Lecture notes: GE 263 – Computational Geophysics The spectral element method
نویسنده
چکیده
The spectral element method (SEM) is a high order numerical method for solving partial differential equations that inherits the accuracy of spectral methods and the geometrical flexibility of the finite element method. These lectures provide an introduction to the SEM for graduate students in Earth science. The construction of the method is described for a model problem in 1D and 2D. The elements of its mathematical basis, including its connection to spectral methods, are outlined to explain the key choices in the construction of the SEM that lead to an accurate and efficient numerical method. Practical guidelines for programmers and users of the SEM and entry points to advanced topics and to the relevant applied math literature are provided. These lectures were preceded by lectures on the finite difference method (FDM) and the finite element method (FEM). Several concepts from the FEM lectures reappear here, with slightly different notations. We favor redundancy in the hope that the resulting exposition of key practical aspects will contribute to attenuate the perceived complexity of programming the FEM and SEM. These lectures were first taught in Caltech on Winter 2009. ∗California Institute of Technology, Seismological Laboratory, [email protected]
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