Our group focuses on computational mechanics and the efficient numerical solution of time-dependent partial differential equations. Recent work in this group has focused on provably stable and high order accurate methods for time-dependent wave propagation and fluid dynamics, as well as their efficient implementation on Graphics Processing Units (GPUs).
We gratefully acknowledge the support of the NSF (DMS-1719818, DMS-1712639, and DMS-CAREER-1943186) in making this work possible.
- July 2020: Jesse Chan was selected to participate in the NAE’s 26th annual US Frontiers of Engineering Symposium.
- June 2020: our preprint “Efficient computation of Jacobian matrices for entropy stable summation-by-parts schemes” with graduate student Christina G. Taylor is now available on arXiv. We derive the structure of Jacobian matrices for entropy stable formulations based on flux differencing. Numerical examples show how these formulas can be applied to two-derivative and implicit time-stepping schemes.
- June 2020: our paper “A weight-adjusted discontinuous Galerkin method for wave propagation in coupled elastic-acoustic media” with PhD student Kaihang Guo and Prof. Sebastian Acosta was accepted to JCP and is now online.
- May 2020: our preprint Mortar-based entropy-stable discontinuous Galerkin methods on non-conforming quadrilateral and hexahedral meshes with Mario Bencomo and David C. Del Rey Fernandez is now available on arXiv. We derive a new high order accurate and entropy stable non-conforming interface treatment which utilizes specific intermediate mortar layers to reduces computational cost.
- May 2020: our preprint High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration with PhD student Philip Wu and Prof. Ethan Kubatko is now available on arXiv.
- April 2020: graduate student Philip Wu successfully defends his MA thesis.
- April 2020: Jesse Chan gives an online talk for the Electromagnetics Seminar in the Department of Electrical and Computer Engineering at University of Houston.
- March 2020: Jesse Chan gives a plenary talk on “Stable high order methods for time-domain wave propagation in complex geometries and heterogeneous media” at the Rice Oil and Gas HPC conference.
- January 2020: Jesse Chan received an NSF CAREER award from the Division of Mathematical Sciences Comp. Math program.
- January 2020: Jesse Chan gave a talk at the R-STEM/ConocoPhillips Applied Mathematics Program (AMP!) on “Applications of K-12 geometry and algebra: barycentric coordinates”. More information here.
- January 2020: Jesse Chan gave a talk at the University of Houston Dept. of Mathematics.
- December 2019: Jesse Chan gave a talk at the University of Toronto Institute of Aerospace (UTIAS).
- November 2019: graduate students Kaihang Guo and Philip Wu presented work on wave propagation in acoustic-elastic media and entropy stable schemes for the shallow water equations at the SIAM LA-TX sectional meeting in Dallas, TX.
- October 2019: our paper “A weight-adjusted discontinuous Galerkin method for the poroelastic wave equation: penalty fluxes and micro-heterogeneities” with Khemraj Shukla, Maarten V. de Hoop, and Priyank Jaiswal has been accepted to the Journal of Computational Physics.
- September 2019: our preprint “Entropy stable reduced order modeling of nonlinear conservation laws” is available as an arXiv preprint.
- September 2019: Jesse Chan gave a talk to the Computational and Applied Mathematics group at ORNL in Oak Ridge, TN.
- August 2019: our paper “Skew-symmetric entropy stable modal discontinuous Galerkin formulations” was accepted to the Journal of Scientific Computing.