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...

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...

Numerical Methods for Large Thermo-Mechanical Systems

Numerical methods are investigated for solving large-scale sparse linear systems of equations, that can be applied to thermo-mechanical models and wafer-slip models. This thesis examines efficient numerical methods, in terms of memory, number of iterations required for convergence, and computation time. To be more specific, algebraic multigrid ...

Accelerating (Compressed) SENSE Scans in MRI

Magnetic Resonance Imaging is a painless procedure to produce high-resolution diagnostic images. Today, it is one of the essential clinical imaging modalities. One of the major challenges involved with this imaging modality is its long scanning time. Parallel imaging in combination with compressed sensing has overcome this challenge to a great...

Preconditioning for Mimetic Spectral Element Method: A Preliminary Study Applied on Elliptic Equations

In order to solve linear system of equations obtained from numerical discretisation fast and accurate, preconditioning on the coefficient matrix is needed. In this thesis research, a preliminary study on preconditioning techniques suitable for Mimetic Spectral Element Method (MSEM) will be presented. The spectral limit change of some important...

Methods for improving the computational performance of sequentially linear analsysis

The numerical simulation of brittle failure with nonlinear finite element analysis (NLFEA) remains a challenge due to robustness issues. These problems are attributed to the softening material behaviour and the iterative nature of the Newton-Raphson type methods used in NLFEA. However, robust numerical simulations become increasingly important,...

Adaptive Deflated Multiscale Solvers

Existing multiscale solvers use a sequence of aggressive restriction, coarse-grid correction and prolongation operators to handle low-frequency modes on the coarse grid. High-frequency errors are resolved by employing a smoother on the fine grid. Deflation preconditioning improves matrix properties, i.e., damps slowly varying errors,...

Efficiency improvement of viscous ship flow computations through use of the Graphics Processing Unit: A performance analysis on different hardware

Maritime hydrodynamics involves strong inertia-driven flows, including free-surface waves, and with Reynolds numbers as high as 109. Numerical modelling of these flows is therefore a true challenge. Especially for the optimization of the design of the aft part of the ship, where viscous effects cannot be discarded. At MARIN, the viscous flow...

Parallel Deflated CG Method to Model Groundwater Flow in a Layered Grid

Groundwater, present beneath the earth’s surface in soil pore spaces, is the primary source of fresh water that we use in day to day life. Hydrologists at Dutch research institute Deltares are developing large groundwater models to support water man- agers in their decision-making process. For example, these models simulate effects such as water...

Development of a deflation-based linear solver in reservoir simulation

Extreme and isolated eigenvalues are known to be harmful to the convergence of the iterative solver. These eigenvalues are produced by strong heterogeneity in the underlying physics. We can improve the quality of the spectrum by ‘deflating’ the harmful eigenvalues. In this thesis, deflation is applied to linear systems in reservoir simulation....

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...

Iterative solutions to sequences of Helmholtz equations

We consider sequences of linear systems of equations that follow from the differential equations that describe the acoustics of a car, where the solution to a single linear system corresponds to the pressure perturbations that are caused by acoustic waves of a certain frequency. We consider several iterative numerical methods which belong to the...

Implementation of the Deflated Preconditioned Conjugate Gradient Method for Bubbly Flow on the Graphical Processing Unit (GPU)

In this work we have implemented the Iterative Method of Conjugate Gradients with two levels of Preconditioning to solve a System of Linear Equations on Graphical Processing Unit (GPU). This system represents the discretized Pressure equation resulting from the Level Set Method Solution of the Incompressible Navier Stokes Equation used to...

Improving the linear solver used in the interactive wave model of a real-time ship simulator

Solution of the vector wave equation using a Krylov solver with an algebraic multigrid approximated preconditioner