文章基本信息

标题：Stokes-Dirac operator for Laplacian ⁎
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作者：Gou Nishida ; Bernhard Maschke
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2019
卷号：52
期号：16
页码：430-435
DOI：10.1016/j.ifacol.2019.11.818
语种：English
出版社：Elsevier
摘要：This paper proposes a particular type of Stokes-Dirac structure for describing a Laplacian used in Poisson’s equations on topologically non-trivial manifolds, i.e., not Euclidian. The operator matrix representation of the structure includes not only exterior differential operators, but also codifferential operators in the sense of the dual of the pairing between differential forms. Since the successive operation of the matrix is equivalent to the Laplace-Beltrami operator, we call it a Stokes-Dirac operator. Furthermore, the Stokes-Dirac operator is augmented by harmonic differential forms that reflect the topological geometry of manifolds. The extension enable us to describe a power balance of particular boundary energy flows on manifolds with a non-trivial shape.
关键词：KeywordsPort-Hamiltonian systemsStokes-Dirac structuresPartial differential equationsDifferential forms