Diffusion magnetic resonance imaging (dMRI) allows uniquely the study of the human brain non-invasively and in vivo. Advances in dMRI offer new insight into tissue microstructure and connectivity, and the possibility of investigating the mechanisms and pathology of neurological diseases. The great potential of the technique relies on indirect inference, as modelling frameworks are necessary to map dMRI measurements to neuroanatomical features. However, this mapping can be computationally expensive, particularly given the trend of increasing dataset sizes and/or the increased complexity in biophysical modelling. Limitations on computing can restrict data exploration and even methodology development. A step forward is to take advantage of the power offered by recent parallel computing architectures, especially Graphics Processing Units (GPUs). GPUs are massive parallel processors that offer trillions of floating point operations per second, and have made possible the solution of computationally intensive scientific problems that were intractable before. However, they are not inherently suited for all types of problems, and bespoke computational frameworks need to be developed in many cases to take advantage of their full potential. In this thesis, we propose parallel computational frameworks for the analysis of dMRI using GPUs within different contexts. We show that GPU-based designs can offer accelerations of more than two orders of magnitude for a number of scientific computing tasks with different parallelisability requirements, ranging from biophysical modelling for tissue microstructure estimation to white matter tractography for connectome generation. We develop novel and efficient GPUaccelerated solutions, including a framework that automatically generates GPU parallel code from a user-specified biophysical model. We also present a parallel GPU framework for performing probabilistic tractography and generating whole-brain connectomes. Throughout the thesis, we discuss several strategies for parallelising scientific applications, and we show the great potential of the accelerations obtained, which change the perspective of what is computationally feasible.

The finite element methods (FEM) have been developed over decades, and together with the growth of computer engineering, they become more and more important in solving large-scale problems in science and industry. The objective of this thesis is to develop high-performance finite element methods (HP-FEM), with two main applications in mind: computational diffusion magnetic resonance imaging (MRI), and simulation of the turbulent flow past a vertical axis wind turbine (VAWT). In the first application, we develop an efficient high-performance finite element framework HP-PUFEM based on a partition of unity finite element method to solve the Bloch-Torrey equation in heterogeneous domains. The proposed framework overcomes the difficulties that the standard approaches have when imposing the microscopic heterogeneity of the biological tissues. We also propose artificial jump conditions at the external boundaries to approximate the pseudo-periodic boundary conditions which allows for the water exchange at the external boundaries for non-periodic meshes. The framework is of a high level simplicity and efficiency that well facilitates parallelization. It can be straightforwardly implemented in different FEM software packages and it is implemented in FEniCS for moderate-scale simulations and in FEniCS-HPC for the large-scale simulations. The framework is validated against reference solutions, and implementation shows a strong parallel scalability. Since such a high-performance simulation framework is still missing in the field, it can become a powerful tool to uncover diffusion in complex biological tissues. In the second application, we develop an ALE-DFS method which combines advanced techniques developed in recent years to simulate turbulence. We apply a General Galerkin (G2) method which is continuous piecewise linear in both time and space, to solve the Navier-Stokes equations for a rotating turbine in an Arbitrary Lagrangian-Eulerian (ALE) framework. This method is enhanced with dual-based a posterior error control and automated mesh adaptation. Turbulent boundary layers are modeled by a slip boundary condition to avoid a full resolution which is impossible even with the most powerful computers available today. The method is validated against experimental data of parked turbines with good agreements. The thesis presents contributions in the form of both numerical methods for high-performance computing frameworks and efficient, tested software, published open source as part of the FEniCS-HPC platform. / <p>QC 20180411</p>