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The goal of this project was to evaluate the viability of a mass-spring-damper based model for modeling of biological tissue. A method for automatically generating such a model from data taken from 3D medical imaging equipment including both the generation of point masses and an algorithm for generating the spring-damper links between these points is presented. Furthermore, an implementation of a simulation of this model running in real-time by utilizing the parallel computational power of modern GPU hardware through OpenCL is described. This implementation uses the fourth order Runge-Kutta method to improve stability over similar implementations. The difficulty of maintaining stability while still providing rigidness to the simulated tissue is thoroughly discussed. Several observations on the influence of the structure of the model on the consistency of the simulated tissue are also presented. This implementation also includes two manipulation tools, a move tool and a cut tool for interaction with the simulation. From the results, it is clear that the mass-springdamper model is a viable model that is possible to simulate in real-time on modern but commoditized hardware. With further development, this can be of great benefit to areas such as medical visualization and surgical simulation. / Målet med detta projekt var att utvärdera huruvida en modell baserad på massa-fjäderdämpare är meningsfull för att modellera biologisk vävnad. En metod för att automatiskt generera en sådan modell utifrån data tagen från medicinsk 3D-skanningsutrustning presenteras. Denna metod inkluderar både generering av punktmassor samt en algoritm för generering av länkar mellan dessa. Vidare beskrivs en implementation av en simulering av denna modell som körs i realtid genom att utnyttja den parallella beräkningskraften hos modern GPU-hårdvara via OpenCL. Denna implementation använder sig av fjärde ordningens Runge-Kutta-metod för förbättrad stabilitet jämfört med liknande implementationer. Svårigheten att bibehålla stabiliteten samtidigt som den simulerade vävnaden ges tillräcklig styvhet diskuteras genomgående. Flera observationer om modellstrukturens inverkan på den simulerade vävnadens konsistens presenteras också. Denna implementation inkluderar två manipuleringsverktyg, ett flytta-verktyg och ett skärverktyg för att interagera med simuleringen. Resultaten visar tydligt att en modell baserad på massa-fjäder-dämpare är en rimlig modell som är möjlig att simulera i realtid på modern men lättillgänglig hårdvara. Med vidareutveckling kan detta bli betydelsefullt för områden så som medicinsk bildvetenskap och kirurgisk simulering.

A key challenge facing the nuclear fusion community is how to design a reactor that will operate in environmental conditions not easily reproducible in the laboratory for materials testing. Finite element analysis (FEA), commonly used to predict components’ performance, typically uses idealised geometries. An emerging technique shown to have improved accuracy is image based finite element modelling (IBFEM). This involves converting a three dimensional image (such as from X ray tomography) into an FEA mesh. A main advantage of IBFEM is that models include micro structural and non idealised manufacturing features. The aim of this work was to investigate the thermal performance of a CFC Cu divertor monoblock, a carbon fibre composite (CFC) tile joined through its centre to a CuCrZr pipe with a Cu interlayer. As a plasma facing component located where thermal flux in the reactor is at its highest, one of its primary functions is to extract heat by active cooling. Therefore, characterisation of its thermal performance is vital. Investigation of the thermal performance of CFC Cu joining methods by laser flash analysis and X ray tomography showed a strong correlation between micro structures at the material interface and a reduction in thermal conductivity. Therefore, this problem leant itself well to be investigated further by IBFEM. However, because these high resolution models require such large numbers of elements, commercial FEA software could not be used. This served as motivation to develop parallel software capable of performing the necessary transient thermal simulations. The resultant code was shown to scale well with increasing problem sizes and a simulation with 137 million elements was successfully completed using 4096 cores. In comparison with a low resolution IBFEM and traditional FEA simulations it was demonstrated to provide additional accuracy. IBFEM was used to simulate a divertor monoblock mock up, where it was found that a region of delamination existed on the CFC Cu interface. Predictions showed that if this was aligned unfavourably it would increase thermal gradients across the component thus reducing lifespan. As this was a feature introduced in manufacturing it would not have been accounted for without IBFEM.The technique developed in this work has broad engineering applications. It could be used similarly to accurately model components in conditions unfeasible to produce in the laboratory, to assist in research and development of component manufacturing or to verify commercial components against manufacturers’ claims.

This thesis provides an analysis of the application for evolutionary scheduling of collective communications. It proposes possible ways to accelerate the application using general purpose computing on graphics processing units (GPU). This work offers a theoretical overview of systems on a chip, collective communications scheduling and more detailed description of evolutionary algorithms. Further, the work provides a description of the GPU architecture and its memory hierarchy using the OpenCL memory model. Based on the profiling, the work defines a concept for parallel execution of the fitness function. Furthermore, an estimation of the possible level of acceleration is presented. The process of implementation is described with a closer insight into the optimization process. Another important point consists in comparison of the original CPU-based solution and the massively parallel GPU version. As the final point, the thesis proposes distribution of the computation among different devices supported by OpenCL standard. In the conclusion are discussed further advantages, constraints and possibilities of acceleration using distribution on heterogenous computing systems.

Un préconditionneur à deux niveaux, reposant sur la technique d’accélération d’Aitken d’une suite de q vecteurs solutions de l’interface d’un pro- cessus itératif de Schwarz Additif Restreint, est conçu. Cette nouvelle technique, dénomée ARAS(q), utilise une approximation grossière de la solution sur l’interface. Différentes méthodes sont proposées, aboutissant au développement d’une tech- nique d’approximation par Décomposition en Valeures Singulières de la suite de vecteurs. Des implémentations parallèles des méthodes d’Aitken-Schwarz sont pro- posées et l’étude conduit à l’implémentation d’un code totalement algébrique, sur un ou deux niveaux de parallélisation MPI, écrit dans l’environnement de la biblio- thèque PETSc. Cette implémentation pleinement parallèle et algébrique procure un outil flexible pour la résolution de systèmes linéaires tels que ceux issus de la dif- férentiation automatique des solutions de Navier-Stokes dépendant des paramètres de la simulation / A two level preconditioner, based on the Aitken acceleration technique of a sequence of q interface’s solution vectors of the Restricted Additive Schwarz iterative process, is designed. This new technique, called ARAS(q), uses a coarse approximation of the solution on the interface. Different methods are discussed, leading to the development of an approximation technique by Singular Value De- composition of the sequence of vectors. Parallel implementations of Aitken-Schwarz methods are proposed, and the study leads to a fully algebraic one-level and two- level MPI implementation of ARAS(q) written into the PETSc library framework. This fully parallel and algebraic code gives an adaptive tool to solve linear systems such as those arising from automatic differentiation of compressible Navier-Stokes solution with respect to the simulation’s parameters

The thesis deals with speedup and accuracy of numerical computation, especially when differential equations are solved. Algorithms, which are fulling these conditions are named semi-analytical. One posibility how to accelerate computation of differential equation is paralelization. Presented paralelization is based on transformation numerical solution into residue number system, which is extended to floating point computation. A new algorithm for modulo multiplication is also proposed. As application applications in solution of differential calculus are the main goal it is discussed numeric integration with modified Euler, Runge - Kutta and Taylor series method in residue number system. Next possibilities and extension for implemented residue number system are mentioned at the end.