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Volume 11, Issue 4
A Parallel Variational Multiscale Method for Incompressible Flows Based on the Partition of Unity

C. Xie & H. Zheng

Int. J. Numer. Anal. Mod., 11 (2014), pp. 854-865.

Published online: 2014-11

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  • Abstract

A parallel variational multiscale method based on the partition of unity is proposed for incompressible flows in this paper. Based on two-grid method, this algorithm localizes the global residual problem of variational multiscale method into a series of local linearized residual problems. To decrease the undesirable effect of the artificial homogeneous Dirichlet boundary condition of local sub-problems, an oversampling technique is also introduced. The globally continuous finite element solutions are constructed by assembling all local solutions together using the partition of unity functions. Numerical simulations demonstrate the high efficiency and flexibility of the new algorithm.

  • Keywords

Incompressible flows, variational multiscale method, local and parallel, partition of unity, oversampling.

  • AMS Subject Headings

65N30, 65M55, 76D07, 76M10

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-11-854, author = {C. Xie and H. Zheng}, title = {A Parallel Variational Multiscale Method for Incompressible Flows Based on the Partition of Unity}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {4}, pages = {854--865}, abstract = {

A parallel variational multiscale method based on the partition of unity is proposed for incompressible flows in this paper. Based on two-grid method, this algorithm localizes the global residual problem of variational multiscale method into a series of local linearized residual problems. To decrease the undesirable effect of the artificial homogeneous Dirichlet boundary condition of local sub-problems, an oversampling technique is also introduced. The globally continuous finite element solutions are constructed by assembling all local solutions together using the partition of unity functions. Numerical simulations demonstrate the high efficiency and flexibility of the new algorithm.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/555.html} }
TY - JOUR T1 - A Parallel Variational Multiscale Method for Incompressible Flows Based on the Partition of Unity AU - C. Xie & H. Zheng JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 854 EP - 865 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/555.html KW - Incompressible flows, variational multiscale method, local and parallel, partition of unity, oversampling. AB -

A parallel variational multiscale method based on the partition of unity is proposed for incompressible flows in this paper. Based on two-grid method, this algorithm localizes the global residual problem of variational multiscale method into a series of local linearized residual problems. To decrease the undesirable effect of the artificial homogeneous Dirichlet boundary condition of local sub-problems, an oversampling technique is also introduced. The globally continuous finite element solutions are constructed by assembling all local solutions together using the partition of unity functions. Numerical simulations demonstrate the high efficiency and flexibility of the new algorithm.

C. Xie and H. Zheng. (2014). A Parallel Variational Multiscale Method for Incompressible Flows Based on the Partition of Unity. International Journal of Numerical Analysis and Modeling. 11 (4). 854-865. doi:
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