Now showing items 1-6 of 6
Discontinuous Galerkin and Finite Difference Methods for the Acoustic Equations with Smooth Coefficients
This thesis analyzes the computational efficiency of two types of numerical methods: finite difference (FD) and discontinuous Galerkin (DG) methods, in the context of 2D acoustic equations in pressure-velocity form with ...
Bernstein-Bézier weight-adjusted discontinuous Galerkin methods for wave propagation in heterogeneous media
Efficient and accurate simulations of wave propagation are central to applications in seismology. In practice, heterogeneities arise from the presence of different types of rock in the subsurface. Additionally, simulations ...
Numerical methods and applications for reduced models of blood flow
The human cardiovascular system is a vastly complex collection of interacting components, including vessels, organ systems, valves, regulatory mechanisms, microcirculations, remodeling tissue, and electrophysiological ...
Optimal Control of Flow and Transport Equation Using Discontinuous Galerkin Methods
This thesis analyzes the accuracy of discontinuous Galerkin methods for solving optimal control problems for flow and transport equations. I derive the optimality conditions for each optimal control problem and I derive ...
Inexact Hierarchical Scale Separation for Linear Systems in Modal Discontinuous Galerkin Discretizations
This thesis proposes the inexact hierarchical scale separation (IHSS) method for the solution of linear systems in modal discontinuous Galerkin (DG) discretizations. Like p-multigrid methods, IHSS alternates between ...
A Hybrid Numerical Scheme for Immiscible Two-Phase Flow
This thesis proposes a hybrid numerical scheme for immiscible, two-phase flow in porous media, for two separate partial differential equation (PDE) formulations. Discontinuous Galerkin (DG) methods are a commonly used ...