Date of Award
8-2024
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
School
Mathematics and Natural Sciences
Committee Chair
James V. Lambers
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
Haiyan Tian
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Zhifu Xie
Committee Member 3 School
Mathematics and Natural Sciences
Committee Member 4
Huiqing Zhu
Committee Member 4 School
Mathematics and Natural Sciences
Abstract
Exponential integrators, such as exponential Runge-Kutta or Rosenbrock methods, are designed specifically for the time integration of stiff systems of ordinary differential equations (ODEs) and allow the use of larger time steps than other general-purpose ODE solvers. However, these methods rely on computing matrix function-vector products that are traditionally computed using a Krylov projection, such as Lanczos or Arnoldi iteration, that involves substantial computational expense at high spatial resolution. Krylov Subspace Spectral (KSS) methods' frequency-dependent approach, designed to circumvent stiffness in linear problems, computes these products with greater scalability. We propose the combination of such KSS methods with exponential integrators in order to produce superior scalability in the solution of time-dependent partial differential equations (PDEs).
ORCID ID
0009-0009-7087-1569
Copyright
2024, Chelsea Drum
Recommended Citation
Drum, Chelsea, "Scalable Solution of Time-Dependent PDEs Through Component-Wise Exponential Integrator" (2024). Dissertations. 2274.
https://aquila.usm.edu/dissertations/2274