This paper solves the problem of computing conformal structures of general 2manifolds represented as triangular meshes. We approximate the De Rham cohomology by simplicial cohomology and represent the Laplace-Beltrami operator, the Hodge star operator by linear systems. A basis of holomorphic one-forms is constructed explicitly. We then obtain a period matrix by integrating holomorphic differen...

The Hodge dual operator ∗ is one of the 3 basic operations on differential forms. (The other 2 are wedge product ∧ and exterior differentiation d.) However most treatments consider only positive-definite inner products, and there are at least 2 standard ways of generalizing this to inner products of arbitrary signature. We outline here a construction of the Hodge dual operator which works for a...

Two generalisations of the Evans function, for the analysis of the linearisation about solitary waves, are shown to be equivalent. The generalisation introduced by Alexander, Gardner and Jones (1990) is based on exterior algebra and the generalisation introduced by Swinton (1992) is based on a matrix formulation and adjoint systems. In regions of the complex plane where both formulations are de...

Simplicial versions of topological abelian gauge theories are constructed which reproduce the continuum expressions for the partition function and Wilson expectation value of linked loops, expressible in terms of R–torsion and linking numbers respectively. The new feature which makes this possible is the introduction of simplicial fields (cochains) associated with the dual triangulation of the ...

Abstract Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge ...

Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is e...

This paper, the third in a series of three introduces the basics of the theory of extensors that are need for the a theory of multvector and extensor fields in arbitrary manifolds, developed in a following series of five papers. Key notions such as the extension and generalization operators of a given linear operator (a (1, 1)-extensor) acting on a real vector space V are introduced and studied...

This paper, the third in a series of eight introduces some of the basic concepts of the theory of extensors needed for our formulation of the differential geometry of smooth manifolds. Key notions such as the extension and generalization operators of a given linear operator (a (1, 1)-extensor) acting on a real vector space V are introduced and studied in details. Also, we introduce the notion o...