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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 and DMS-1712639) in making this work possible.

Recent news:

  • 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” 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.
  • July 2019: Jesse Chan and Kaihang Guo give talks at USNCCM 2019 in Austin, TX.
  • July 2019: our paper “Efficient entropy stable Gauss collocation methods” was accepted to the SIAM Journal on Scientific Computing.
  • July 2019: Jesse Chan gave a talk at ICIAM 2019 in Valencia, Spain.
  • June 2019: Jesse Chan gave a talk at the R-STEM ConocoPhillips Applied Mathematics Program (AMP!).
  • June 2019: Jesse Chan gave a talk at NAHOM 2019 in San Diego, CA.
  • May 2019: our preprint “A weight-adjusted discontinuous Galerkin method for wave propagation in coupled elastic-acoustic media” is available as an arXiv preprint, and introduces a new provably stable high order DG methods for wave propagation in coupled acoustic-elastic media. As with previous weight-adjusted DG papers, the method is time-explicit, high order accurate, and applicable to sub-cell micro heterogeneities, anisotropic media, and curved meshes.