Using Premodifier for Phase Retrieval Problem

Phase Retrieval Problem is very common and has a lot of applications in fields such as microscope, astronomy, crystallography, optical imaging etc.. In this problem, PSF and the pupil function are given, and the goal is to reconstruct the phase of the object. For camera which has 8 bits color depth, the maximum number of colors that can be...

Implementation direct solver to allow for better preconditioners in iterative solver

In order to decrease the time that the viscous-flow solver PARNASSOS needs to simulate ship-generated waves, direct solvers are introduced in order to make the iterative solver used in PARNASSOS converge faster

Suitability of Shallow Water Solving Methods for GPU Acceleration

In the past 15 years the field of general purpose computing on graphics processing units, or GPUs, has become well developed and the practice is becoming more mainstream. Computational demands of simulation software are continuously increasing. As such for many applications traditionally computed on the central processing unit the question...

Fast iterative methods for solving the incompressible Navier-Stokes equations

This thesis approaches the solution of the linearized finite element discretization of the Navier-Stokes operator matrix via the use of Krylov subspace methods preconditioned by SIMPLE-type pre conditioners aided by deflation. It includes an explanation of the theoretical setting of the problem as well as a collection of numerical experiments...

Fourier Analysis of Iterative Methods for the Helmholtz Problem

This thesis attempts to explain the convergence behaviour of solving Helmholtz problem by investigating its spectral properties. Fourier analysis is employ to solve the eigenvalues of the matrices that are involved in the iterative methods. The numerical experiment is conducted to verify the conclusions by Fourier analysis and also to reveal...

Efficient solution methods for the incompressible Stokes problem

Acceleration of the 2D Helmholtz model HARES

Hierarchically semi-separable representation and its applications

In this thesis, we study a important class of structured matrices: "Hierarchically Semi-Separable" matrices, for which an efficient hierarchically state based representation called Hierarchically Semi- Separable (HSS) representation can be used to represent it with a small amount of parameters that are linear in the dimension of the matrix....