Invitation to the Seminar:

Solving Helmholtz at Scale: A DPG Multigrid Solver for High-Frequency Wave Propagation

Jacob Badger

Aerospace Engineering and Engineering Mechanics

Oden Institute for Computational Engineering & Sciences

University of Texas at Austin

jcbadger@utexas.edu

https://oden.utexas.edu/people/directory/Jacob-Badger

Abstract:

Wave propagation problems arise in a number of contexts including natural resource exploration, medical imaging, and nuclear fusion research, to name a few. However, developing scalable numerical algorithms for solving time-harmonic wave propagation problems is a notoriously difficult problem. The primary difficulty is this: time-harmonic wave propagation operators are indefinite, thus classical discretization techniques (e.g., Galerkin finite elements, finite difference, etc.) yield indefinite discrete systems that preclude use of many scalable solution algorithms. The discontinuous Petrov-Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan can be used to circumvent this difficulty; as a minimum residual method DPG produces Hermitian positive-definite discrete systems, even for indefinite operators.

In this seminar I will detail the design and implementation of a scalable DPG multigrid (DPG-MG) solver for high-frequency Helmholtz problems. The current implementation of the DPG-MG solver enables solution of challenging problems on general geometries and heterogeneous media with over 10 billion degrees of freedom in minutes. Two applications considered here include seismic modeling of a subduction zone (inspired by the Nankai Trough) and simulation of electromagnetic fields in a tokamak device. Finally, I will discuss ongoing work targeting high-frequency wave propagation problems with up to 1 trillion degrees of freedom on emerging exascale architectures.