Volume 11, Issue 2
A Modified Discontinuous Galerkin Method for Solving Efficiently Helmholtz Problems

Magdalena Grigoroscuta-Strugaru, Mohamed Amara, Henri Calandra & Rabia Djellouli

Commun. Comput. Phys., 11 (2012), pp. 335-350.

Published online: 2012-12

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  • 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. 

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@Article{CiCP-11-335, author = {}, title = {A Modified Discontinuous Galerkin Method for Solving Efficiently Helmholtz Problems}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {2}, pages = {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. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.081209.070710s}, url = {http://global-sci.org/intro/article_detail/cicp/7365.html} }
TY - JOUR T1 - A Modified Discontinuous Galerkin Method for Solving Efficiently Helmholtz Problems JO - Communications in Computational Physics VL - 2 SP - 335 EP - 350 PY - 2012 DA - 2012/12 SN - 11 DO - http://doi.org/10.4208/cicp.081209.070710s UR - https://global-sci.org/intro/article_detail/cicp/7365.html KW - AB -

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. 

Magdalena Grigoroscuta-Strugaru, Mohamed Amara, Henri Calandra & Rabia Djellouli. (2020). A Modified Discontinuous Galerkin Method for Solving Efficiently Helmholtz Problems. Communications in Computational Physics. 11 (2). 335-350. doi:10.4208/cicp.081209.070710s
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