News archive
News archive
Dec 2024: the arXiv preprint of "An Entropy Stable High-Order Discontinuous Galerkin Method on Cut Meshes" by recent graduate Christina Taylor is now available.
Dec 2024: Jesse Chan gave an invited talk at the Jameson-Kim-Wang Birthday Conference.
Nov 2024: the arXiv preprint of "A robust first order meshless method for time-dependent nonlinear conservation laws" with undergraduate Samuel Kwan is now available.
Nov 2024: Our paper "An Energy Stable High-Order Cut Cell DG Method with State Redistribution for Wave Propagation" with group alum Christina G. Taylor was accepted to the Journal of Computational Physics.
Oct 2024: Jesse Chan served on a career panel for the Rice INFORMS student chapter.
Oct 2024: Raven S. Johnson, Brian Christner, Raymond Park, Samuel Kwan (UG), Vincent Wang (UG), and Jesse Chan presented talks and posters at the SIAM TXLA 2024 Annual Meeting.
Oct 2024: Raven S. Johnson, Brian Christner, Raymond Park, and Vincent Wang (UG) presented talks and posters at the Annual NASC RTG Workshop
Sept 2024: Ray Qu presented a poster at the MORe2024 conference and successfully defended his MA thesis.
August 2024: Jesse Chan gave a talk at the NASA Ames AMS seminar
August 2024: Beatrice Riviere, Jesse Chan, and Matthias Heinkenschloss ran the RTG "High School Summer Internship" program for rising juniors
July 2024: Jesse Chan, Ray Qu, Raven S. Johnson, and Christina G. Taylor gave talks at WCCM 2024 in Vancouver.
July 2024: Jesse Chan gave a plenary talk at ICCFD 12 in Kobe, Japan.
July 2024: Christina G. Taylor successfully defended her PhD thesis on "Energy and Entropy Stable Cut-cell Discontinuous Galerkin Methods"
June 2024: Raven S. Johnson, Yimin Lin, and Jesse Chan gave talks at the NAHOMCon 2024 conference.
June 2024: Raven S. Johnson, Raymond Park, and Jesse Chan gave talks on mathematical modeling, mathematics and music, and mathematics and poetry to Houston-area high school students as part of the Summer Math Days outreach program.
April 2024: our paper “An Energy Stable High-Order Cut Cell Discontinuous Galerkin Method with State Redistribution for Wave Propagation” with Christina G. Taylor and Lucas C. Wilcox (NPS) is now available on arXiv.
March 2024: Jesse Chan presented at the 2024 ALGORITMY conference.
March 2024: Jesse Chan and Beatrice Riviere organized the 2024 Finite Element Rodeo.
December 2023: graduate student Christina Taylor successfully defended their PhD proposal.
November 2023: graduate student Yimin Lin successfully defended their PhD defense.
October 2023: graduate student Raven S. Johnson successfully defended their MA thesis.
October 2023: graduate students Yimin Lin, Christina G. Taylor, and Raven S. Johnson presented talks at the first RTG-NASC workshop. Ray Qu presented a poster.
October 2023: Jesse Chan gave a talk in the Dept. of Applied Math at Brown University.
September 2023: Our paper “Efficient implementation of modern entropy-based discontinuous Galerkin methods for conservation laws” with the developers of Trixi.jl and FLEXI was accepted at ACM: Transactions on Mathematical Software.
September 2023: Jesse Chan gave a talk in the Numerical Analysis Seminar at University of Maryland College Park.
August 2023: our preprint “High order entropy stable schemes for the quasi-one-dimensional shallow water and compressible Euler equations” with undergraduate students Ruofeng Liu and Prani Nalluri (as well as alumni Xinhui Wu) is now available on arXiv.
July 2023: Jesse Chan’s interview with the Houston Asian American Archive is on Youtube
June 2023: our preprint “High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting” with PhD student Yimin Lin is now available on arXiv.
May 2023: Jesse Chan presented a virtual talk at Princeton Plasma Physics Laboratory.
May 2023: Beatrice Riviere, Matthias Heinkenschloss, and Jesse Chan were awarded an NSF RTG grant.
March 2023: Jesse Chan was elected Secretary for the SIAM TX-LA section.
March 2023: Yimin Lin successfully passed his PhD proposal, and will continue to work towards his PhD defense.
March 2023: Jesse Chan presented at the Finite Element Rodeo at Texas A&M.
March 2023: Christina G. Taylor and Jesse Chan presented at SIAM CSE 2023 in Amsterdam.
February 2023: Our paper “Discrete Adjoint Computations for Relaxation Runge–Kutta Methods” with Mario Bencomo was accepted to Journal of Scientific Computing.
January 2023: Our paper “Entropy-stable Gauss collocation methods for ideal magneto-hydrodynamics” with Andres Rueda-Ramirez, Florian Hindenlang, and Gregor Gassner was accepted to Journal of Computational Physics.
December 2023: Our paper “A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations” with PhD student Yimin Lin was accepted to Journal of Computational Physics.
November 2022: Jesse Chan gave a talk at the Department of Mathematics at The Ohio State University.
September 2022: Jesse Chan gave a talk at the Department of Applied Mathematics at Naval Postgraduate School.
July 2022: Jesse Chan gave talks at NAHOMCon and in the CRUNCH seminar at Brown University.
July 2022: PhD student Christina Taylor attended the Simula Summer School in Computational Physiology.
June 2022: our paper "High-Order Methods on Curvilinear Elements" with Alexander Cicchino, David C. Del Rey Fernandez, Siva Nadarajah, and Mark H. Carpenterwas published in the [Journal of Computational Physics](https://doi.org/10.1016/j.jcp.2022.111259).
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](https://arxiv.org/pdf/2203.10238.pdf) 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](https://arxiv.org/abs/2112.10517).
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](https://arxiv.or\
g/abs/2112.07749). 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"](https://arxiv.org/abs/2005.03237) 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"](https://arxiv.org/abs/2006.07504) 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](https://arxiv.org/abs/2108.06476).
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](https://arxiv.org/abs/2107.11408).
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.
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](https://arxiv.org/abs/2011.11089) 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](https://arxiv.org/abs/2005.02516) 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
](https://arxiv.org/abs/2011.01529) 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](https://arxiv.org/abs/2010.09994) 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](https://arxiv.org/abs/2009.12768) 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](https://engineering.rice.edu/news/chan-veeraraghavan-selected-naes-us-frontiers-engineering-symposium).
June 2020: our preprint ["Efficient computation of Jacobian matrices for entropy stable summation-by-parts schemes"](https://arxiv.org/abs/2006.07504) 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"](https://www.sciencedirect.com/science/article/pii/S002199912030406X) 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](https://arxiv.org/abs/2005.03237) 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](https://arxiv.org/abs/2005.02516) 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 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](https://kenkennedy.rice.edu/news/2020-rice-oil-gas-high-performance-computing-draws-leaders-oil-and-gas-high-performance).
January 2020: Jesse Chan received an [NSF CAREER award](https://engineering.rice.edu/news/jesse-chan-ang-chen-receive-nsf-career-awards) 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](https://www.facebook.com/RiceCAAM/posts/2763081467106010).
<img src="../files/amp.jpg" width="650" />
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 Xinhui (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"](https://www.sciencedirect.com/science/article/pii/S0021999119307661) 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](https://arxiv.org/abs/1909.09103).
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"](https://arxiv.org/abs/1902.01828) 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"](https://arxiv.org/abs/1809.01178) with David C. Del Rey Fernandez and Mark C. Carpenter 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](https://arxiv.org/abs/1905.09145), 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](https://arxiv.org/abs/1904.02578). 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](https://arxiv.org/abs/1902.01828). We construct DG formulations which retain entropy stability under relaxed quadrature accuracy, which are applicable to hybrid meshes with mixed element types.
September 2018: our preprint "Efficient entropy stable Gauss collocation schemes" is available as an [arXiv preprint](https://arxiv.org/abs/1809.01178). Entropy stable collocation-DG schemes on tensor product elements typically utilize Gauss-Lobatto quadratures. We extend entropy stable collocation schemes to more accurate Gauss quadratures, which improve error significantly on curved meshes.
September 2018: our preprint "Leapfrog Time-stepping for Hermite methods", which describes a high order extension of the well-known Yee-scheme for time-domain wave propagation, is available as an [arXiv preprint](https://arxiv.org/abs/1808.10481).
August 2018: Kaihang Guo successfully defended his MA thesis on low-complexity GPU-accelerated DG methods for wave propagation in media with sub-cell heterogeneities. This work is available online in an [arXiv preprint](https://arxiv.org/abs/1808.08645).
August 2018: Jesse Chan is featured in the CAAM [video](https://www.youtube.com/watch?v=lMfHpvXGPAY) for the School of Engineering.
June 2018: our paper on [discretely entropy stable DG methods](https://www.sciencedirect.com/science/article/pii/S0021999118301153) is now online. We show how to generalize the construction of discretely entropy stable methods to ``modal'' DG formulations. The resulting formulations extend semi-discrete entropy stability theory to arbitrary bases and standard finite element quadrature rules.
May 2018: our paper on [explicit time-stepping isogeometric methods](https://www.sciencedirect.com/science/article/pii/S0045782518300240) is now online. In this paper, we show how to efficiently combine isogeometric finite elements with explicit time-stepping while avoiding the inversion of a dense mass matrix. These methods also have the advantage of a better CFL constant at high orders of approximation.
Jan 2018: Kaihang Guo receives the [K2i fellowship](https://caamweb.rice.edu/news/k2i-fellowships-2017) from the Ken Kennedy Institute.
Jan 2018: our paper on [provably stable DG methods for elasticity with sub-cell heterogeneities](https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5720) is available online. This work extends the "weight-adjusted mass matrix" (generalized mass lumping) to matrix-valued weights and applies it to elastic wave propagation. By factoring material coefficients into the mass matrix, we simplify the formulation of stable DG methods for both isotropic and anisotropic media.