Layer potential evaluations on distributed memory machines

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

Gao, Hao ; Kloeckner ; Andreas

关键词: Layer Potentials;    Distributed Memory Parallelism;    Integral Equations;    Singular Integrals;    Fast Multipole Method;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/108032/GAO-THESIS-2020.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.