Speaker : Christian Glusa, Sandia National Laboratories 

Time : 15:00 - 16:00 CET (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

YouTube : https://youtu.be/zJ5kwMJg2s0

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: fractional Laplacian, multigrid, hierarchical matrices

Abstract: The naive discretization of nonlocal operators leads to matrices with significant density, as compared to classical PDEs. This makes the efficient solution of nonlocal models a challenging task. In this presentation, we will discuss ongoing research into efficient hierarchical matrix assembly and geometric and algebraic multigrid preconditioners that are suitable for nonlocal models.

Biography: Christian Glusa is a staff member in the Center for Computing Research at Sandia National Laboratories. His interests include scalable linear solvers such as multigrid and domain decomposition methods, and their application to problems in electromagnetics and fractional order equations.

Christian received a PhD in applied mathematics from Brown University in 2017, and undergraduate degrees from Karlsruhe Institute of Technology (KIT) and Ecole Polytechnique in 2012

Bibliography

[1] Mark Ainsworth and Christian Glusa. “Aspects of an adaptive finite element method for the fractional Laplacian: A priori and a posteriori error estimates, efficient imple- mentation and multigrid solver”. In: Computer Methods in Applied Mechanics and Engineering (2017). issn: 0045-7825. doi: https : / / doi . org / 10 . 1016 / j . cma . 2017 . 08 . 019. url: http : / / www . sciencedirect . com / science / article / pii / S0045782517305996.

[2] Mark Ainsworth and Christian Glusa. “Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains”. In: Contemporary Computational Mathematics-A Celebration of the 80th Birthday of Ian Sloan. Springer, 2018, pp. 17–57.

[3] Olena Burkovska, Christian Glusa, and Marta D’Elia. “An optimization-based approach to parameter learning for fractional type nonlocal models”. In: Computers & Mathematics with Applications (2021). issn: 0898-1221. doi: 10.1016/j.camwa. 2021.05.005. url: https://www.sciencedirect.com/science/article/pii/S0898122121001851.

[4] Marta D’Elia and Christian Glusa. “A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems”.In: Numerical Methods for Partial Differential Equations (2021). doi: 10.1002/num.22865.

[5] Marta D’Elia, Christian Glusa, and Enrique Ot´arola. “A Priori Error Estimates for the Optimal Control of the Integral Fractional Laplacian”. In: SIAM Journal on Control and Optimization 57.4 (2019), pp. 2775–2798. doi: 10.1137/18M1219989. eprint: https://doi.org/10.1137/18M1219989. url: https://doi.org/10.1137/18M1219989.