A quasi-optimal coarse problem and an augmented Krylov solver for the Variational Theory of Complex RaysReport as inadecuate




A quasi-optimal coarse problem and an augmented Krylov solver for the Variational Theory of Complex Rays - Download this document for free, or read online. Document in PDF available to download.

1 Department of Engineering Cambridge 2 LMT - Laboratoire de Mécanique et Technologie

Abstract : The Variational Theory of Complex Rays VTCR is an indirect Trefftz method designed to study systems governed by Helmholtz-like equations. It uses wave functions to represent the solution inside elements, which reduces the dispersion error compared to classical polynomial approaches but the resulting system is prone to be ill conditioned. This paper gives a simple and original presentation of the VTCR using the discontinuous Galerkin framework and it traces back the ill-conditioning to the accumulation of eigenvalues near zero for the formulation written in terms of wave amplitude. The core of this paper presents an efficient solving strategy that overcomes this issue. The key element is the construction of a search subspace where the condition number is controlled at the cost of a limited decrease of attainable precision. An augmented LSQR solver is then proposed to solve efficiently and accurately the complete system. The approach is successfully applied to different examples.

Keywords : Discoutinuous Galerkin Trefftz method Augmented Krylov solver Helmholtz equation Variational Theory of Complex Rays





Author: L Kovalevsky - Pierre Gosselet -

Source: https://hal.archives-ouvertes.fr/



DOWNLOAD PDF




Related documents