Math Colloquium: A fast wavelet transform for numerically solving hyperbolic PDEs
A fast wavelet transform for numerically solving hyperbolic PDEs
Dr. David Neilsen
Professor of Physics & Astronomy
Brigham Young University
Many solutions of nonlinear, hyperbolic PDEs have solutions with fine-scale features or even discontinuities, which are difficult to capture numerically. These solutions, however, often have a sparse representation in a wavelet basis, which has multiple scales to efficiently encode information. The interpolating wavelet basis is well adapted to solving PDEs numerically, the fast transform uses polynomial interpolation on dyadic grids, and we add adaptivity by thresholding the wavelet coefficients in the expansions. We have developed a new computer platform, Dendro-GR, to solve PDEs using the interpolating wavelet basis to robustly adapt the spatial resolution. I will present examples from computational fluid dynamics and general relativity.
David Neilsen researches numerical relativity, relativistic fluids, and computational physics at Brigham Young University, where he is Professor of Physics and Astronomy. He received his PhD at the Center for Relativity at the University of Texas at Austin, and was a post-doctoral researcher at UT Austin and Louisiana State University before joining BYU.
All are welcome. Those with interest in the topic.
When and Where
Open to the Public