Towards Robust Numerical Solvers for Nuclear Fusion Simulations Using JOREK

One of the most well-established codes for modeling non-linear Magnetohydrodynamics (MHD) for tokamak reactors is JOREK, which solves these equations with a Bézier surface based finite element method. This code produces a highly sparse but also very large linear system. The main solver behind the code uses the Generalized Minimum Residual Method...

Ultrasound imaging through aberrating layers

Whereas aberrating layers are typically viewed as an impediment to medical ultrasound imaging, they can, surprisingly, also be used to our benefit. As long as we can model the effect of an aberrating layer, we can utilize ‘model-based imaging’, the imaging technique explored throughout this thesis, to reconstruct ultrasound images where...

Practical Implementation of a Quantum Algorithm for the Solution of Systems of Linear Systems of Equations

With the rapid development of Quantum Computers (QC) and QC Simulators, there will be an increased demand for functioning Quantum Algorithms in the near future. Some of the most ubiquitously useful algorithms are solvers for linear systems of equations. Since the conception of the Quantum Linear Solver Algorithm (QLSA) by Harrow, Hassidim and...

Fast grasping of unknown objects using principal component analysis

Fast grasping of unknown objects has crucial impact on the efficiency of robot manipulation especially subjected to unfamiliar environments. In order to accelerate grasping speed of unknown objects, principal component analysis is utilized to direct the grasping process. In particular, a single-view partial point cloud is constructed and...

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...

Robust Algorithms for Discrete Tomography

Tomography methods concentrate on reconstructing objects from multiple projections that are obtained by sending, for example, X-rays through the object. Applications of these methods are, among others, radiology (CT-, MRI- and PET scans), geophysics and material science. The tomographic problems can be formulated as a system of linear equations....

Interpreting IDR(s) as a deflation method

In this paper the IDR(s) method is interpreted in the context of deflation methods. It is shown that IDR(s) can be seen as a Richardson iteration preconditioned by a variable deflation–type preconditioner. The main result of this paper is the IDR projection theorem, which relates the spectrum of the deflated system in each IDR(s) cycle to all...

Sparse approximations of inverse matrices

Fast solution of nonsymmetric linear systems on Grid computers using parallel variants of IDR(s)

IDR(s) is a family of fast algorithms for iteratively solving large nonsymmetric linear systems [14]. With cluster computing and in particular with Grid computing, the inner product is a bottleneck operation. In this paper, three techniques are combined in order to alleviate this bottleneck. Firstly, the efficient and stable IDR(s) algorithm...