Thesis
A fast multipole boundary element method and its application in diffusion problems
Washington State University
Master of Science (MS), Washington State University
2012
Handle:
https://hdl.handle.net/2376/103185
Abstract
Boundary Element Method (BEM) solves partial differential equations by using boundary integral equations (BIEs). In the BEM, only the boundaries of a problem domain need to be discretized. This reduction in dimension brings about many advantages, such as saving computational time and memory in the modeling procedure, which makes it suitable for modeling stress concentration problems, infinite domain problems and thin shell-like structures and materials. When using BEM for large-scale modeling, the solution efficiency has been a major problem due to the dense and nonsymmetrical matrices involved in the computation. To tackle this issue, researchers have applied many fast methods to accelerate BEM solution. Among them, the fast multipole method (FMM) pioneered by Rokhlin and Greengard in the mid-1980s shows a great advantage in efficiency and compatibility with BEM. With the help of FMM, the solutions of BEM can be accelerated by several folds to reduce the computation time. One of the areas that simulation and numerical methods are frequently used in both v engineering and research is diffusion related problems. Researchers have successfully developed the conventional BEM for solving diffusion problems. However, with the growing demand for simulating large engineering models, the limitation in efficiency and memory storage of conventional BEM is becoming a big concern. In fact, a realistic model can reach a million-level of degrees of freedom in BEM. For this reason, FMM is considered as a candidate to accelerate the conventional BEM. This work aims to develop a new fast multipole boundary element method (FMBEM) that can solve the linear problems in dynamic states, especially the diffusion process. In the thesis, we first review the BIE and the conventional BEM procedures for diffusion problems. Based on this, we propose our own fast multipole algorithm. Then the realization of FMBEM is introduced. The method is further developed by introducing the discontinuous linear element, which can improve the accuracy of FMBEM. A numerical example is tested using both conventional BEM and FMBEM to analyze the performance of the new method. Finally, we show several applications of the FMBEM in solving realistic problems that can be described by diffusion equation.
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Details
- Title
- A fast multipole boundary element method and its application in diffusion problems
- Creators
- Bo Wang
- Contributors
- Linda Chen (Degree Supervisor)
- Awarding Institution
- Washington State University
- Academic Unit
- Mechanical and Materials Engineering, School of
- Theses and Dissertations
- Master of Science (MS), Washington State University
- Publisher
- Washington State University; Pullman, Wash. :
- Identifiers
- 99900525184801842
- Language
- English
- Resource Type
- Thesis