6 papers
Synthetic Acceleration Preconditioners for Parametric Radiative Transfer Equations based on Trajectory-Aware Reduced Order Models
Ning Tang, Zhichao Peng
The parametric radiative transfer equation (RTE) arises in multi-query applications, such as design optimization, inverse problems, and uncertainty quantification, which require so…
An Inexact Low-Rank Source Iteration for Steady-State Radiative Transfer Equation with Diffusion Synthetic Acceleration
Wei Guo, Zhichao Peng
We propose an inexact low-rank source iteration with diffusion synthetic acceleration (SI-DSA) for solving the multidimensional steady-state radiative transfer equation (RTE) in th…
Superconvergence Extraction of Upwind Discontinuous Galerkin Method Solving the Radiative Transfer Equation
Andres Galindo-Olarte, Zhichao Peng, Jennifer K. Ryan
We theoretically analyze the superconvergence of the upwind discontinuous Galerkin (DG) method for both the steady-state and time-dependent radiative transfer equation (RTE), and a…
Adaptive and hybrid reduced order models to mitigate Kolmogorov barrier in a multiscale kinetic transport equation
Tianyu Jin, Zhichao Peng, Yang Xiang
In this work, we develop reduced order models (ROMs) to predict solutions to a multiscale kinetic transport equation with a diffusion limit under the parametric setting. When the u…
A -Adaptive Hermite Method for Nonlinear Dispersive Maxwell's Equations
Yann-Meing Law, Zhichao Peng, Daniel Appelö +1
In this work, we introduce a novel Hermite method to handle Maxwell's equations for nonlinear dispersive media. The proposed method achieves high-order accuracy and is free of any…
AAROC: Reduced Over-Collocation Method with Adaptive Time Partitioning and Adaptive Enrichment for Parametric Time-Dependent Equations
Lijie Ji, Zhichao Peng, Yanlai Chen
Nonlinear and nonaffine terms in parametric partial differential equations can potentially lead to a computational cost of a reduced order model (ROM) that is comparable to the cos…