Layer potential evaluations on distributed memory machines

One of the main challenges of using integral equation methods (IEM) for solving partial differential equations is evaluating layer potentials with singular kernels. Quadrature by Expansion (QBX) is a quadrature method to evaluate such layer potentials accurately for targets near or on the source boundary, by forming expansions in the high-accuracy region away from the boundary, and evaluating the targets using the expansions. Recently, a new algorithm, called 'GIGAQBX', has combined QBX with the Fast Multipole Method to achieve linear complexity in terms of the number of degrees of freedom. Despite this advancement, QBX is still computationally expensive. To enable IEM on large-scale problems, this thesis investigates evaluating layer potentials on distributed-memory machines. The distributed algorithm introduced in this thesis is based on GIGAQBX and shows GIGAQBX contains plenty of parallelism. We evaluate our algorithm on the Comet supercomputer at the San Diego Supercomputer Center and show that it exhibits good strong scaling up to 1536 cores.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Gao, Hao

Contributors dc:contributor

• Kloeckner, Andreas

• Layer Potentials
• Distributed Memory Parallelism
• Integral Equations
• Singular Integrals
• Fast Multipole Method

Statement dc:rights

• Copyright 2020 Hao Gao

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/108032

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/108032