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Document Type
Thesis - University Access Only
Award Date
2015
Degree Name
Master of Science (MS)
Department / School
Mathematics and Statistics
First Advisor
Jung-Han Kimu
Abstract
For certain formulations of partial differential equations, proper time-parallel pre conditioners can be successfully applied in space-time finite element simulations. Such an approach may enable the extraction of more parallelism to better utilize high performance computing resources. In this thesis, we have implemented a fully implicit numerical approach based on space-time finite element methods for the Klein-Gordon equation in the 1(space)+1(time) dimension. The proposed numerical method is applied to generate successful simulation results of spin-0 particle propagation in a charged scalar field. The time additive Schwarz method is vital to make successful simulations with KSP (Krylov Subspace Methods) solvers. Also, a fully implicit numerical approach based on the space-time finite element method is implemented for the semilinear wave equation in 1(space) + 1(time) dimensions to explore critical collapse and search for self-similar solutions. Previous work studied this behavior by exploring the threshold of singularity formation using time marching finite difference techniques while this work introduces an adaptive time parallel numerical method to the problem. The semilinear wave equation with a p = 7 term is examined in spherical symmetry. The impact of mesh refinement and the time additive Schwarz preconditioner in conjunction with Krylov Subspace Methods are examined. The time parallelizable algorithm is implemented through PETSc(Portable, Extensible, Toolkit for Scientific Computation, developed by Argonne National Laboratory).
Library of Congress Subject Headings
Wave equation
Klein-Gordon equation
Differential equations, Partial
Decomposition (Mathematics)
Description
Includes bibliographical references (pages 82-85)
Format
application/pdf
Number of Pages
97
Publisher
South Dakota State University
Recommended Citation
Lim, Hyun, "A Study of Time Decomposition Method for the Semilinear Wave Equations" (2015). Electronic Theses and Dissertations. 1811.
https://openprairie.sdstate.edu/etd/1811
Rights Statement
