Numerical approximations of a norm-preserving gradient flow and applications to an optimal partition problem

Qiang Du; Fanghua Lin

doi:10.1088/0951-7715/22/1/005

Numerical approximations of a norm-preserving gradient flow and applications to an optimal partition problem

Qiang Du, Fanghua Lin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We present and analyse numerical approximations of a norm-preserving gradient flow and consider applications to an optimal eigenvalue partition problem. We consider various discretizations and demonstrate that many of the properties shared by the continuous counterpart can be preserved at the discrete level. The numerical algorithms are then used to study the nonlinear and non-local interfacial dynamics associated with the optimal partition.

Original language	English (US)
Pages (from-to)	67-83
Number of pages	17
Journal	Nonlinearity
Volume	22
Issue number	1
DOIs	https://doi.org/10.1088/0951-7715/22/1/005
State	Published - Jan 1 2009

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)
Applied Mathematics

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10.1088/0951-7715/22/1/005

Cite this

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abstract = "We present and analyse numerical approximations of a norm-preserving gradient flow and consider applications to an optimal eigenvalue partition problem. We consider various discretizations and demonstrate that many of the properties shared by the continuous counterpart can be preserved at the discrete level. The numerical algorithms are then used to study the nonlinear and non-local interfacial dynamics associated with the optimal partition.",

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AB - We present and analyse numerical approximations of a norm-preserving gradient flow and consider applications to an optimal eigenvalue partition problem. We consider various discretizations and demonstrate that many of the properties shared by the continuous counterpart can be preserved at the discrete level. The numerical algorithms are then used to study the nonlinear and non-local interfacial dynamics associated with the optimal partition.

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Numerical approximations of a norm-preserving gradient flow and applications to an optimal partition problem

Abstract

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