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Full-Text Articles in Physical Sciences and Mathematics
The Auxiliary Space Preconditioner For The De Rham Complex, Jay Gopalakrishnan, Martin Neumüller, Panayot S. Vassilevski
The Auxiliary Space Preconditioner For The De Rham Complex, Jay Gopalakrishnan, Martin Neumüller, Panayot S. Vassilevski
Portland Institute for Computational Science Publications
We generalize the construction and analysis of auxiliary space preconditioners to the n-dimensional finite element subcomplex of the de Rham complex. These preconditioners are based on a generalization of a decomposition of Sobolev space functions into a regular part and a potential. A discrete version is easily established using the tools of finite element exterior calculus. We then discuss the four-dimensional de Rham complex in detail. By identifying forms in four dimensions (4D) with simple proxies, form operations are written out in terms of familiar algebraic operations on matrices, vectors, and scalars. This provides the basis for our implementation of …
Derivation Of The Hellinger-Reissner Variational Form Of The Linear Elasticity Equations, And A Finite Element Discretization, Bram Fouts
REU Final Reports
In this paper we are going to derive the linear elasticity equations in the Strong Form to the Hellinger Reissner Form. We find a suitable solution to solve our stress tensor. Then we will use finite element discretization from. We will run tests on a unit cube and multiple other shapes, which are described at the end. We view the different magnitudes of the displacement vector of each shape.