ABSTRACT
In this chapter, the author reorganises and synthesises material from his last ten years' work. The chapter is organised into four main sections. First, the author summarises the basic theory, the spectral element numerical solution, and focuses on some implementation issues. The method's effectiveness in dealing with real applications is illustrated through the description of two case studies: the strong ground motion estimation in Catania (Sicily, Italy) for a catastrophic earthquake, and the study of the influence of a massive structure on the nearby ground motion.
The Chebyshev spectral element method (SPEM) is a high-order finite element technique, which solves the variational formulation of the equation. The computational domain is decomposed into non-overlapping quadrilateral subdomains. In each subdomain, the solution of the variational problem is expressed as a truncated expansion of Chebyshev orthogonal polynomials, as in the spectral methods. This section describes the mathematical formulation and the modelling algorithm.
