordering in a Hierarchical Semi-Separable Compression Solver for Fractional Diffusion Problems

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## Abstract

The performance of a hierarchical solver for systems of linear algebraic equations arising from finite elements (FEM) discretization of Fractional diffusion problems is the subject of this study. We consider the integral definition of Fractional Laplacian in a bounded domain introduced through the Ritz potential. The problem is non-local and the related FEM system has a dense matrix. We utilize the Structured Matrix Package (STRUMPACK) and its implementation of a Hierarchical Semi-Separable compression in order to solve the system of linear equations. Our main aim is to improve the performance and accuracy of the method by proposing and analyzing 2 schemes for reordering of the unknowns. The numerical tests are run on the high performance cluster AVITOHOL at IICT–BAS.

## Keywords

Fractional laplacian STRUMPACK Hierarchical Semi-Separable compression Solving dense systems of linear algebraic equations## Notes

### Acknowledgements

We acknowledge the provided access to the e-infrastructure of the Centre for Advanced Computing and Data Processing, with the financial support by the Grant No BG05M2OP001-1.001-0003, financed by the Science and Education for Smart Growth Operational Program (2014–2020) and co-financed by the European Union through the European structural and Investment funds.

This paper is partially supported by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICTinSES)”, contract No DO1–205/23.11.2018, financed by the Ministry of Education and Science in Bulgaria.

The partial support trough the Bulgarian NSF Grant DN 12/1 is highly acknowledged.

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