GPU-accelerated Domain Decomposition Methods for Helmholtz Equation
Name
Ziya Mammadov
Abstract
The Helmholtz equation, used in various fields like acoustics, optics, and seismology, is a partial differential equation that describes how waves propagate in various physical systems. The Helmholtz matrix arises from the discretization of the Helmholtz problem when solving the Helmholtz equation numerically using finite difference or finite element methods. In practice, the numerical solution of the Helmholtz equation can be challenging due to the size of the discredited problem as well as the spectral properties of the matrix. The thesis explores iterative methods to solve the Helmholtz equation, speeding up the computations by using the power of GPUs. A special domain decomposition preconditioning technique, the Restricted Additive Average Schwarz method, is applied in a setup that allows using multiple subdomains to solve simultaneously in one go on a GPU. For this purpose a special implementation of the Conjugate Gradients iterative solver in PyOpenCL using complex arithmetics was developed, allowing to solve for multiple right-hand side vectors simultaneously. Performance evaluation for the overall solution of the discretized Helmholtz equation is performed experimentally to compare the efficiency of different subdomain solution techniques.
Graduation Thesis language
English
Graduation Thesis type
Master - Computer Science
Supervisor(s)
Eero Vainikko
Defence year
2024