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Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Numerical Analysis and Computation

Utah State University

2018

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Full-Text Articles in Physical Sciences and Mathematics

Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg Dec 2018

Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms …

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Second Order Fully Discrete Energy Stable Methods On Staggered Grids For Hydrodynamic Phase Field Models Of Binary Viscous Fluids, Yuezheng Gong, Jia Zhao, Qi Wang Apr 2018

Second Order Fully Discrete Energy Stable Methods On Staggered Grids For Hydrodynamic Phase Field Models Of Binary Viscous Fluids, Yuezheng Gong, Jia Zhao, Qi Wang

Mathematics and Statistics Faculty Publications

We present second order, fully discrete, energy stable methods on spatially staggered grids for a hydrodynamic phase field model of binary viscous fluid mixtures in a confined geometry subject to both physical and periodic boundary conditions. We apply the energy quadratization strategy to develop a linear-implicit scheme. We then extend it to a decoupled, linear scheme by introducing an intermediate velocity term so that the phase variable, velocity field, and pressure can be solved sequentially. The two new, fully discrete linear schemes are then shown to be unconditionally energy stable, and the linear systems resulting from the schemes are proved …

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