Discrete Exterior Calculus

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Ebrahimi, Esmail | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43767 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Esfahani Zadeh, Mostafa; Daneshgar, Amir
Abstract:
In this thesis, a discrete exterior calculus is studied. Discrete exterior calculus is an attempt to create a discrete analogy of differential geometry and topology which is potentially applicable in computer science and physics. At first, simplicial complexes are presented as approximation of smooth manifolds. Then discrete forms and discrete exterior derivative are defined. We will observe that Stokes, theorem can be stated and proved in discrete analogy too. We will obtain Hodge operator by using dual complex and after that discrete Laplacian and Heat kernel will be calculated by using Hodge operator. In addition, we will define discrete vector field independent of discrete forms and then by using interpolation functions we will define discrete sharp and flat operators between vector fields and forms. At last, we will present and study vector calculus operators specially divergence and discrete gradient
Keywords:
Discrete Forms ; Discrete Vector Fields ; Discrete Laplace Operator ; Discrete Divergence

No TOC