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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 modern many-core architectures.

We gratefully acknowledge the support of the NSF (DMS-1719818, and DMS-CAREER-1943186) in making this work possible.

Recent news:

  • May 2022: graduate student Philip (Xinhui) Wu has successfully defended his PhD.
  • May 2022: Jesse Chan gave a talk during the workshop “New trends in numerical methods for hyperbolic conservation laws” at Purdue University.
  • March 2022: our preprint “On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows” is available on arXiv and has been accepted.
  • March 2022: Jesse Chan gave a seminar talk in the Department of Applied Mathematics at Naval Postgraduate School.
  • March 2022: Jesse Chan gave a seminar talk in the Department of Mathematics and Statistics at Mississippi State University.
  • January 2022: our preprint “A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations” with PhD student Yimin Lin and Ignacio Tomas is now on arXiv.
  • December 2021: our preprint “Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws” is now available on arXiv.
  • December 2021: our preprint “Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation” with student Philip (Xinhui) Wu and Nathaniel Trask is now availble on arXiv. In this work, we show how to combine entropy stable schemes with a low order sub-cell positivity preserving scheme. We also extend previous work constructing sparse SBP operators on tensor product elements to triangular elements.
  • November 2021: Mario Bencomo, Yimin Lin, and Jesse Chan gave talks at the SIAM TX-LA conference in South Padre Island.
  • September 2021: our paper “Mortar-based entropy stable discontinuous Galerkin methods for non-conforming quadrilateral and hexahedral meshes” with postdoc Mario Bencomo and David C. Del Rey Fernandez has been accepted to the Journal of Scientific Computing.
  • September 2021: our paper “Efficient computation of Jacobian matrices for entropy stable summation-by-parts schemes” with graduate student Christina G. Taylor has been accepted to JCP.
  • September 2021: our preprint on “Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing” is now available on arXiv.
  • August 2021: our paper “High order weight-adjusted discontinuous Galerkin methods on moving curved meshes” with CAAM alum Kaihang Guo has been accepted to IJNME.
  • August 2021: our paper “A high order discontinuous Galerkin method for the symmetric form of the anisotropic viscoelastic wave equation” with Khemraj Shukla and Maarten V. de Hoop was accepted to CAMWA.
  • July 2021: our paper “Discrete adjoint computations for relaxation Runge-Kutta methods” with postdoc Mario Bencomo is now available on arXiv.
  • July 2021: Jesse Chan, Philip Wu, and Yimin Lin gave talks at USNCCM 16.
  • June 2021: student Philip Wu gave a talk at SIAM Geosciences on high order entropy stable discretizations on networks and multi-dimensional domains.
  • April 2021: Graduate student Christina Taylor successfully defends her MA thesis.
  • April 2021: Graduate student Kaihang Guo successfully defends his PhD thesis.
  • March 2021: Graduate student Christina Taylor was awarded an NSF GRFP.
  • March 2021: our paper “Entropy stable discontinuous Galerkin methods for nonlinear conservation laws on networks and multi-dimensional domains” with grad student Philip Wu was accepted to the Journal of Scientific Computing.
  • Philip Wu, Yimin Lin, Christina Taylor, and Jesse Chan gave talks at SIAM CSE 21.
  • March 2021: Graduate student Yimin Lin was awarded Best Poster at SIAM CSE 21.
  • March 2021: Philip Wu, Yimin Lin, Christina Taylor, and Jesse Chan gave talks at SIAM CSE 21.
  • February 2021: Jesse Chan gave an online talk in the Computational Mathematics seminar within the Mathematics Department at Australian National University.