38 citations · 92 across the 18 of their papers we have counts for
18 papers
Reduced order model for parametric Boltzmann equation and its application to inverse problems
Shanyin Tong, Jingwei Hu, Fengyan Li +3
The Boltzmann equation plays an important role in modeling mesoscopic behavior in a wide range of scientific and engineering applications. However, its numerical solution is comput…
Structure-Preserving Reduced-Order Modeling via Low-Rank Transport Signatures
Jiajia Yu, Jingwei Hu, Fengyan Li +3
Parametrized PDEs with density-valued solutions are often difficult to approximate with classical linear reduced-order models, especially in transport-dominated regimes. We introdu…
Multi-Scale Kinetic Simulation: Asymptotic Preserving IMEX-BDF-DG Schemes with Three Implicit-Explicit Partitionings
Kimberly Matsuda, Fengyan Li
Kinetic transport models are mesoscopic mathematical descriptions of the transport of particles as well as their interactions with the background media or among themselves, and the…
Reduced Basis Methods for Parametric Steady-State Radiative Transfer Equation
Kimberly Matsuda, Yanlai Chen, Yingda Cheng +1
The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host m…
A micro-macro decomposed reduced basis method for the time-dependent radiative transfer equation
Zhichao Peng, Yanlai Chen, Yingda Cheng +1
Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability d…
An Energy-Based Discontinuous Galerkin Method with Tame CFL Numbers for the Wave Equation
Daniel Appelö, Lu Zhang, Thomas Hagstrom +1
We extend and analyze the energy-based discontinuous Galerkin method for second order wave equations on staggered and structured meshes. By combining spatial staggering with local…
A learning-based projection method for model order reduction of transport problems
Zhichao Peng, Min Wang, Fengyan Li
The Kolmogorov -width of the solution manifolds of transport-dominated problems can decay slowly. As a result, it can be challenging to design efficient and accurate reduced ord…
A reduced basis method for radiative transfer equation
Zhichao Peng, Yanlai Chen, Yingda Cheng +1
Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient and ac…
Asymptotic preserving IMEX-DG-S schemes for linear kinetic transport equations based on Schur complement
Zhichao Peng, Fengyan Li
We consider a linear kinetic transport equation under a diffusive scaling, that converges to a diffusion equation as the Knudsen number . In [3, 21], to ac…
Stability-enhanced AP IMEX1-LDG method: energy-based stability and rigorous AP property
Zhichao Peng, Yingda Cheng, Jing-Mei Qiu +1
In our recent work [22], a family of high order asymptotic preserving (AP) methods, termed as IMEX-LDG methods, are designed to solve some linear kinetic transport equations, inclu…
Dispersion Analysis of Finite Difference and Discontinuous Galerkin Schemes for Maxwell's Equations in Linear Lorentz Media
Yan Jiang, Puttha Sakkaplangkul, Vrushali A. Bokil +2
In this paper, we consider Maxwell's equations in linear dispersive media described by a single-pole Lorentz model for electronic polarization. We study two classes of commonly use…
An Ultra-Weak Discontinuous Galerkin Method for Schrödinger Equation in One Dimension
Anqi Chen, Fengyan Li, Yingda Cheng
In this paper, we develop an ultra-weak discontinuous Galerkin (DG) method to solve the one-dimensional nonlinear Schrödinger equation. Stability conditions and error estimates are…
Energy Stable Discontinuous Galerkin Methods for Maxwell's Equations in Nonlinear Optical Media
Vrushali A. Bokil, Yingda Cheng, Yan Jiang +1
The propagation of electromagnetic waves in general media is modeled by the time-dependent Maxwell's partial differential equations (PDEs), coupled with constitutive laws that desc…
High Order Asymptotic Preserving Nodal Discontinuous Galerkin IMEX Schemes for the BGK Equation
Tao Xiong, Juhi Jang, Fengyan Li +1
In this paper, we develop high-order asymptotic preserving (AP) schemes for the BGK equation in a hyperbolic scaling, which leads to the macroscopic models such as the Euler and co…
Analysis of Asymptotic Preserving DG-IMEX Schemes for Linear Kinetic Transport Equations in a Diffusive Scaling
Juhi Jang, Fengyan Li, Jing-Mei Qiu +1
In this paper, some theoretical aspects will be addressed for the asymptotic preserving DG-IMEX schemes recently proposed in [J. Jang, F. Li, J.-M. Qiu and T. Xiong, submitted, arx…
High Order Asymptotic Preserving DG-IMEX Schemes for Discrete-Velocity Kinetic Equations in a Diffusive Scaling
Juhi Jang, Fengyan Li, Jing-Mei Qiu +1
In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit…
Error Estimates of Runge-Kutta Discontinuous Galerkin Methods for the Vlasov-Maxwell System
He Yang, Fengyan Li
In this paper, error analysis is established for Runge-Kutta discontinuous Galerkin (RKDG) methods to solve the Vlasov-Maxwell system. This nonlinear hyperbolic system describes th…
Discontinuous Galerkin Methods for the Vlasov-Maxwell Equations
Yingda Cheng, Irene M. Gamba, Fengyan Li +1
Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservati…