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Computational Aspects of the Ultra-Weak Variational Formulation

✍ Scribed by Tomi Huttunen; Peter Monk; Jari P. Kaipio

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
337 KB
Volume
182
Category
Article
ISSN
0021-9991

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✦ Synopsis

The ultra-weak variational formulation (UWVF) approach has been proposed as an effective method for solving Helmholtz problems with high wave numbers. However, for coarse meshes the method can suffer from instability. In this paper we consider computational aspects of the ultra-weak variational formulation for the inhomogeneous Helmholtz problem. We introduce a method to improve the UWVF scheme and we compare iterative solvers for the resulting linear system. Computations for the acoustic transmission problem in 2D show that the new approach enables Helmholtz problems to be solved on a relatively coarse mesh for a wide range of wave numbers.

πŸ“œ SIMILAR VOLUMES

Application of the variational Germano i
Application of the variational Germano identity to the variational multiscale formulation
✍ A. A. Oberai; D. Sondak πŸ“‚ Article πŸ“… 2011 πŸ› Wiley (John Wiley & Sons) 🌐 English βš– 197 KB

We examine the connection between the variational multiscale (VMS) formulation and the variational counterpart of the Germano identity (VGI). We note that they are both based on the same multiscale construct of a given coarse scale space and a user-defined projector into this space, which defines th