A Domain Decomposition Solver for the Discontinuous Enrichment Method for the Helmholtz Equation

Cessenat O., Despres B., Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensionalHelmholtz problem, SIAM J. Numer. Anal., 35, 1, pp. 255-299, (1998)

Farhat C., Roux F.-X., A method of finite element tearing and interconnecting and its parallel solution algorithm, Internat. J. Numer. Meths. Engrg., 32, 6, pp. 1205-1227, (1991)

Farhat C., Macedo A., Lesoinne M., A two-level domain decompositionmethod for the iterative solution of high frequency exterior Helmholtz problems, Numer. Math., 85, 2, pp. 283-308, (2000)

Farhat C., Harari I., Franca L.P., The discontinuous enrichment method, Comput. Methods Appl. Mech. Engrg., 190, 48, pp. 6455-6479, (2001)

Farhat C., Harari I., Hetmaniuk U., A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime, Comput. Methods Appl. Mech. Engrg., 192, 11-12, pp. 1389-1419, (2003)

Farhat C., Tezaur R., Weidemann-Goiran P., Higher-order extensions of a discontinuous Galerkin method for mid-frequency Helmholtz problems, Internat. J. Numer. Methods Engrg., 61, 11, pp. 1938-1956, (2004)

Farhat C., Tezaur R., Toivanen J., A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers, Internat. J. Numer. Methods Engrg., 78, 13, pp. 1513-1531, (2009)

Melenk J.M., Babuska I., The partition of unity finite element method: Basic theory and applications, Comput. Methods Appl. Mech. Engrg., 139, 1-4, pp. 289-314, (1996)

Tezaur R., Farhat C., Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of midfrequency Helmholtz problems, Internat. J. Numer. Methods Engrg., 66, 5, pp. 796-815, (2006)

Wang D., Tezaur R., Toivanen J., Farhat C., Overview of the discontinuous enrichment method, the ultra-weak variational formulation, and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons, Internat. J. Numer. Methods Engrg., 89, 4, pp. 403-417, (2012)

Cessenat O., Despres B., Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensionalHelmholtz problem, SIAM J. Numer. Anal., 35, 1, pp. 255-299, (1998)

Farhat C., Roux F.-X., A method of finite element tearing and interconnecting and its parallel solution algorithm, Internat. J. Numer. Meths. Engrg., 32, 6, pp. 1205-1227, (1991)

Farhat C., Macedo A., Lesoinne M., A two-level domain decompositionmethod for the iterative solution of high frequency exterior Helmholtz problems, Numer. Math., 85, 2, pp. 283-308, (2000)

Farhat C., Harari I., Franca L.P., The discontinuous enrichment method, Comput. Methods Appl. Mech. Engrg., 190, 48, pp. 6455-6479, (2001)

Farhat C., Harari I., Hetmaniuk U., A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime, Comput. Methods Appl. Mech. Engrg., 192, 11-12, pp. 1389-1419, (2003)

Farhat C., Tezaur R., Weidemann-Goiran P., Higher-order extensions of a discontinuous Galerkin method for mid-frequency Helmholtz problems, Internat. J. Numer. Methods Engrg., 61, 11, pp. 1938-1956, (2004)

Farhat C., Tezaur R., Toivanen J., A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers, Internat. J. Numer. Methods Engrg., 78, 13, pp. 1513-1531, (2009)

Melenk J.M., Babuska I., The partition of unity finite element method: Basic theory and applications, Comput. Methods Appl. Mech. Engrg., 139, 1-4, pp. 289-314, (1996)

Tezaur R., Farhat C., Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of midfrequency Helmholtz problems, Internat. J. Numer. Methods Engrg., 66, 5, pp. 796-815, (2006)

Wang D., Tezaur R., Toivanen J., Farhat C., Overview of the discontinuous enrichment method, the ultra-weak variational formulation, and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons, Internat. J. Numer. Methods Engrg., 89, 4, pp. 403-417, (2012)