Een snellere oplosmethode voor lineaire stelsels

De Scheduled Relaxation Jacobi (SRJ) methode is een toepassing van de Jacobi methode met relaxatiegewichten. De relaxatiegewichten worden gebruikt in een iteratie cyclus. Daarnaast zijn de relaxatiegewichten zodanig gekozen, dat het optimaal werkt voor de Laplace vergelijking. Met de SRJ methode is het gelukt om de Jacobi methode 100x sneller te...

Het toepassen van complexe methodes voor het schatten van afgeleiden

It is possible to estimate derivatives of real functions with complex methods. These complex methods can increase speed or accuracy. The functions needs to be known to determine the derivative with a complex method.

An elastic model for meshfitting for the Level-set Method

The numerical errors involving the application of the level-set method to a problem can be minimized by fitting a mesh (usually a triangular mesh in two dimensions) to the zero level-set curve defined by the level-set function. These numerical errors depend on two things: the size and skewness of the triangles in the mesh. To fit the mesh, Timo...

Filtration of natural organic matter and micro pollutants

This study discusses the filtration of micro-pollutants and natural organic matter<br/>from water by a granular activated carbon filter. To determine the efficiency of a<br/>filter, simulations are run to predict it’s efficiency. This study will describe a demo application and it’s underlying model that are used to determine the efficiency of a...

De verstrooiing van het licht berekend voor het Asahi-U substraat

In dit project is gewerkt aan een manier om de reflectie van het licht op de textuur van een zonnecel te berekenen. Deze reflectie is berekenend voor de verschillende hoeken van inval en uitval en omgezet in een reflectie matrix. In dit<br/>project is verder gewerkt aan een al bestaand wiskundig model. Dat model was<br/>in staat het door de...

Constructing the medial axis of a discrete level-set curve

In (mathematical) physics one can encounter problems with a fase change, the so called Stefan problems. Numerical methods to solve these problems often use a level-set function which indicates the distance to the fase boundary. Problems can arise in the medial axis points of the zero set. Therefore it can be usefull to calculate this medial axis...

Simulating COVID-19 contact tracing queue using compartment models

This research is mainly about optimising compartment models for COVID-19 and then using them for different applications that can be used to consult authorities. A compartment model describes the dynamics of a disease by implementing differential equations for the different states that belong to that disease. This is done using parameters which...

Reframing existence and uniqueness theorems for the non-homogeneous wave equation

This thesis is about the wave equation. The wave equation describes waves that propagate through a certain medium. The solution of the wave equation is a mathematical description of what that wave looks like. There are many fields of study where the wave equation is used to model processes that behave like travelling waves. For instance, a...

Can You Parallelize Time?: Moving through the complexity of time

This Bachelor End Project Thesis is about creating parallel variants of time-dependent methods. To achieve this, the time-dependent problem is formulated as a large system of linear equations that is solved iteratively. This linear system is determined from the time-dependent linear heat equation in 1D that all the analysis is about. The...

Fourier Analysis of the microvascular function of women with and without migraine

Erasmus MC is conducting a study on the increased risk of cardiovascular disease in women who have migraine. For this purpose, 50 healthy women and 50 women with migraine in age category of 40-60 years were compared using measurements of their dermal blood flow.<br/>These measurements are done using two different imaging devices: Laser Speckle...