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Research interests:

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:

  • 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.
  • April 2019: Jesse Chan gave a talk at the GMIG project review.
  • April 2019: our preprint “A weight-adjusted discontinuous Galerkin method for the poroelastic wave equation: penalty fluxes and micro-heterogeneities” is available as an arXiv preprint. We introduce provably stable high order DG methods for wave propagation in poroelastic media. Attractive features of the scheme include resolution of sub-cell micro-heterogeneities and simple upwind-like penalty flux terms.
  • February 2019: our preprint “Skew-symmetric entropy stable modal discontinuous Galerkin formulations” is as an arXiv preprint. We construct DG formulations which retain entropy stability under relaxed quadrature accuracy, which are applicable to hybrid meshes with mixed element types.