Date of Award
Summer 8-2015
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
Committee Chair
James V. Lambers
Committee Chair Department
Mathematics
Committee Member 2
Ching-Shyang Chen
Committee Member 2 Department
Mathematics
Committee Member 3
Haiyan Tian
Committee Member 3 Department
Mathematics
Committee Member 4
Huiqing Zhu
Committee Member 4 Department
Mathematics
Abstract
Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff systems of ODE, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this dissertation, it is proposed to modify EPI methods by using Krylov subspace spectral (KSS) methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. This improvement allowed the benefits of KSS methods observed in linear PDE to be extended to the nonlinear case. Numerical experiments demonstrate that this modification causes the number of Krylov projection steps to become dramatically reduced, thus improving efficiency and scalability.
Masters thesis: http://aquila.usm.edu/masters_theses/208/
Copyright
2015, Alexandru Cibotarica
Recommended Citation
Cibotarica, Alexandru, "Solution of Nonlinear Time-Dependent PDE Through Componentwise Approximation of Matrix Functions" (2015). Dissertations. 103.
https://aquila.usm.edu/dissertations/103