GPU acceleration of matrix-based methods in computational electromagnetics

[摘要] ENGLISH ABSTRACT: This work considers the acceleration of matrix-based computational electromagnetic (CEM)techniques using graphics processing units (GPUs). These massively parallel processors havegained much support since late 2006, with software tools such as CUDA and OpenCL greatlysimplifying the process of harnessing the computational power of these devices. As with anyadvances 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 facedat present.For the purpose of this dissertation, CUDA is used in an investigation of the accelerationof two methods in CEM that are used to tackle a variety of problems. The first of these is theMethod 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 areconsidered. 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 meansthat implementations developed here along with the results presented are immediately applicableto the same wide array of applications where these methods are employed.Both the assembly and solution of the matrix equation implementations presented result insigni cant speedups over multi-core CPU implementations, with speedups of up to 300x and10x, respectively, being measured. The implementations presented also overcome one of themajor limitations in the use of GPUs as accelerators (that of limited memory capacity) withproblems up to 16 times larger than would normally be possible being solved.The second matrix-based technique considered is the Finite Element Method (FEM), whichallows for the accurate modelling of complex geometric structures including non-uniform dielectricand magnetic properties of materials, and is particularly well suited to handling boundedstructures such as waveguide. In this work the CUDA acceleration of the cutoff and dispersionanalysis of three waveguide configurations is presented. The modelling of these problems usingan open-source software package, FEniCS, is also discussed.Once again, the problem can be approached from a linear algebra perspective, with theformulation in this case resulting in a generalised eigenvalue (GEV) problem. For the problemsconsidered, a total solution speedup of up to 7x is measured for the solution of the generalisedeigenvalue problem, with up to 22x being attained for the solution of the standard eigenvalueproblem that forms part of the GEV problem.

[发布机构] Stellenbosch University