16 citations · 20 across the 8 of their papers we have counts for
8 papers
A ghost-point based second order accurate finite difference method on uniform orthogonal grids for electromagnetic scattering around PEC
Hwi Lee, Yingjie Liu
We propose a finite difference method to solve Maxwell's equations in time domain in the presence of a perfect electric conductor that impedes the propagations of electromagnetic w…
Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part II: 2D Problems
Haoxiang Huang, Yingjie Liu, Vigor Yang
In our prior work [arXiv:2109.09316], neural network methods with inputs based on domain of dependence and a converging sequence were introduced for solving one dimensional conserv…
Accuracy Enhancing Interface Treatment Algorithm: the Back and Forth Error Compensation and Correction method
Wenbin Dong, Yingjie Liu, Hansong Tang
The accuracy of information transmission while solving domain decomposed problems is crucial to smooth transition of a solution around the interface/overlapping region. This paper…
Neural Networks with Inputs Based on Domain of Dependence and A Converging Sequence for Solving Conservation Laws, Part I: 1D Riemann Problems
Haoxiang Huang, Yingjie Liu, Vigor Yang
Recent research works for solving partial differential equations (PDEs) with deep neural networks (DNNs) have demonstrated that spatiotemporal function approximators defined by aut…
A Finite Difference Method on Irregular Grids with Local Second Order Ghost Point Extension for Solving Maxwell's Equations Around Curved PEC Objects
Haiyu Zou, Yingjie Liu
A new finite difference method on irregular, locally perturbed rectangular grids has been developed for solving electromagnetic waves around curved perfect electric conductors (PEC…
Back and Forth Error Compensation and Correction Method for Linear Hyperbolic Systems with Application to the Maxwell's equations
Xin Wang, Yingjie Liu
We study the Back and Forth Error Compensation and Correction (BFECC) method for linear hyperbolic PDE systems. The BFECC method has been applied to schemes for advection equations…
A Methodology for Projection-Based Model Reduction with Black-Box High-Fidelity Models
S. Ashwin Renganathan, Yingjie Liu, Dimitri N. Mavris
This paper presents a methodology that enables projection-based model reduction for black-box high-fidelity models such as commercial CFD codes. The methodology specifically addres…
Well-Balanced Central Schemes on Overlapping Cells with Constant Subtraction Techniques for the Saint-Venant Shallow Water System
Suo Yang, Alexander Kurganov, Yingjie Liu
We develop well-balanced central schemes on overlapping cells for the Saint-Venant shallow water system and its variants. The main challenge in deriving the schemes is related to t…