Iterative methods for time-harmonic waves: Towards accuracy and scalability

The bottleneck in designing iterative solvers for the Helmholtz equation lies in balancing the trade-off between accuracy and scalability. Both the accuracy of the numerical solution and the number of iterations to reach convergence deteriorate in higher dimensions and increase with the wavenumber. To address these issues in this dissertation,...

Image Reconstruction for Low-Field MRI

Each year, hundreds of thousands of infants develop hydrocephalus ("water on the brain"). This is a disease that, if untreated, leads to brain damage and ultimately death. The prevalence of hydrocephalus is relatively high in children living in the Global South (in sub-Saharan countries, for example), but access to advanced imaging technology is...

Development of a Closed-loop degaussing system: Towards magnetic unobservable vessels

The focus of this thesis is to study the magnetic behavior of ferromagnetic materials, parameter estimates of the material properties of ferromagnetic materials, and to introduce a mathematical physics model that can accurately describe the temporal changes of the magnetic state of a naval vessel. The aspects mentioned are important steps in the...

Preconditioning Optimal Flow Control Problems Using Multilevel Sequentially Semiseparable Matrix Computations

Optimal flow control problems are important for applications in science and engineering. Solving such problems usually requires the solution of a large linear generalized saddle-point system. This linear system is sparse and highly indefinite. In order to solve such systems using Krylov subspace methods, efficient preconditioners are necessary...

GPU acceleration of preconditioned solvers for ill-conditioned linear systems

In this work we study the implementations of deflation and preconditioning techniques for solving ill-conditioned linear systems using iterative methods. Solving such systems can be a time-consuming process because of the jumps in the coefficients due to large difference in material properties. We have developed implementations of the iterative...