Titlebook: Higher-Order Numerical Methods for Transient Wave Equations; Gary C. Cohen Book 2002 Springer-Verlag Berlin Heidelberg 2002 Finite Differe

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Stability of the Schemeshis has already been done by specialists (see for example [58] or [62]). What we are going to do here is give an intuitive approach to the notion of stability of a scheme for the wave equations. This approach is actually based on plane wave solutions which can be regarded as elementary solutions of the wave equations, as we saw in Sect. 3.1.

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Spectral Elementsm the 1D case by the means of Cartesian and tensor products. In order to construct spectral elements on non-regular meshes, we must first introduce the reference elements, i.e. elements defined on the unit square or the unit cube.

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Modeling Unbounded Domainsesting part of the solution is often located around the obstacle which is a small part of the domain of propagation. On the other hand, the whole domain of propagation is generally too large to be taken into account by a numerical model on a computer.

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Mass-Lumped Mixed Formulations and Edge Elements the following, we shall study quadrilateral and hexahedral edge elements with mass-lumping. More precisely, this section will deal with the so-called first family of Nédélec’s (or edge) elements [92] on orthogonal meshes.

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Book 2002nd presents the most efficient methods, respecting both accuracy and stability for each sort of problem. A central role is played by the notion of the dispersion relation for analyzing the methods. The last chapter is devoted to unbounded domains which are modeled using perfectly matched layer (PML) techniques. Numerical examples are given.

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Book 2002h and industry. To attack the problems coming from the propagative character of the solution, the author constructs higher-order numerical methods to reduce the size of the meshes, and consequently the time and space stepping, dramatically improving storage and computing times. This book surveys hig

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