Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jcp.2005.11.019
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dc.titleA splitting moving mesh method for reaction-diffusion equations of quenching type
dc.contributor.authorLiang, K.
dc.contributor.authorLin, P.
dc.contributor.authorOng, M.T.
dc.contributor.authorTan, R.C.E.
dc.date.accessioned2014-10-28T02:29:27Z
dc.date.available2014-10-28T02:29:27Z
dc.date.issued2006-07-01
dc.identifier.citationLiang, K., Lin, P., Ong, M.T., Tan, R.C.E. (2006-07-01). A splitting moving mesh method for reaction-diffusion equations of quenching type. Journal of Computational Physics 215 (2) : 757-777. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jcp.2005.11.019
dc.identifier.issn00219991
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/102766
dc.description.abstractThis paper studies the numerical solution of multi-dimensional nonlinear degenerate reaction-diffusion differential equations with a singular force term over a rectangular domain. The equations may generate strong quenching singularities. Our work focuses on a variable temporal step Peaceman-Rachford splitting method with an adaptive moving mesh in space. The temporal and spatial adaptation is implemented based on arc-length type of estimations of the time derivative of the solution since the time derivative of the solution approaches infinity when the quenching occurs. The multi-dimensional problem is split into a few one-dimensional problems and the splitting procedure can also be parallelized so that the computational time is significantly reduced. The physical monotonicity of the solution and stability of this variable step moving mesh scheme are analyzed for the time away from the quenching. As stability analysis may not be valid when it is very close to the quenching, thus an exact linear problem is introduced to justify the stability near the quenching time. Finally we provide some numerical examples to illustrate our results as well as to demonstrate the viability and efficiency of the method for the quenching problem or other problems with point singularities. We will also show the significant reduction in computational time required with parallel implementation of the algorithm on a computer with multi-CPU. © 2005 Elsevier Inc. All rights reserved.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1016/j.jcp.2005.11.019
dc.sourceScopus
dc.subjectADI monotonicity
dc.subjectMoving mesh method
dc.subjectNonlinear reaction-diffusion equations
dc.subjectParallelization
dc.subjectPeaceman-Rachford splitting
dc.subjectQuenching singularity
dc.typeArticle
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1016/j.jcp.2005.11.019
dc.description.sourcetitleJournal of Computational Physics
dc.description.volume215
dc.description.issue2
dc.description.page757-777
dc.description.codenJCTPA
dc.identifier.isiut000237458200021
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