Krylov subspace methods are methods to find solutions to high-dimensional linear systems efficiently. One of those methods is the Induced Dimension Reduction method, a method that has been implemented in a parallel Fortran package. To ensure the efficiency of this package, it is important that low-level computations go fast, like creating the LU decomposition.

In this paper, a parallel algorithm for the LU decomposition is developed and improved. Later, the algorithm is extended to work efficiently for matrices with a special structure, band matrices. From this, it follows that the algorithms created do show an increase in efficiency and a decrease in computational time. Furthermore, initial testing after integration in the IDR package also shows an improvement in computational time.

This research investigates efficient matrix-vector multiplication and storage techniques for a Fortran implementation of the Conjugate Gradient (CG) method on GPUs. The CG method is a widely used iterative algorithm for solving large, sparse linear systems.

Because its performance is heavily influenced by the efficiency of matrix operations it is important to make use of parallel computing to run the computations on a GPU. Three types of matrices were considered as A, a dense symmetric positive-definite matrix and two sparse matrices, defined by the discretization of a 1D Laplace equation and a 2D Poisson equation respectively. For sparse matrices, the Compressed Diagonal Storage (CDS) format was implemented to reduce memory usage and computational cost. For parallel execution, three implementations were benchmarked: Standard Fortran, OpenACC, and CUDA Fortran. The results show that CDS significantly improves both memory efficiency and runtime performance for sparse matrices, while CUDA outperforms OpenACC and Standard Fortran in terms of speed, especially for large matrices. Standard Fortran remains competitive for small matrices due to low overhead, but it scales poorly. The convergence behavior of the CG method was also found to be highly dependent on the condition number of the matrix, with the 2D Poisson matrix exhibiting much faster convergence than the 1D Laplace matrix.

This study concludes that efficient storage and GPU-based matrix operations, particularly using CUDA, are critical for scalable performance in solving large linear systems with the CG method. Future work could explore combining the portability and ease of use of Standard Fortran with GPU acceleration to achieve both maintainability and high performance.

Vascular calcification, the deposition of calcium in the vessel wall, is associated with several vascular diseases, including atherosclerosis, diabetes mellitus, and hypertension.
Fluid-structure interaction (FSI) is recommended to simulate blood flow incorporating vascular calcification. However, FSI applied to a three-dimensional (3D) model takes several days to simulate.
To reduce the computational complexity, 1D reduced order models (ROMs) are often used instead.

Reduced order modeling decreases the computational complexity of a model by removing dimensions of the coordinate system within a model. The cylindrical coordinate system is used in hemodynamics, especially in ROMs. The 1D ROM for hemodynamics is obtained by removing the azimuthal dimension (accomplished by assuming axial symmetry for all properties within arteries) and the radial dimension (accomplished by applying a predefined velocity profile to blood flow) from the 3D model. However, incorporating vascular calcification can make the geometry of arteries and flow within arteries asymmetric. A 2D ROM can increase the accuracy of the 1D ROM by including one of the two removed dimensions. Research regarding 2D blood flow mainly focuses on including the radial dimension, which cannot implement asymmetric calcification since axisymmetry is assumed.

This study obtains a 2D ROM for blood flow by removing the dimension corresponding to the radial distance from the three-dimensional model and by assuming that axial velocity is continuous in the neighborhood near the artery's origin. The 2D ROM obtains axisymmetric velocity by only allowing a single velocity profile. However, enabling a family of velocity profiles can make flow within arteries asymmetric. Hence, this study contributes to hemodynamics by studying blood flow that allows a family of velocity profiles.

A non-physiological steady-state solution has been obtained analytically, in which the volumetric flow rate vanishes, and numerical methods are developed to simulate the 2D ROM, which incorporates dimensional (Godunov) splitting, linear approximate solvers, and high-resolution methods. Jump-discontinuities within the mechanical properties of the vascular walls are smoothened for the 2D simulations. Numerical methods for the 2D ROM yield significant errors within the smoothening region for simulations with coarse grids.
The numerical method obtains the non-physiological steady-state solutions for arteries without calcification and has a relative error of O(Δx^1.500) for arteries with axisymmetric calcification. The 2D ROM cannot numerically obtain the non-physiological steady-state solution for arteries with asymmetric calcification due to the numerical errors within the smoothening range.

 3D and 2D numerical simulations with pulsatile blood flow are compared. The 3D simulation without calcification has a significantly higher diastolic pressure, larger inner wall radii, and larger volumetric flow rates than the 2D simulation. The differences in blood flow observed between pulsatile blood flow without calcification and with calcification match decently between the 3D simulations and the 2D simulations, except for locations within the smoothening region.

Proton therapy is a form of radiation therapy, that leverages the unique properties of protons to maximize dose deposition in treatment volumes. The usefulness of proton therapy treatment, in sparing healthy tissue, becomes even more evident with the incorporation of the FLASH effect. FLASH delivers ultra-high dose rates with minimal treatment time while maintaining therapeutic efficiency in eradicating tumours. How- ever, due to practical challenges such as energy layer switching in pencil beam scanning systems the clinical applications are limited. This thesis researched the development of patient-specific ridge filters (RFs) for proton therapy using an optimization algorithm. Ridge filters are energy modulators that help enable dose delivery without energy layer switching, making the FLASH effect feasible as was shown in 2018 [1]. Previous studies used static and dynamic methods [2] and fluence-based optimization [3] to construct patient-specific RFs. This study presents a novel framework for optimizing patient-specific RFs using a combination of TOPAS, a Monte Carlo particle simulation software that accurately models particle transport, and PyGAD, a Python-based genetic algorithm (GA) module. This class of optimizers is effective in cases where no derivatives are avail- able or are very difficult to compute. GAs do this by testing various simulations and evaluating these using a fitness function. The methodology involves simulating dose distribution in a scoring volume, optimizing ridge pin geometry, and evaluating performance using fitness functions. The results demonstrate that the proposed framework effectively generates patient-specific RFs with min- imal deviation from the desired dose distribution in simple cases, with a maximum dose difference of 2.66 % and mean dose of 99.21 % over the region of interest. Comparative analysis with prior approaches shows that the framework achieves similar results. However, applying the framework to cases with obstructions in the scoring volume requires further refinement of the algorithm. The findings provide a basis for using GAs for constructing patient-specific RFs for FLASH proton therapy. Future work should be aimed at refining the GA and Monte Carlo simulation and assessing the viability of producing the generated RFs.

The numerical solution of the Helmholtz equation presents significant challenges in computational mathematics and scientific computing, particularly for high-frequency problems in heterogeneous media. This dissertation addresses these challenges through the development of high-performance iterative methods, focusing on the critical balance between numerical efficiency and practical implementation on modern computing architectures.

The research is motivated by the growing computational demands in seismic imaging and other wave propagation applications, where increasing frequencies and larger domains necessitate more efficient solution strategies. Traditional approaches often struggle with the combined challenges of wavenumber-dependent convergence, pollution errors, and substantial memory requirements, particularly for three-dimensional problems in heterogeneous media.

This work presents a comprehensive framework for solving large-scale Helmholtz problems through matrix-free parallel implementations of preconditioned iterative methods. The framework combines Complex Shifted Laplace Preconditioner (CSLP) with advanced deflation techniques, implemented in a manner that eliminates the need for explicit matrix storage while maintaining computational efficiency. A key innovation is the development of matrix-free implementations for higher-order deflation methods combined with the CSLP preconditioner, achieved through carefully designed re-discretization schemes that preserve the advantages of Galerkin coarsening.

The methodology progresses from two-dimensional implementations to fully three-dimensional frameworks, incorporating increasingly sophisticated preconditioning techniques. A significant achievement is the development of a matrix-free parallel multilevel deflation preconditioner that exhibits near wavenumber-independent convergence while maintaining excellent parallel scalability. The implementation utilizes a hybrid MPI+OpenMP parallelization strategy, effectively addressing both computational and memory challenges in extreme-scale scenarios.

Extensive numerical experiments validate the effectiveness of these methods across a range of problem types, from academic test cases to industrial-scale applications. Notably, the framework successfully resolves a challenging seismic model, involving approximately 3.8 billion degrees of freedom, while achieving 86\% parallel efficiency when scaling to 2304 CPU cores. This demonstration of practical viability for large-scale heterogeneous problems represents a significant advance in computational capabilities for seismic imaging applications.

The research makes several fundamental contributions to the field of numerical analysis and scientific computing. First, it establishes new approaches for matrix-free implementation of state-of-the-art preconditioners, significantly reducing memory requirements while maintaining numerical efficiency. Second, it demonstrates the achievement of close-to wavenumber-independent convergence through carefully designed deflation strategies in a parallel computing environment. Third, it provides a comprehensive framework for solving extreme-scale Helmholtz problems that combines numerical robustness with practical applicability.

The methodologies developed in this work contribute to the broader field of scientific computing, demonstrating how careful algorithm design, combined with modern computing architectures, can address previously intractable problems in wave propagation modeling.

This thesis explores the improvement of computational efficiency in simulating two-dimensional conveyor belt systems by applying model order reduction (MOR) techniques. Conveyor belts, crucial for material handling in various industries, are traditionally modeled using finite element methods (FEM), which can be computationally demanding, particularly for long-term simulations with a high number of grid elements. To address this, MOR techniques aim to reduce high-dimensional models into lowerdimensional models.
The study investigates three MOR approaches—modal decomposition, Proper Orthogonal Decomposition (POD), and Dynamic Mode Decomposition (DMD)—to apply on existing software built by VORtech that simulates two-dimensional conveyor belt systems. When considering MOR to reduce the two-dimensional system, challenges arise related to nonlinearities, differential algebraic equations (DAEs), and complex modeling steps. Among the methods tested, DMD proved to be the most effective, offering significant reductions in computational time while maintaining accuracy. POD also demonstrated accuracy but had less impact on speed due to the time-consuming complex modeling steps in the simulation software. These complex modeling steps are not investigated in detail in this thesis and therefore not reducible with the intrusive POD. Because of the non-intrusive nature of DMD, this method was able to incorporate these extra processes in the reduced order model.
The study concludes with recommendations for future research, emphasizing the need for optimization of the code segments that handle the complex modeling steps. In addition, conventional modeling approaches as alternatives to the complex interpolation step could be explored, to enhance the applicability of MOR. Furthermore, DMD with control or parametric DMD could be explored to obtain a reduced order model by interpreting misalignments of rollers as controls or parameters. Finally, a method is proposed to make modal decomposition useful for models, where the solutions depend highly on the external forces. Although this method is not applied to the model considered in this thesis, it would be interesting to explore this modified modal decomposition method on other models that are significantly influenced by the external forces.

To diagnose diseases using low-field MRI devices, automatic image recognition techniques are required to detect anomalies in a given image. A critical component of this process is image segmentation, which involves dividing the image into coherent regions with similar features to detect the anomalies. Low quality images make segmentation difficult by the existence of noise in the images. The Chan-Vese model is a segmentation technique to segment images into two regions. This report aims to segment the low quality images obtained by the low-field MRI devices with use of the Chan-Vese model. This model is found to be particularly well-suited for handling the challenges posed by low-quality images which the low-field MRI devices produce. Future research should investigate if it is possible to further segment the region with the objects, such that each object has a separate region.

Angiogenesis, i.e. the formation of blood vessels from existing ones, plays a vital role in bone or wound healing. The expansion of vascularization facilitates the healing process through the delivery of oxygen and nutrients to the injured site and through the removal of waste products. Clinical observations indicate that impaired angiogenesis can impede the healing process, or can result in non-healing outcomes.
The computational model developed in this thesis predicts tip/stalk cell patterning, marking the initial phase of sprouting angiogenesis. Growth factors signal endothelial cells to differentiate into tip and stalk cells. Tip cells branch from the existing vessel, leading the sprout, while stalk cells proliferate and follow behind, forming the newly emerged blood vessel. Understanding tip/stalk cell patterning is vital to ensure successful angiogenesis, as an excess or deficiency in tip cells leads to improper healing.
Despite several experimental studies and mathematical models exploring the signaling pathways behind tip cell selection, there is a noticeable gap regarding the effect of extracellular matrix (ECM) stiffness on this process. Given that alterations in stiffness occur in various physiological and pathological processes, comprehension of this effect is clinically relevant. This thesis aims to address the existing gap by investigating the specific influence of ECM stiffness on tip/stalk cell patterning.
A computational model is created that simulates a vessel sprout under stimulation of growth factors. This model is able to predict the cell patterning over various ECM stiffness levels, and highlights the relevance of incorporating ECM stiffness in the investigation of angiogenic treatments.
Enhancing the models’ accuracy and validating the ECM stiffness-dependent model predictions requires additional experimental data. However, further development of the model has great potential for deepening our understanding of angiogenesis dynamics and for facilitating the investigation of treatment strategies.

HER2+ breast cancer patients, as observed by oncologist Agnes Jager from Erasmus Medical Centre (EMC), often achieve radiologic complete response (rCR) earlier than expected under standard treatments. To address this, Jager has partnered with Delft University of Technology to develop a computational model aimed at personalizing treatment schedules, potentially reducing chemotherapy cycles and minimizing side effects.

Building on previous MSc theses by Nathalie Oudhof, Eva Slingerland, and Rutger Engelberts, this thesis aims to improve the predictive capability of the Drug-Induced Mechanically Coupled Reaction-Diffusion (DI-MRCD) model and test its performance on a larger dataset consisting of 13 patients. The DI-MRCD model combines dynamic contrast-enhanced (DCE) and diffusion-weighted imaging (DWI) magnetic resonance imaging (MRI) data with patient-specific parameters to simulate the reaction of breast cancer tumours on chemotherapy. Key improvements include optimizing and generalizing the pre-processing pipeline for a larger patient cohort and enhancing input reliability by independently computing apparent diffusion coefficients (ADC).

Further refinements to the DI-MRCD model include updates to chemotherapy and shear modulus parameters, switching to a Trust Region Reflective (TRF) optimization method, and introducing a tissue-specific proliferation rate and natural cell death term. Despite these enhancements providing more insight, control, and making the model biologically more realistic, the model struggled to converge, highlighting the challenge of fitting patient-specific parameters with limited data points.

Future improvements could include resolving the convergence issues, incorporating additional calibration parameters, allowing the proliferation rate to travel with tumour cells as they diffuse, incorporating chemotherapy doses into the chemotherapy term, using Bayesian optimization for better parameter estimation, and making the results more explanatory by integrating other patient data.

Integrated electrical power flow simulations are concerned with solving the steady-state load flow problem on integrated transmission and distribution electricity networks. We have developed a framework to run these simulations efficiently, whilst keeping in mind the differences between these network types and accommodating the practical considerations of system operators. We need such a framework to analyse the interaction that these systems might have as a result of the energy transition.

To develop a framework to run integrated power flow simulations, we have worked in two stages. Firstly, we have studied how we can model an integrated network. We have found two ways of modelling an integrated network: using a homogeneous configuration in which both networks are modelled using three phases and using a hybrid network configuration in which both networks keep their original configuration but in which the coupling substation takes care of the phase dimension mismatch between the two sides. Next to that, we have found two ways of solving an integrated system: either by coupling them into one system and solving that as a whole (we call this the unified approach) or by keeping two separate systems and iterating between these networks (we call this the Manager‐Fellow Splitting (MFS) method).

We have concluded that the unified methods are generally faster than MFS methods and that a hybrid network configuration leads to faster results, making the interconnected method the most efficient.

In the second stage, we have focused on the efficiency of these simulations. During every Newton‐Raphson iteration in power flow simulations, a linear system is solved. We have therefore studied several Krylov subspace and preconditioning techniques that can solve this linear system efficiently. We have applied Krylov and preconditioning combinations to integrated network simulations to check again the performances of the simulations on large test cases . During this stage, we applied them to networks up to a size of 800,000 buses as we were interested in efficient scaling of the methods that were originally the object of study.

In the second stage, we saw that the MFS methods were performing better than unified methods. Furthermore, preconditioned Krylov subspace methods had a similar performance to direct methods. t is difficult to judge why this happened. A reason could be that the library in which we performed these simulations, PETSc, is optimised for parallel computations in which multiple smaller blocks are solved at the same time whilst we were doing only sequential computations.

Finally, we have striven to incorporate operational convenience for Transmission and Distribution System Operators (TSOs and DSOs) during the development of this integration framework, by considering their computational and privacy concerns. The way that this framework is built, can take away some of their concerns.

To summarise, we have created an open‐source framework to run efficient steady-state power flow simulations on integrated transmission and distribution networks. This framework is tested on simplified test cases but shows potential for large system simulations. Moreover, it takes into account the considerations of system operators and can be utilised in other applications besides integrated analysis.

Every year, 180000 new cases of hydrocephalus are diagnosed among infants in Sub-Saharan Africa. Unfortunately, more than two-thirds of the population in this region lacks access to essential medical imaging technologies, such as magnetic resonance imaging (MRI). To address this issue, a collaborative effort between the TU Delft, Leiden University Medical Center, Penn State, and Mbarara University of Science and Technology has led to the development of a low-cost, portable, low-field MRI system. However, images obtained from this scanner are often noisy and distorted and might contain artefacts, therefore, need preprocessing before they can be utilized in diagnostics. The enhancement of their quality can be achieved through both hardware calibration and optimization, as well as the application of filtering, enhancement, and segmentation techniques. In this master's project, we propose a two-step PDE-based segmentation approach. Additionally, we compare it with the modified approach where presegmentation in the initial phase of the standard algorithm is introduced. Both approaches yield segmentation results comparable to the ground truth or manually performed segmentation. Nonetheless, there remains room for further improvement in both denoising and segmentation techniques.

With breast cancer being the leading cause of death in the Netherlands, while also being expected to have double the amount of cases in the next ten years, it is vital that treatment is optimised. Over the last decade, research has been done to incorporate mathematical modelling in this process, especially in the case of HER2+ breast cancer patients. This aggressive form has poor chances of survival, but responds well to chemotherapy and is expected to be quite predictable. In previous works of N. Oudhof and E. Slingerland, a mechanically coupled reaction-diffusion model with an extension of chemotherapy was implemented in 2D, using three MRI scans to predict tumour response. The first two scans, taken right before and during treatment, are used to find patient-specific parameters corresponding to proliferation, tumour movement and chemotherapy efficacy. This calibrated model is then used to predict the third scan, taken at the end of treatment. Calibrating this model to individual patients takes up to a day, however. \\

This thesis aims to extend this model to a higher resolution 3D setting, which should also hand doctors predictions within a working day. To increase speed, the linear-elastic sub-problem of finding shear stress due to tissue types and tumour growth was first optimised. With a novel Laplacian preconditioner in the Conjugate Gradient method, using FFT's and a tridiagonal solver, the time needed was vastly improved. Second, the maximum order of error needed for accurate temporal integration was confirmed to be quite high. Hence a state-of-the-art Parareal implementation was made, using Runge-Kutta 4 and Crank Nicholson as the respective fine and course solver, which succeeded in being both faster and more accurate than simple first-order methods. Then it was found that the underdeterminedness of the problem is best tackled using Total Variation Regularisation on the proliferation parameter and Tikhonov Regularisation on the other two parameters. This ensures that unique solutions can be found in reasonable time, that properly reflect expectations of these parameters in practical settings. The best set of parameters were found fastest with Powell's Dog-leg method, for which a novel way of finding the Jacobian analytically was used. \\

On simulated data, the error in the amount of tumour cells in the third image went down to single-digit percentage rate, with a maximal shape correlation coefficient. This prediction can be made within a few hours, which means that the feasibility of solving this problem in practical settings has been established successfully. On the real data, the calibration succeeded in calibrating the model on the first two scans, but the predictions still have room of improvement. The most important suggestion of this work is that more research must be done in the verification of the suitability of this model to the available real data, using the techniques presented here. Further improvements can be made by exploring more possibilities of using parallelisation, and by obtaining more data. Before obtaining more data, one should investigate the impact of the timing of the scans on the calibration results.

This thesis aims to develop an advanced numerical solver capable of efficiently computing the resonant states of quantum mechanical two-body and three-body problems, thereby expanding our understanding of these complex systems. The quantum three-body problems feature at least two dimensions, which necessitates substantial computational efforts. Therefore, in order to tackle these challenging computations, we need to seek assistance from supercomputers. By harnessing the capabilities of high-performance computing, we can significantly reduce the amount of time spent waiting for programs to run for hours.

In this thesis, we first introduce some basic knowledge about quantum few-body problems and resonant states, showing how the physical problem gives rise to a mathematical problem, the quadratic eigenvalue problem (QEP). Building upon the physical background, our journey in developing the methodology begins with two fundamental components: discretization and eigensolver. The pseudo-spectral methods are introduced to represent the quadratic eigenvalue problem as a matrix problem, by which we can solve the problem numerically through some eigensolvers. We describe a classical approach called linearization for solving QEPs, which transforms the quadratic problem into a generalized eigenvalue problem. Following the linear transformation, we apply the Jacobi-Davidson QZ (JDQZ) method, an iterative eigensolver, to solve the linearized problem. Alternatively, we could also use the Jacobi-Davidson (JD) method to approximate the quadratic eigenvalue problem's eigenpairs directly. In this thesis, we provide an outline of the Jacobi-Davidson process for solving both linear and quadratic problems. Two routes for solving QEPs are utilized and compared: linearization combined with the Jacobi-Davidson QZ method, and the quadratic Jacobi-Davidson method. Through our research and analysis, we demonstrate that the Jacobi-Davidson algorithm exhibits superior computational efficiency when adapted to solve QEPs directly.

Another significant objective of this thesis is to parallelize the eigensolver on supercomputers. We implement a hybrid distributed/shared memory parallelization of the Jacobi-Davidson algorithm to solve quadratic eigenvalue problems that arise from one-dimensional three-body problems. We leverage the tensor structure inherent in the three-body problem to optimize computational efficiency. Specifically, we implement an efficient tensor product scheme for the application of the stiffness and damping operators, which are realized as dense matrix-matrix products. By incorporating a preconditioner that also preserves the tensor structure, we enhance the performance of our Jacobi-Davidson algorithm in computing three-body resonance poles within an acceptable speed.

In our research, we have made a significant advancement in predicting the clinical outcome of high-risk non-muscle invasive bladder cancer (HR-NMIBC) by combining clinicopathological data with image-related features. This integrated approach has shown remarkable improvements in the accuracy of artificial intelligence techniques for outcome prediction.

We developed a novel methodology that effectively combines information from cell nuclei per patient, resulting in enhanced classification accuracy. By integrating clinicopathological data with image-related features extracted from medical imaging, we demonstrated the power of AI in more accurately predicting clinical outcomes for HR-NMIBC.

Our study provides a comprehensive view of the disease, taking into account both macroscopic characteristics and microscopic details observed at the cellular level. By aggregating information from thousands of cell nuclei for each patient, we transformed raw data into a format suitable for machine learning algorithms, improving the performance of AI techniques in clinical outcome prediction.

However, it is essential to address the potential biases and imbalanced variables present in the dataset. We noticed gender imbalance, differences in tumor size, and uneven grading levels, which may affect the generalizability of our conclusions.

To enhance our analysis, we retrained a convolutional neural network (CNN) using our image dataset, achieving high accuracy in segmenting hematoxylin and eosin stained images and accurately identifying cell nuclei boundaries. Additionally, we implemented an innovative clustering technique called FlowSOM, enabling us to group and classify millions of cell nuclei based on their characteristics, providing valuable insights into cellular heterogeneity.

Our AI models exhibited high performance metrics, particularly the random forest algorithm, which proved most suitable for the task. We also conducted a variable importance analysis, revealing specific cell clusters with significant impact on predicting clinical outcomes, emphasizing the relevance of cellular size and shape in disease progression and treatment response.

Proton irradiation therapy is a powerful form of cancer treatment, promising better dose conformity as compared to conventional radiotherapy. Due to the complex scattering properties of protons, the optimization process that is needed to accurately target the cancer cells whilst causing minimal damage to
the surrounding healthy tissue and minimizing detrimental effects, is very time-consuming. This means that the CT scan it is based on has lost part of its accuracy in describing the to be irradiated tissue. To account for this, the surrounding tissue is irradiated more to ensure effective treatment, reducing dose conformity and thus increasing the probability of detrimental side effects.
To solve this problem, a new proton therapy method concept, called Online Adaptive Proton Therapy, or OAPT, calls for a CT scan to be taken about 30 seconds before the treatment, allowing the planned treatment to be adapted to any anatomical changes that have occurred since the previous scan where the original treatment planning was based on. The computations required for this adaptation, and the required quality assurance, currently still take significantly longer than 30 seconds on current computational hardware, making the concept not yet viable in its current form. However, using GPU-acceleration, parts of the algorithm that is used for this can be significantly sped up to reduce overall computational time, potentially making the concept viable for real world application. In this thesis, the research question ”How can GPU-offloading decrease computation time for proton therapy dose calculations?” is answered by accelerating two model algorithms representative of two time-consuming steps in the proton therapy optimization process and analyzing the performance, on
an NVIDIA V100S GPU, of the accelerated code. Furthermore, a model is postulated and validated to characterize and predict the performance of a GPU accelerated algorithm. Using OpenACC, both algorithms achieved speedups between 30x and 440x excluding data transfer time, and between 0.88x and 40x including data transfer time, with both values depending on the problem size, with larger problems yielding larger speedups. Further research is needed on the validity of the derived model on different hardware and for different algorithms. Furthermore, additional research on the effect of implementing these accelerated algorithms on the total computation time of the real world algorithm is advised.

Intensity modulated proton therapy is an advanced radiotherapy technique that is used to treat cancer patients. In order to successfully treat a patient, sufficient dose to the tumor is required. However, during the fractionated treatment, multiple errors can cause a difference between the planned and actual dose delivery. To ensure adequate dose delivery in potential error scenarios, robust treatment plans are acquired as these are less sensitive to uncertainties inherent to proton therapy. However, robust optimization is challenging.

First, as robust optimization accounts for multiple error scenarios, the time needed to generate optimal treatment plans increases significantly. Therefore, it is investigated in this thesis if the optimization time can be reduced while preserving treatment plan quality. This is investigated through two different methods. In the first method, the number of error scenarios accounted for during optimization is reduced. We found that this can significantly reduce optimization time, while improved target coverage and lower risk on side effects are obtained. However, the near-maximum dose to the tumor was found to be less favourable. The second method investigated is variance optimization. This method significantly reduces optimization time. However, for similar target coverage, the risk of side effects increases.

Another challenge related to robust optimization is the increase in delivered dose to healthy tissues surrounding the tumor, which increases the risk of side effects. Therefore, it is investigated in this thesis if the risk of side effects can be lowered by allowing higher maximum dose to the tumor. It is found that this method indeed reduces the risk of side effects. However, the increased maximum dose to the tumor may not be clinically desired as the increase may lead to higher risks of other side effects: edema and fibrosis. The clinically desired trade-off between near-maximum dose and normal tissue sparing should be established.

A common problem in wireless communication is the existence of multipath propagation. This means that a transmitted signal is received multiple times because of reflections caused by the environment. We present two ways of modeling multipath propagation of an acoustic underwater signal. We discretise these models to solve them numerically. During the solving process, we are presented with inconsistent, overdetermined systems of linear equations. We investigate two methods to go about these systems: the ordinary least squares method and the total least squares method. We reconstruct a signal using both of these methods and compare their results. The method of least squares reconstructs the signal moderately well. For the total least squares method this is not the case. It turns out that it is not straightforward to formulate a total least squares problem in the corresponding model. We suspect that, in part, this is why the signal reconstruction does not work well for the total least squares method.

Fog plays a major role in chain collisions. Proper fog detection is essential for the Dutch road authority to anticipate foggy weather conditions. Dozens of stations in the Netherlands can measure fog. However, fog can be a very local phenomenon. Therefore, more local measurements are needed. There are about 5,000 traffic cameras in the Netherlands. Several studies on detecting fog on traffic cameras have been done. The most successful studies used machine learning classification models to detect fog. The biggest challenge they face is the extreme imbalance, limited diversity, and limited accuracy of the dataset. Obtaining adequate precision is one of the primary challenges since the extreme imbalance of the dataset significantly impacts precision. The main objective of this research is to improve the dataset and investigate many machine learning configurations. Another objective is to examine the possibilities of generating synthetic data.

This thesis uses a clever (re)labeling method, significantly improving the dataset's quality. However, it turned out that the dataset still has its limitations. A large portion of false positives are caused by labeling errors. After comparing several machine learning models, it follows that a 9-layer ResNET model is optimal. Adding more layers will not result in better performance. Unexpectedly, initializing ResNET with pre-trained weights actually decreases performance. In addition, the effect of oversampling and/or using a weighted binary cross-entropy loss is investigated. Just oversampling leads to overfitting, but using a weighted binary cross-entropy loss isn't ideal either. The best performance is achieved by combining weighted binary cross-entropy loss with oversampling. Decision threshold optimization substantially improved the results. The experiments allowed for selecting the ideal configuration, which substantially increased performance. The best-performing configuration achieved a strong correlation in the Matthews correlation coefficient.

Finally, the possibilities of generating synthetic data are investigated. ADASYN and SMOTe seem attractive at first sight, but from a recent study, it follows that they don't work better than random oversampling. One of the most promising ideas for generating synthetic data is to add fog to clear images. In this thesis, a conceptual algorithm is designed to add artificial fog to clear images. Most generated images look convincing, but there is much room for improvement.

The aim of this thesis was to test the efficiency in practice of an analytical propagator with collision detection for N-body Keplerian systems. This can be used to simulate the evolution of a protoplanetary disk, which gives insight into how planetary systems form. The analytic propagator calculates collisions one by one, while a numerical propagator would compute each time step. The idea of using the analytic propagator is that collisions are rare in astronomical scales, such that jumping from collision to collision and calculating it, is more efficient than calculating all the time steps that are between collisions. Simplifying the orbits of the planetesimals into perfect Keplerian orbits, analytical solutions exist which are used by the analytic propagator.

In this thesis, the runtimes of simulations were measured as well as other properties directly related to the runtime. The overall efficiency of the algorithm with respect to N seemed to be O(N³), which is one power less than previously predicted. The prediction was that the runtime of the full simulation is O(N²ε + N⁴s³/Ia³). Here ε is the maximum eccentricity, s/a is the ratio of a planetesimal's radius to the semi-major axis of its orbit, and I is the maximum inclination. This was calculated by estimating the total number of collisions to be O(N²s²/Ia²) and the runtime for each collision to be O(N²s/a). But the number of collisions turns from quadratic to linear in N, implying that above a certain N almost all planetesimals collide, which reduces the power of N by one. For comparison, the octree code has an algorithmic efficiency of O(N logN) per time step, and the number of steps for a fixed integration time grows as O(N^4/3 log N).