SIAM Student Chapter Seminar: Difference between revisions
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A vertical Lagrangian coordinate has been used in global climate models for nearly two decades and has several advantages over other discretizations, including reducing the dimensionality of the physical problem. As the Lagrangian surfaces deform over time, it is necessary to accurately and conservatively remap the vertical Lagrangian coordinate back to a fixed Eulerian coordinate. A popular choice of remapping algorithm is the piecewise parabolic method, a modified version of which is used in the atmospheric component of the Department of Energy's Energy Exascale Earth System Model. However, this version of the remapping algorithm creates unwanted noise at the model top and planetary surface for several standard test cases. We explore four alternative modifications to the algorithm and show that the most accurate of these eliminates this noise. | A vertical Lagrangian coordinate has been used in global climate models for nearly two decades and has several advantages over other discretizations, including reducing the dimensionality of the physical problem. As the Lagrangian surfaces deform over time, it is necessary to accurately and conservatively remap the vertical Lagrangian coordinate back to a fixed Eulerian coordinate. A popular choice of remapping algorithm is the piecewise parabolic method, a modified version of which is used in the atmospheric component of the Department of Energy's Energy Exascale Earth System Model. However, this version of the remapping algorithm creates unwanted noise at the model top and planetary surface for several standard test cases. We explore four alternative modifications to the algorithm and show that the most accurate of these eliminates this noise. | ||
=== Nov 29 === | === Nov 29, Bryan Oakley === | ||
The solution to the diffusion equation is known to converge exponentially to its steady state, and the rate is given by the spectral gap of the elliptic operator. Using variational techniques, we will maximize the spectral gap over choices of spatially dependent diffusion functions. Using this characterization, we can obtain bounds on the optimal rate of convergence. | The solution to the diffusion equation is known to converge exponentially to its steady state, and the rate is given by the spectral gap of the elliptic operator. Using variational techniques, we will maximize the spectral gap over choices of spatially dependent diffusion functions. Using this characterization, we can obtain bounds on the optimal rate of convergence. | ||
Revision as of 14:35, 18 October 2021
- When: Mondays at 4 PM
- Where: See list of talks below
- Organizers: Evan Sorensen
- Faculty advisers: Jean-Luc Thiffeault, Steve Wright
- To join the SIAM Chapter mailing list: email siam-chapter+join@g-groups.wisc.edu.
Fall 2021
| date and time | location | speaker | title | |
|---|---|---|---|---|
| Sept 20, 4 PM | Ingraham 214 | Julia Lindberg (Electrical and Computer Engineering) | Polynomial system solving in applications | |
| Sept 27, 4 PM, | Zoom (refreshments and conference call in 307) | Wil Cocke (Developer for ARCYBER) | Job talk-Software Development/Data Science | |
| Oct 4, 2:45 PM | B119 Van Vleck | Anjali Nair (Math) | Reconstruction of Reflection Coefficients Using the Phonon Transport Equation | |
| Oct 18, 4 PM | 6104 Social Sciences | Jason Tochinsky (Math) | Improving the Vertical Remapping Algorithm in the Department of Energy’s Energy Exascale Earth Systems Model | |
| Oct 25, 4 PM, | Zoom (refreshments and conference call in 307) | Patrick Bardsley (Machine Learning Engineer at Cirrus Logic) | ||
| Nov 8, 4 PM, | Zoom (refreshments and conference call in 307) | Liban Mohammed (Machine Learning Engineer at MITRE) | ||
| Nov 15, 4 PM, | Zoom (refreshments and conference call in 307) | Kurt Ehlert (Trading Strategy Developer at Auros) | ||
| Nov 29, 4 PM | TBA | Bryan Oakley (Math) | "Optimal Spatially Dependent Diffusion" | |
| Dec 6, 4 PM | Ingraham 214 | Hongxu Chen (Math) |
Abstracts
Sept 20, Julia Lindberg
Polynomial systems arise naturally in many applications in engineering and the sciences. This talk will outline classes of homotopy continuation algorithms used to solve them. I will then describe ways in which structures such as irreducibility, symmetry and sparsity can be used to improve computational speed. The efficacy of these algorithms will be demonstrated on systems in power systems engineering, statistics and optimization
Sept 27, Wil Cocke
I mostly work as a software developer with an emphasis on data science projects dealing with various Command specific projects. The data science life-cycle is fairly consistent across industries: collect, clean, explore, model, interpret, and repeat with a goal of providing insight to the organization. During my talk, I will share some lessons learned for mathematicians interested in transitioning to software development/ data science.
Oct 4, Anjali Nair
The phonon transport equation is used to model heat conduction in solid materials. I will talk about how we use it to solve an inverse problem to reconstruct the thermal reflection coefficient at an interface. This takes the framework of a PDE constrained optimization problem, and I will also mention the stochastic methods used to solve it.
Oct 18, Jason Torchinsky
A vertical Lagrangian coordinate has been used in global climate models for nearly two decades and has several advantages over other discretizations, including reducing the dimensionality of the physical problem. As the Lagrangian surfaces deform over time, it is necessary to accurately and conservatively remap the vertical Lagrangian coordinate back to a fixed Eulerian coordinate. A popular choice of remapping algorithm is the piecewise parabolic method, a modified version of which is used in the atmospheric component of the Department of Energy's Energy Exascale Earth System Model. However, this version of the remapping algorithm creates unwanted noise at the model top and planetary surface for several standard test cases. We explore four alternative modifications to the algorithm and show that the most accurate of these eliminates this noise.
Nov 29, Bryan Oakley
The solution to the diffusion equation is known to converge exponentially to its steady state, and the rate is given by the spectral gap of the elliptic operator. Using variational techniques, we will maximize the spectral gap over choices of spatially dependent diffusion functions. Using this characterization, we can obtain bounds on the optimal rate of convergence.