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Showing 1 to 7 of 7 for “"Hodge Decomposition"”.
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Application of Helmholtz/Hodge Decomposition to Finite Element Methods for Two-Dimensional Maxwell's Equations
… this work we apply the two-dimensional Helmholtz/Hodge decomposition to develop new finite element schemes for two-dimensional Maxwell's equations. We begin with the introduction of Maxwell's equations and a brief survey of finite element methods for Maxwell's equations. Then we review the related …
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Smoothed particle hydrodynamics
… flow - a pure SPH solution of the Helmholtz-Hodge decomposition. Also, a new version of the Laplacian for SPH is proposed and the advantages and disadvantages of different gradient and Laplacian approximation formulas used in SPH are also discussed. A new treatment of boundary conditions is …
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Extension of the Hodge theorem to certain non-compact manifolds
We prove an analogue of the Hodge cohomology theorem for a certain class of non-compact manifolds. Specifically, let M be a compact manifold with boundary OM, and let g be a metric on Int(M). Assume that there exists a collar neighborhood of the boundary ... We then describe doubly weighted Sobolev …
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The eleven dimensional supergravity equations, resolutions and Lefschetz fiber metrics
… roots of the linearized system using the Hodge decomposition, and using the edge calculus and scattering theory we prove that the moduli space of solutions, near the Freund-Rubin states, is parameterized by three pairs of data on the bounding 6-sphere. In the second part, we consider the …
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Adams Operations and the Dennis Trace Map
… trace map preserves the Adams operations and the Hodge decomposition. In the second part of the thesis we give a tool for comparing the Adams operations on K-theory with the ones on Hochschild homology in the non rational case. We do so by giving a formula for the Dennis trace map, as a map from a …
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Hodge Laplacians on simplicial meshes and graphs
… equations, and our model problem is the Hodge Laplacian Poisson problem on differential k-forms on n dimensional manifolds. One of our major contributions in this work is the computational quantification of the solution using the weak mixed formulation of this problem on simplicial meshes …
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Complex Analysis on Planar Cell Complexes
This paper is an examination of the theory of discrete complex analysis that arises from the framework of a planar cell complex. Construction of this theory is largely integration-based. A combination of two cell complexes, the double and its associated diamond complex, allows for the development …