5 papers · 1 filter
Physics-informed neural networks for solving two-phase flow problems with moving interfaces
Qijia Zhai, Pengtao Sun, Xiaoping Xie +2
In this paper, a meshfree method using physics-informed neural networks (PINNs) is developed for solving two-phase flow problems with moving interfaces, where two immiscible fluids…
A Domain Decomposition Deep Neural Network Method with Multi-Activation Functions for Solving Elliptic and Parabolic Interface Problems
Qijia Zhai
We present a domain decomposition-based deep learning method for solving elliptic and parabolic interface problems with discontinuous coefficients in two to ten dimensions. Our Mul…
Robust globally divergence-free HDG finite element method for steady thermally coupled incompressible MHD flow
Min Zhang, Zimo Zhu, Qijia Zhai +1
This paper develops an hybridizable discontinuous Galerkin (HDG) finite element method of arbitrary order for the steady thermally coupled incompressible Magnetohydrodynamics (MHD)…
A Priori Error Estimation of Physics-Informed Neural Networks Solving Allen--Cahn and Cahn--Hilliard Equations
Guangtao Zhang, Jiani Lin, Qijia Zhai +4
Physics-Informed Neural Networks (PINNs) encounter accuracy limitations when solving the Allen--Cahn (AC) and Cahn--Hilliard (CH) partial differential equations (PDEs). To overcome…
A New Reduced Basis Method for Parabolic Equations Based on Single-Eigenvalue Acceleration
Qijia Zhai, Qingguo Hong, Xiaoping Xie
In this paper, we develop a new reduced basis (RB) method, named as Single Eigenvalue Acceleration Method (SEAM), for second-order parabolic equations with homogeneous Dirichlet bo…