Efficient spectral methods and stable time discretizations for a class of parabolic type PDES
Abstract
This thesis focuses on numerical methods for a class of nonlinear parabolic type PDEs in materials science, fluid dynamics, and finance. My contribution in the spatial discretization consists of two parts. First, an efficient spectral-Galerkin methods for systems of coupled second-order equations is proposed. Second, a GPU parallelized spectral collocation method for 2-D elliptic equations is designed and implemented. For the time discretization, I propose energy stable schemes for anisotropic Cahn-Hilliard systems in crystalline growth, a linear and energy stable scheme for the Navier-Stokes-Cahn-Hilliard system in the moving contact line problem, and second order stable schemes for the Merton jump diffusion model in European option pricing. I also prove the stability and convergence for the first-order rotational velocity correction projection method for the incompressible Navier-Stokes equation.
Degree
Ph.D.
Advisors
Shen, Purdue University.
Subject Area
Applied Mathematics|Mathematics
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