Investigation of general-purpose computing on graphics processing units and its application to the finite element analysis of electromagnetic problems

In this dissertation, the hardware and API architectures of GPUs are investigated, and the corresponding acceleration techniques are applied on the traditional frequency domain finite element method (FEM), the element-level time-domain methods, and the nonlinear discontinuous Galerkin method. First, the assembly and the solution phases of the FEM are parallelized and mapped onto the granular GPU processors. Efficient parallelization strategies for the finite element matrix assembly on a single GPU and on multiple GPUs are proposed. The parallelization strategies for the finite element matrix solution, in conjunction with parallelizable preconditioners are investigated to reduce the total solution time. Second, the element-level dual-field domain decomposition (DFDD-ELD) method is parallelized on GPU. The element-level algorithms treat each finite element as a subdomain, where the elements march the fields in time by exchanging fields and fluxes on the element boundary interfaces with the neighboring elements. The proposed parallelization framework is readily applicable to similar element-level algorithms, where the application to the discontinuous Galerkin time-domain (DGTD) methods show good acceleration results. Third, the element-level parallelization framework is further adapted to the acceleration of nonlinear DGTD algorithm, which has potential applications in the field of optics. The proposed nonlinear DGTD algorithm describes the third-order instantaneous nonlinear effect between the electromagnetic field and the medium permittivity. The Newton-Raphson method is incorporated to reduce the number of nonlinear iterations through its quadratic convergence. Various nonlinear examples are presented to show the different Kerr effects observed through the third-order nonlinearity. With the acceleration using MPI+GPU under large cluster environments, the solution times for the various linear and nonlinear examples are significantly reduced.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Meng, Huan-Ting

Contributors dc:contributor

• Jin, Jianming
• Schutt-Ainé, José E.
• Chen, Deming
• Kloeckner, Andreas

• Finite-Element Method (FEM)
• Graphics Processing Unit (GPU)
• General-purpose computing on graphics processing units (GPGPU)
• Massive Parallelization
• Compute Unified Device Architecture (CUDA)
• Discontinuous Galerkin Time-Domain Method
• discontinuous Galerkin time-domain (DGTD)
• Element-Level Decomposition
• Dual-Field Domain Decomposition
• dual-field domain decomposition- element level decomposition (DFDD-ELD)
• Kerr Nonlinearity
• Third-Order Nonlinearity
• Nonlinear Optics
• Newton-Raphson Method

Statement dc:rights

• Copyright 2015 Huan-Ting Meng

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/87997

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/87997