Volume 8, Issue 4
A Lions Domain Decomposition Algorithm for Radiation Diffusion Equations on Non-Matching Grids

Li Yin, Jiming Wu & Zihuan Dai

Numer. Math. Theor. Meth. Appl., 8 (2015), pp. 530-548.

Published online: 2015-08

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  • Abstract

We develop a Lions domain decomposition algorithm based on a cell functional minimization scheme on non-matching multi-block grids for nonlinear radiation diffusion equations, which are described by the coupled radiation diffusion equations of electron, ion and photon temperatures. The $L^2$ orthogonal projection is applied in the Robin transmission condition of non-matching surfaces. Numerical results show that the algorithm keeps the optimal accuracy on the whole computational domain, is robust enough on distorted meshes and curved surfaces, and the convergence rate does not depend on Robin coefficients. It is a practical and attractive algorithm in applying to the two-dimensional three-temperature energy equations of Z-pinch implosion simulation.

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@Article{NMTMA-8-530, author = {}, title = {A Lions Domain Decomposition Algorithm for Radiation Diffusion Equations on Non-Matching Grids}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2015}, volume = {8}, number = {4}, pages = {530--548}, abstract = {

We develop a Lions domain decomposition algorithm based on a cell functional minimization scheme on non-matching multi-block grids for nonlinear radiation diffusion equations, which are described by the coupled radiation diffusion equations of electron, ion and photon temperatures. The $L^2$ orthogonal projection is applied in the Robin transmission condition of non-matching surfaces. Numerical results show that the algorithm keeps the optimal accuracy on the whole computational domain, is robust enough on distorted meshes and curved surfaces, and the convergence rate does not depend on Robin coefficients. It is a practical and attractive algorithm in applying to the two-dimensional three-temperature energy equations of Z-pinch implosion simulation.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.m1403}, url = {http://global-sci.org/intro/article_detail/nmtma/12422.html} }
TY - JOUR T1 - A Lions Domain Decomposition Algorithm for Radiation Diffusion Equations on Non-Matching Grids JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 530 EP - 548 PY - 2015 DA - 2015/08 SN - 8 DO - http://doi.org/10.4208/nmtma.2015.m1403 UR - https://global-sci.org/intro/article_detail/nmtma/12422.html KW - AB -

We develop a Lions domain decomposition algorithm based on a cell functional minimization scheme on non-matching multi-block grids for nonlinear radiation diffusion equations, which are described by the coupled radiation diffusion equations of electron, ion and photon temperatures. The $L^2$ orthogonal projection is applied in the Robin transmission condition of non-matching surfaces. Numerical results show that the algorithm keeps the optimal accuracy on the whole computational domain, is robust enough on distorted meshes and curved surfaces, and the convergence rate does not depend on Robin coefficients. It is a practical and attractive algorithm in applying to the two-dimensional three-temperature energy equations of Z-pinch implosion simulation.

Li Yin, Jiming Wu & Zihuan Dai. (2020). A Lions Domain Decomposition Algorithm for Radiation Diffusion Equations on Non-Matching Grids. Numerical Mathematics: Theory, Methods and Applications. 8 (4). 530-548. doi:10.4208/nmtma.2015.m1403
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