Volume 24, Issue 3
Domain Decomposition with Nonmatching Grids for Exterior Transmission Problems Via FEM and DTN Mapping

Ju-E Yang & De-Hao Yu

DOI:

J. Comp. Math., 24 (2006), pp. 323-342.

Published online: 2006-06

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  • Abstract

In this paper, we are concerned with a non-overlapping domain decomposition method (DDM) for exterior transmission problems in the plane. Based on the natural boundary integral operator, we combine the DDM with a Dirichlet-to-Neumann (DtN) mapping and provide the numerical analysis with nonmatching grids. The weak continuity of the approximation solutions on the interface is imposed by a dual basis multiplier. We show that this multiplier space can generate optimal error estimate and obtain the corresponding rate of convergence. Finally, several numerical examples confirm the theoretical results.

  • Keywords

Domain decomposition Nature boundary element Nonmatching grids Weak continuity D-N alternating Dual basis Projection operator Error estimate

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@Article{JCM-24-323, author = {}, title = {Domain Decomposition with Nonmatching Grids for Exterior Transmission Problems Via FEM and DTN Mapping}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {3}, pages = {323--342}, abstract = { In this paper, we are concerned with a non-overlapping domain decomposition method (DDM) for exterior transmission problems in the plane. Based on the natural boundary integral operator, we combine the DDM with a Dirichlet-to-Neumann (DtN) mapping and provide the numerical analysis with nonmatching grids. The weak continuity of the approximation solutions on the interface is imposed by a dual basis multiplier. We show that this multiplier space can generate optimal error estimate and obtain the corresponding rate of convergence. Finally, several numerical examples confirm the theoretical results. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8755.html} }
TY - JOUR T1 - Domain Decomposition with Nonmatching Grids for Exterior Transmission Problems Via FEM and DTN Mapping JO - Journal of Computational Mathematics VL - 3 SP - 323 EP - 342 PY - 2006 DA - 2006/06 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8755.html KW - Domain decomposition KW - Nature boundary element KW - Nonmatching grids KW - Weak continuity KW - D-N alternating KW - Dual basis KW - Projection operator KW - Error estimate AB - In this paper, we are concerned with a non-overlapping domain decomposition method (DDM) for exterior transmission problems in the plane. Based on the natural boundary integral operator, we combine the DDM with a Dirichlet-to-Neumann (DtN) mapping and provide the numerical analysis with nonmatching grids. The weak continuity of the approximation solutions on the interface is imposed by a dual basis multiplier. We show that this multiplier space can generate optimal error estimate and obtain the corresponding rate of convergence. Finally, several numerical examples confirm the theoretical results.
Ju-E Yang & De-Hao Yu. (1970). Domain Decomposition with Nonmatching Grids for Exterior Transmission Problems Via FEM and DTN Mapping. Journal of Computational Mathematics. 24 (3). 323-342. doi:
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