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.
- December 2020: Jesse Chan gave an online talk at the LLNL Data-driven physical simulation seminar.
- November 2020: our preprint Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations is now up on arXiv. We extend the entropy stable treatment of viscous terms to general “modal” DG formulations, which also enables a simple and explicit entropy stable treatment wall boundary conditions.
- November 2020: Jesse Chan gave an online talk at CU Boulder’s Ann and HJ Smead Aerospace Engineering Sciences Department.
- November 2020: our paper High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration with PhD student Xinhui (Philip) Wu and Prof. Ethan J. Kubatko was accepted to CAMWA.
- November 2020: our preprint A high order discontinuous Galerkin method for the symmetric form of the anisotropic viscoelastic wave equation is now online. We derive a symmetric form of the anisotropic viscoelastic wave equation which is then used to construct a stable high order DG formulation.
- October 2020: Jesse Chan gave an online talk at the SIAM TX-LA sectional meeting.
- October 2020: our preprint Entropy stable discontinuous Galerkin methods for nonlinear conservation laws on networks and multi-dimensional domains is now online. We show how to couple together three or more 1D channels or 1D and 2D domains in an entropy stable fashion, assuming that the simulations on each individual domain/channel are entropy stable.
- September 2020: our preprint High order weight-adjusted discontinuous Galerkin methods for wave propagation on moving curved meshes is now online. We show that by using weight-adjusted mass matrices (a generalization of mass lumping) an Arbitrary Lagrangian-Eulerian formulation, we can avoid the cost of assembling and inverting matrices on moving curved meshes while retaining energy stability up to a term which rapidly converges to zero.
- September 2020: Yimin Lin has successfully passed his MA thesis defense.
- September 2020: Kaihang Guo has successfully passed his PhD proposal.
- 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 J. 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 Xinhui (Philip) Wu and Prof. Ethan Kubatko is now available on arXiv.
- April 2020: graduate student Xinhui (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.