Helmholtz Solver in unstructured mesh with Spectral Element Method
Date Issued
2005
Date
2005
Author(s)
Hung, Li-Hsin
DOI
zh-TW
Abstract
Helmholtz Solver in unstructured mesh with
Spectral Element Method
Abstract
Due to fast convergence, small diffusion and dispersion errors, higher order numerical methods, such as the spectral element methods have been shown computationally more efficient than the conventional lower order methods in a full Navier Stokes simulations. Traditionally, the element for the spectral element method is in a structured quadrilateral region. The extension from one dimension to higher dimensions is relatively straight forward. In order to broaden the application of spectral element methods to more complex geometries, the use of unstructured elements in the triangular region for two dimensions, and tetrahedral region in three dimensions is to be investigated in this thesis.
The objective of this study is to develop an efficient solver to solve a Helmholtz equation in 2D or 3D unstructured meshed domain. A computer code has been developed. The details of algorithms are addressed in this thesis.
The code is validated by various examples with complex geometries. Different problems with Dirichlet and Neumann boundary conditions are also tested. .
Key Words: spectral element, hp method, finite element, unstructured element, Helmholtz equation
Subjects
寬頻元素
有限元素
非結構性元素
Helmholtz方程式
spectral element
hp method
finite element
unstructured element
Helmholtz equation
Type
thesis
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