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dc.contributor.authorHuo, Xiaokai
dc.contributor.authorLiu, Hailiang
dc.date.accessioned2019-12-22T13:23:42Z
dc.date.available2019-12-22T13:23:42Z
dc.date.issued2019-12-02
dc.identifier.urihttp://hdl.handle.net/10754/660733
dc.description.abstractWe propose a new fully-discretized finite difference scheme for a quantum diffusion equation, both in 1D and 2D dimensions. The scheme is a first proven positivity-preserving energy stable fully-discretized scheme using standard finite difference discretizations. The difficulty in proving the positivity-preserving property is because the equation is of fourth order in space and maximum principle fails to hold. To overcome this difficulty, we reformulate the scheme as an optimization problem using the variational structure and use the singularity of the energy functional at zero to prove positivenesss of the numerical scheme. The proposed scheme is also shown to be mass conservative and consistent.
dc.description.sponsorshipThe first author is funded by KAUST. The second author is funded by the National Science Foundation under Grant DMS1812666. The authors are grateful to Athanasios E. Tzavaras for valuable suggestions and comments.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/1912.00813
dc.rightsArchived with thanks to arXiv
dc.titleA positivity-preserving energy stable scheme for a quantum diffusion equation
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.eprint.versionPre-print
dc.contributor.institutionIowa State University, Department of Mathematics, Ames, IA
dc.identifier.arxivid1912.00813
kaust.personHuo, Xiaokai
refterms.dateFOA2019-12-22T13:24:19Z


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