Dimension reduction techniques for multi-dimensional numerical integrations based on Fourier-cosine series expansion

A wide range of practical problems involve computing multi-dimensional integrations. However, in most cases, it is hard to find analytical solutions to these multi-dimensional integrations. Their numerical solutions always suffer from the `curse of dimension', which means the computational complexity grows exponentially with respect to the...

Predicting the number of students in the Netherlands

In this thesis the Conjugate Gradient method used in the forecasting of the number of students in the Netherlands is investigated. The addition of international students to the forecasting led to mathematical problem of which a solution could not be computed. While the numerical method is working as intended, the work presented in this thesis...

GPU acceleration of FEM solver with applications to Geotechnical Engineering

In finite element software one has to solve a system of non-linear equations, which is commonly simplified to a sequence of linear system. We research the possibility to solve these systems on a GPU to improve the solve time. We are particularly interested in systems arising from geotechnical models. We compare several combinations of Krylov...

Two-level preconditioning applied on the ssSNPBLUP model

The single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) model can potentially be used in animal breeding for genetic evaluations. It has been reported that this model has convergence issues when the Preconditioned Conjugate Gradient (PCG) method is applied. This is due to the linear system being ill-conditioned...

Simulating Level-set Percolation on the Discrete Gaussian Free Field with Arbitrary Conductances: Using a Conjugate Gradient Sampler

Level-set percolation on the Discrete Gaussian Free Field (DGFF) turned out to be a hot topic within mathematical physics over the last couple of years. In particular, the DGFF on Z^d , with homogeneously weighted nearest-neighbour interactions, i.e. all conductances equal to 1, has been studied in detail. These models can be simulated with...

Super Resolution Techniques Applied to Low-Field MRI

This work is part of the low-fieldMRI project, which aims to bring portable, affordable, low-fieldMRI scanners to low-income countries. Replacing the superconducting magnets of conventional scanners with standard ones can significantly reduce the costs, but it also has a negative impact on the Signal-to-Noise Ratio (SNR). In order to circumvent...

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...

Het effect van een anisotropiecoëfficiënt in de Poissonvergelijking op de convergentie van de CG-methode en de ICCG(0)-methode

Allerlei diffusieverschijnselen in de natuurkunde kunnen omschreven worden<br/>met de Poissonvergelijking op een gebied met te kiezen randvoorwaarden. Er zijn echter ook verschijnselen waarin er een gelaagdheid optreedt zodat er in verticale<br/>richting minder makkelijk diffusie kan plaatsvinden. Dit leidt tot een vergelijking<br/>met...

Developing a CUDA solver for large sparse matrices for MARIN

The Maritime Research Institute Netherlands (MARIN) supplies innovative products for the offshore industry and shipping companies. Among their products are highly realistic real-time bridge simulators. Currently, the waves are deterministic and are not affected by ships, moles, breakwaters, piers, or any other object. To bring the simulators to...