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Efficient methods for large-scale time-harmonic wave simulations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Marsic, Nicolas |
| Copyright Year | 2016 |
| Abstract | There is a growing consensus that state of the art low-order finite element technology requires, and will continue to require, too extensive computational resources to provide the necessary resolution for complex simulations, even at the rate of computational power increase. The requirement for precise resolution naturally leads to consider methods, with a higher-order of grid convergence than the classical second-order provided by most industrial grade codes. In particular, for high-frequency time-harmonic wave simulations, high-order schemes allow to efficiently resolve the rapid small scale spatial oscillations of the solution, and allow to alleviate the pollution effect. Whitney elements are extensively used to model electromagnetic wave problems, and several high-order extensions have been proposed in the literature. As for standard Lagrange elements, though, the computational cost of solving the linear system of equations rapidly becomes overshadowed by the assembly time of the system itself, as the order of the basis functions increases. The first objective of this thesis is to solve this problem, by reformulating the assembly algorithm into a computationally more efficient procedure. Afterward, this newly developed higher-order approach is tested on different simulations requiring a high precision. Moreover, the application of the finite element method on these high-frequency problems leads to very large, complex and possibly indefinite linear systems. Unfortunately, direct sparse solvers do not scale well for solving such large systems, and Krylov subspace iterative solvers can exhibit slow convergence or even diverge. Domain decomposition methods provide an elegant alternative to these previous techniques, by iterating between sub-problems of smaller sizes, amenable to sparse direct solvers. In this thesis, the emphasis is placed on a particular family of domain decomposition method: the optimized Schwarz algorithm. The second objective of this work is to analyze the performances of this technique, when higher-order finite elements are used. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://orbi.ulg.ac.be/bitstream/2268/192527/1/marsic_phd.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
