The finite element method is a numerical method used to solve partial differential equations. GPUs are special computing units that can perform many simple operations in parallel. If the problem is parallelisable, the GPU will often be more cost or energy efficient at solving the problem. The aim of this project, is to explore how GPUs can be used to solve FEM problems. The wave equation is discretised with hat functions and Hermite polynomials. The problem is then time integrated with Runge-kutta 4 and three solvers are used to compute the derivates of each step; a direct Gaussian solver, a direct solver with LU-decomposition and a conjugate gradient solver. The project found that some operations, especially linear algebra operations, were highly parallelisable and suitable for GPUs. This made the conjugate gradient solver, a good choice for GPU-computing. Conversely, direct solvers were harder to parallelise, as each row must be computed serially. In general, the GPU was faster for all relevant grid sizes.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-531342 |
| Date | January 2024 |
| Creators | Eric, Björfors, Jesper, Carlsson, William, Ekberg, Albin, Liljefors, Erik, Näslund |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | MATVET-F ; 24008 |
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