This chapter completes the multi-dimensional formulation by explaining how the two- and three-dimensional expansions developed in Chapter 3 can be extended into a tessellation of multiple domains. These extensions are decomposed into three sections: local operations such as integration and differentiation; global operations such as the construction of global matrix systems; and pre- and post-processing issues such as boundary representation, high-order mesh generation, and particle tracking. A matrix formulation is introduced to help illustrate the algebraic systems that need to be constructed when computationally implementing the spectral/hp method. Formulation of both Galerkin and collocation projections are considered in this manner. The exercises at the end of the chapter include implementation of a two-dimensional spectral/hp element solver for a multi-element Galerkin projection.
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