Live Coding Session : Verifying Spectral Accuracy in the Advection-Diffusion Solvers has been archived.
Live Coding Session : Verifying Spectral Accuracy in the Advection-Diffusion Solvers has been archived and is no longer active.
Live Coding Session : Verifying Spectral Accuracy in the Advection-Diffusion Solvers
Follow along as Joe works through adding utilities for the advection-diffusion solvers to verify spectral accuracy.
Friday, January 14, 2022, 4:00 PM - 7:00 PM (UTC-06:00)
Created by: Higher Order methods
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News from Live Coding Session : Verifying Spectral Accuracy in the Advection-Diffusion Solvers
Updates on our activities and progress.
A reference for error discussions
As we get closer to our livestream for this week, there are a couple more references that I would like to share with you to help you on your journey in Spectral Element Methods. In this week's whiteboarding session, I'll briefly touch on tr...
Published on January 13, 2022 by Joe Schoonover
Reference Materials
For those of you interested in diving into the literature on spectral element methods, I've got a few references that I've been using to build the content for this and future livestreams I'd like to share. A great book The...
Published on January 13, 2022 by Joe Schoonover
First Draft of Notes Available Online!
Hey everyone! After a few hours of delay on getting these notes together (covid booster shot today), I've gotten the first draft of notes together that outlines the derivation for the DGSEM advection-diffusion solver. There are still a few...
Published on January 7, 2022 by Joe Schoonover
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About this event
At this publicly available livestream, we'll be building out more of the command line interface to add triggers for executing convergence tests. These convergence tests will run a sequence of simulations, gradually increasing the interpolant polynomial degree, while maintaining a fixed CFL number, to measure the max error for scenarios where we can calculate the solution exactly.
Verifying a spectral element method for linear PDEs
In the last quarter of 2021, we finished putting together the advection-diffusion solvers in 2-D and 3-D using the Discontinuous Galerkin Spectral Element Method with Gauss-Legendre Quadrature (NDGSEM). While the solutions qualitatively "look correct", it's time to really make sure that we've actually implemented the NDGSEM to solve the advection-diffusion equations.
Spectral Element Methods enjoy both algebraic and spectral accuracy through h-p refinement strategies. Under p-refinement, we increase the polynomial degree for the interpolants within elements which provides spectral accuracy. This means that the rate of error convergence depends only on how smooth the solution is. For complete functions, with infinitely many derivatives, the rate of error convergence is exponential. We can exploit this fact to develop tests to verify we achieve this kind of error convergence behavior.
Support this livestream
You can support this livestream and other activities in Spectral Element Library in Fortran project by making a donation to the SELF project.
At this publicly available livestream, we'll be building out more of the command line interface to add triggers for executing convergence tests. These convergence tests will run a sequence of simulations, gradually increasing the interpolant polynomial degree, while maintaining a fixed CFL number, to measure the max error for scenarios where we can calculate the solution exactly.
Verifying a spectral element method for linear PDEs
In the last quarter of 2021, we finished putting together the advection-diffusion solvers in 2-D and 3-D using the Discontinuous Galerkin Spectral Element Method with Gauss-Legendre Quadrature (NDGSEM). While the solutions qualitatively "look correct", it's time to really make sure that we've actually implemented the NDGSEM to solve the advection-diffusion equations.
Spectral Element Methods enjoy both algebraic and spectral accuracy through h-p refinement strategies. Under p-refinement, we increase the polynomial degree for the interpolants within elements which provides spectral accuracy. This means that the rate of error convergence depends only on how smooth the solution is. For complete functions, with infinitely many derivatives, the rate of error convergence is exponential. We can exploit this fact to develop tests to verify we achieve this kind of error convergence behavior.
Support this livestream
You can support this livestream and other activities in Spectral Element Library in Fortran project by making a donation to the SELF project.
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