Idealization of Wave Propagation and Solution Techniques
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In this chapter, all the necessary tools required for the spectral element formulation are derived. The most important of these is the determination of wavenumbers and wave amplitudes. An nth-order differential equation will yield an nth-order characteristic equation for the wavenumbers, which are normally difficult to solve. Here, we adopt some traditional techniques based on the theory of linear algebra to solve for wavenumbers and wave amplitudes. This chapter also describes the general spectral finite element formulation procedure, which is applied to form elements for isotropic waveguides.
KeywordsSingular Value Decomposition Discrete Fourier Transform Companion Matrix Spectral Element Inhomogeneous Wave
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