Doctoral Degrees (High Performance Computing)

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    GPU acceleration of matrix-based methods in computational electromagnetics
    (Stellenbosch : University of Stellenbosch, 2011-03) Lezar, Evan; Davidson, D. B.; University of Stellenbosch. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
    ENGLISH ABSTRACT: This work considers the acceleration of matrix-based computational electromagnetic (CEM) techniques using graphics processing units (GPUs). These massively parallel processors have gained much support since late 2006, with software tools such as CUDA and OpenCL greatly simplifying the process of harnessing the computational power of these devices. As with any advances in computation, the use of these devices enables the modelling of more complex problems, which in turn should give rise to better solutions to a number of global challenges faced at present. For the purpose of this dissertation, CUDA is used in an investigation of the acceleration of two methods in CEM that are used to tackle a variety of problems. The first of these is the Method of Moments (MOM) which is typically used to model radiation and scattering problems, with the latter begin considered here. For the CUDA acceleration of the MOM presented here, the assembly and subsequent solution of the matrix equation associated with the method are considered. This is done for both single and double precision oating point matrices. For the solution of the matrix equation, general dense linear algebra techniques are used, which allow for the use of a vast expanse of existing knowledge on the subject. This also means that implementations developed here along with the results presented are immediately applicable to the same wide array of applications where these methods are employed. Both the assembly and solution of the matrix equation implementations presented result in signi cant speedups over multi-core CPU implementations, with speedups of up to 300x and 10x, respectively, being measured. The implementations presented also overcome one of the major limitations in the use of GPUs as accelerators (that of limited memory capacity) with problems up to 16 times larger than would normally be possible being solved. The second matrix-based technique considered is the Finite Element Method (FEM), which allows for the accurate modelling of complex geometric structures including non-uniform dielectric and magnetic properties of materials, and is particularly well suited to handling bounded structures such as waveguide. In this work the CUDA acceleration of the cutoff and dispersion analysis of three waveguide configurations is presented. The modelling of these problems using an open-source software package, FEniCS, is also discussed. Once again, the problem can be approached from a linear algebra perspective, with the formulation in this case resulting in a generalised eigenvalue (GEV) problem. For the problems considered, a total solution speedup of up to 7x is measured for the solution of the generalised eigenvalue problem, with up to 22x being attained for the solution of the standard eigenvalue problem that forms part of the GEV problem.
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    Modelling subject-specific patellofemoral joint dynamics
    (Stellenbosch : University of Stellenbosch, 2010-12) Muller, Jacobus Hendrik; Scheffer, C.; Elvin, A.; University of Stellenbosch. Faculty of Engineering. Dept. of Mechanical and Mechatronic Engineering.
    ENGLISH ABSTRACT: A methodology to facilitate analysis of dynamic subject-specific patellofemoral function is presented. An enhanced understanding of patellofemoral biomechanics will enable orthopaedic surgeons to identify the mechanisms responsible for imbalances in the joint stabilisers, while also providing objective information on which to base treatment methods. Dynamic patellofemoral function of three volunteers was simulated with a musculoskeletal computational model. The individuals underwent scans from which three-dimensional models of their patellofemoral joints were constructed. Skeletal muscles and soft tissue stabilisers were added to the skeletal models, after which subject-specific motion was simulated. After trochlear engagement, the patellae of the volunteers followed a lateral path, whereas patella tilt was subject-specific. Comparison of the predicted tilt and mediolateral position values at 30 degrees knee flexion to in-vivo MRI values showed a mean accuracy of 62.1 % and 96.9 % respectively. The patellofemoral contact load . quadriceps tendon load ratio varied between 0.7 and 1.3, whereas the mediolateral load component . resultant load ratio ranged between 0 and 0.4. Both parameters. values were similar to previous findings. The medial patellofemoral ligament tension decreased with knee flexion, while the patellar tendon-quadriceps tendon ratio followed a similar trend to that of previous findings (varied between 0.4 and 1.2). After induction of a tubercle osteotomy in the coronal plane, Volunteer One.s patella engaged the trochlear groove at an earlier knee flexion angle, while the patella of Volunteer Two only underwent a small medial displacement. Finite element analyses were employed to investigate the influence of the osteotomy on the patellofemoral pressure distribution. The mean pressure in Volunteer One.s patellofemoral joint was alleviated (17 % smaller) at all angles of flexion with the exception of 60 degrees (12 % greater). Pressure in Volunteer Two.s joint was alleviated at 30 and 45 degrees knee flexion (6 % smaller), while it was elevated (9.1 % greater) at other angles of flexion. Two commercial patellofemoral prostheses were tested on the three Volunteers. joints in the virtual environment. Prosthesis Two delivered patella shift and tilt patterns similar to the baseline values. Patellar tendon tension was slightly greater after resurfacing, with the tensions elevated most with Prosthesis Two. Medial patellofemoral ligament tension was reduced most with Prosthesis Two, while lateral retinaculum tension was increased slightly. Prosthesis Two was the best candidate to reproduce patella kinematics, while the patellofemoral kinetics was largely independent from the type of prosthesis used. The prostheses performed worse for Volunteer Three, supporting the need for the development of patient-specific prostheses. Three validated subject-specific musculoskeletal models facilitated the analysis of the individuals. patellofemoral biomechanics. The technique can potentially be employed by orthopaedic surgeons to visualise the change that an osteotomy or patellofemoral arthroplasty might induce on an individual.s patellofemoral joint. This technique might aid in the development of a tool to assist biomedical engineers in the development of new patellofemoral prostheses. Most importantly, the outcome of surgical intervention may be predicted beforehand, and a treatment procedure may be tailored to optimally fit the patellofemoral biomechanics of that individual.