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Volume 19, Issue 4
Partition Property of Domain Decomposition Without Ellipticity

Mo Mu & Yun-Qing Huang

J. Comp. Math., 19 (2001), pp. 423-432.

Published online: 2001-08

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  • Abstract

Partition property plays a central role in domain decomposition methods. Existing theory essentially assumes certain ellipticity. We prove the partition property for problems without ellipticity which are of practical importance. Example applications include implicit schemes applied to degenerate parabolic partial differential equations arising from superconductors, superfluids and liquid crystals. With this partition property, Schwarz algorithms can be applied to general non-elliptic problems with an $h$-independent optimal convergence rate. Application to the time-dependent Ginzburg-Landau model of superconductivity is illustrated and numerical results are presented.  

  • Keywords

Partition property, Domain decomposition, Non-ellipticity, Degenerate parabolic problems, Time-dependent Ginzburg-Landau model, Superconductivity, Preconditioning, Schwarz algorithms.

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COPYRIGHT: © Global Science Press

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@Article{JCM-19-423, author = {Mu , Mo and Huang , Yun-Qing}, title = {Partition Property of Domain Decomposition Without Ellipticity}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {4}, pages = {423--432}, abstract = {

Partition property plays a central role in domain decomposition methods. Existing theory essentially assumes certain ellipticity. We prove the partition property for problems without ellipticity which are of practical importance. Example applications include implicit schemes applied to degenerate parabolic partial differential equations arising from superconductors, superfluids and liquid crystals. With this partition property, Schwarz algorithms can be applied to general non-elliptic problems with an $h$-independent optimal convergence rate. Application to the time-dependent Ginzburg-Landau model of superconductivity is illustrated and numerical results are presented.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8994.html} }
TY - JOUR T1 - Partition Property of Domain Decomposition Without Ellipticity AU - Mu , Mo AU - Huang , Yun-Qing JO - Journal of Computational Mathematics VL - 4 SP - 423 EP - 432 PY - 2001 DA - 2001/08 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8994.html KW - Partition property, Domain decomposition, Non-ellipticity, Degenerate parabolic problems, Time-dependent Ginzburg-Landau model, Superconductivity, Preconditioning, Schwarz algorithms. AB -

Partition property plays a central role in domain decomposition methods. Existing theory essentially assumes certain ellipticity. We prove the partition property for problems without ellipticity which are of practical importance. Example applications include implicit schemes applied to degenerate parabolic partial differential equations arising from superconductors, superfluids and liquid crystals. With this partition property, Schwarz algorithms can be applied to general non-elliptic problems with an $h$-independent optimal convergence rate. Application to the time-dependent Ginzburg-Landau model of superconductivity is illustrated and numerical results are presented.  

Mu , Mo and Huang , Yun-Qing. (2001). Partition Property of Domain Decomposition Without Ellipticity. Journal of Computational Mathematics. 19 (4). 423-432. doi:
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