Year: 2012
Communications in Computational Physics, Vol. 11 (2012), Iss. 2 : pp. 335–350
Abstract
A new solution methodology is proposed for solving efficiently Helmholtz problems. The proposed method falls in the category of the discontinuous Galerkin methods. However, unlike the existing solution methodologies, this method requires solving (a) well-posed local problems to determine the primal variable, and (b) a global positive semi-definite Hermitian system to evaluate the Lagrange multiplier needed to restore the continuity across the element edges. Illustrative numerical results obtained for two-dimensional interior Helmholtz problems are presented to assess the accuracy and the stability of the proposed solution methodology.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.081209.070710s
Communications in Computational Physics, Vol. 11 (2012), Iss. 2 : pp. 335–350
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
-
Mortar Coupling of hp-Discontinuous Galerkin and Boundary Element Methods for the Helmholtz Equation
Erath, Christoph | Mascotto, Lorenzo | Melenk, Jens M. | Perugia, Ilaria | Rieder, AlexanderJournal of Scientific Computing, Vol. 92 (2022), Iss. 1
https://doi.org/10.1007/s10915-022-01849-0 [Citations: 3] -
DG and hp‐DG for highly indefinite Helmholtz problems
Melenk, Jens Markus | Parsania, Asieh | Sauter, StefanPAMM, Vol. 13 (2013), Iss. 1 P.443
https://doi.org/10.1002/pamm.201310215 [Citations: 0] -
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
A Survey of Trefftz Methods for the Helmholtz Equation
Hiptmair, Ralf | Moiola, Andrea | Perugia, Ilaria2016
https://doi.org/10.1007/978-3-319-41640-3_8 [Citations: 39] -
General DG-Methods for Highly Indefinite Helmholtz Problems
Melenk, J. M. | Parsania, A. | Sauter, S.Journal of Scientific Computing, Vol. 57 (2013), Iss. 3 P.536
https://doi.org/10.1007/s10915-013-9726-8 [Citations: 67] -
A Posteriori Error Estimation of $hp$-$dG$ Finite Element Methods for Highly Indefinite Helmholtz Problems
Sauter, S. | Zech, J.SIAM Journal on Numerical Analysis, Vol. 53 (2015), Iss. 5 P.2414
https://doi.org/10.1137/140973955 [Citations: 13] -
An Element Decomposition Method for the Helmholtz Equation
Wang, Gang | Cui, Xiangyang | Li, GuangyaoCommunications in Computational Physics, Vol. 20 (2016), Iss. 5 P.1258
https://doi.org/10.4208/cicp.110415.240316a [Citations: 6]