Now showing items 1-5 of 5
Accelerated PDE Constrained Optimization using Direct Solvers
In this thesis, I propose a method to reduce the cost of computing solutions to optimization problems governed by partial differential equations (PDEs). Standard second order methods such as Newton require the solution of ...
A fast direct solver for boundary value problems with locally-perturbed geometries
Many problems in science and engineering can be formulated as integral equations with elliptic kernels. In particular, in optimal control and design problems, the domain geometry evolves and results in a sequence of ...
GPU-accelerated discontinuous Galerkin methods on hybrid meshes: applications in seismic imaging
Seismic imaging is a geophysical technique assisting in the understanding of subsurface structure on a regional and global scale. With the development of computer technology, computationally intensive seismic algorithms ...
Hermite Methods for the Simulation of Wave Propagation
Simulations of wave propagation play a crucial role in science and engineering. In applications of geophysics, they are the engine of many seismic imaging algorithms. For electrical engineers, they can be a useful tool for ...
Robust and efficient numerical algorithms for the discrete prolate spheroidal wave functions
This thesis presents novel algorithms for the numerical evaluation of the discrete prolate spheroidal wave functions (DPSWFs) and their associated integral operator eigenvalues. The DPSWFs and associated eigenvalues arise ...