Open AccessBook
Finite Element Analysis of Acoustic Scattering
Frank Ihlenburg
- 13 Aug 1998
TL;DR: A cognitive journey towards the reliable simulation of scattering problems using finite element methods, with the pre-asymptotic analysis of Galerkin FEM for the Helmholtz equation with moderate and large wave number forming the core of this book, is described in this article.
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Abstract: A cognitive journey towards the reliable simulation of scattering problems using finite element methods, with the pre-asymptotic analysis of Galerkin FEM for the Helmholtz equation with moderate and large wave number forming the core of this book. Starting from the basic physical assumptions, the author methodically develops both the strong and weak forms of the governing equations, while the main chapter on finite element analysis is preceded by a systematic treatment of Galerkin methods for indefinite sesquilinear forms. In the final chapter, three dimensional computational simulations are presented and compared with experimental data. The author also includes broad reference material on numerical methods for the Helmholtz equation in unbounded domains, including Dirichlet-to-Neumann methods, absorbing boundary conditions, infinite elements and the perfectly matched layer. A self-contained and easily readable work.
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Citations
•Book
Finite Element Analysis
B. A. Szabó,Ivo Babuška +1 more
- 29 Mar 1991
TL;DR: In this article, the authors present a general solution based on the principle of virtual work for two-dimensional linear elasticity problems and their convergence rates in one-dimensional dimensions. But they do not consider the case of three-dimensional LEL problems.
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Fluid‐Structure Interaction Problems
Roger Ohayon,Jean-Sébastien Schotté +1 more
- 15 Nov 2004
TL;DR: In this paper, reduced order models leading to symmetric matrix systems are described using static well-posed behavior of the irrotational fluid, and the fluid-structure boundary value local equations, expressed in terms of fluid scalar field variables for the fluid and displacement variables for structure, are regularized for zero-frequency limit.
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Finite elements in computational electromagnetism
TL;DR: In this paper, finite element Galerkin schemes for a number of linear model problems in electromagnetism were discussed, and the finite element schemes were introduced as discrete differential forms, matching the coordinate-independent statement of Maxwell's equations in the calculus of differential forms.
A review of finite-element methods for time-harmonic acoustics
TL;DR: State-of-the-art finite-element methods for time-harmonic acoustics governed by the Helmholtz equation are reviewed and Mesh resolution to control phase error and bound dispersion or pollution errors measured in global norms for large wave numbers in finite- element methods are described.
412
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
TL;DR: For the small wave-number limit hk → 0, it is shown the discontinuous Galerkin gives a higher order of accuracy than the standardGalerkin procedure, thereby confirming the conjectures of Hu and Atkins.
334
References
An observation concerning Ritz-Galerkin methods with indefinite bilinear forms
TL;DR: Schatz et al. as mentioned in this paper considered the Ritz-Galerkin method with a bilinear form and showed that the existence and uniqueness of the method can be established in a priori.
Diffraction and refraction of surface waves using finite and infinite elements
Peter Bettess,O. C. Zienkiewicz +1 more
TL;DR: In this article, the wave problem is introduced and a derivation of Berkhoff's surface wave theory is outlined, and appropriate boundary conditions are described, for finite and infinite boundaries.
456
On the coupling of boundary integral and finite element methods
Claes Johnson,J.-Claude Nédélec +1 more
TL;DR: In this article, the error estimates for a procedure obtained by combining the boundary integral method and the usual finite element method are shown. But they are only for a special case of the problem described in this paper.