27 citations · 118 across the 26 of their papers we have counts for
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Low-cost non-iterative Sylvester solvers for dynamical low-rank approximation of reaction-diffusion equations
Joy Saha, Jun Yang, Peimeng Yin
In this work, we develop low-cost non-iterative Sylvester solvers for dynamical low-rank approximation of reaction-diffusion equations and incorporate them into a basis-update \& G…
Sparsely connected rank-inspired neural network
Yunqing Huang, Wu Su, Nianyu Yi +1
We propose a Sparsely Connected Rank-Inspired Neural Network (SCRINN) for function approximation and the numerical solution of partial differential equations (PDEs). By introducing…
A Convex Splitting Spectral Method for the Phase Field Crystal Equation: Energy Stability, Computational Stability Maps, and Three-Dimensional GPU Simulations
Saulo Orizaga, Peimeng Yin, Deep Choudhuri
We present an efficient Fourier spectral method based on the convex splitting framework of Eyre~\cite{eyre1998unconditionally} for the phase field crystal (PFC) equation. The propo…
A linear, fully decoupled, and unconditionally energy-stable SAV-FEM for the Cahn--Hilliard--Navier--Stokes model
Jinting Yang, Nianyu Yi, Peimeng Yin
In this paper, we develop a linear, fully decoupled, and unconditionally energy-stable fully discrete finite element scheme for the Cahn--Hilliard--Navier--Stokes (CHNS) system by…
A fully decoupled and structure-preserving relaxation Crank--Nicolson finite element method for Gross--Pitaevskii--Poisson model
Dongqian Li, Huini Liu, Yin Yang +1
We propose a fully decoupled, structure-preserving relaxation Crank--Nicolson finite element method (FEM) for the coupled Gross--Pitaevskii--Poisson (GPP) system modeling ultracold…
Towards finite element methods for fourth-order elliptic equation. Part I: general boundary conditions
Xihao Zhang, Hengguang Li, Nianyu Yi +1
This paper is part of a series developing finite element methods for fourth-order elliptic equations on polygonal domains. Here, we investigate how boundary conditions influe…
A positivity-preserving hybrid DDG method for Poisson--Nernst--Planck systems
Hailiang Liu, Zhongming Wang, Peimeng Yin
In earlier work [H. Liu and Z. Wang, J. Comput. Phys., 328(2017)], an arbitrary high-order conservative and energy-dissipative direct discontinuous Galerkin (DDG) scheme was develo…
Neural network-enhanced -adaptive finite element algorithm for parabolic equations
Jiaxiong Hao, Yunqing Huang, Nianyu Yi +1
In this paper, we propose a novel -adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional -adaptive fin…
A second-order dynamical low-rank mass-lumped finite element method for the Allen-Cahn equation
Jun Yang, Nianyu Yi, Peimeng Yin
In this paper, we propose a novel second-order dynamical low-rank mass-lumped finite element method for solving the Allen-Cahn (AC) equation, a semilinear parabolic partial differe…
Unconditional energy stable hybrid IEQ-FEMs for the Cahn-Hilliard-Navier-Stokes equations
Yaoyao Chen, Dongqian Li, Yin Yang +1
We investigate two unconditionally energy stable invariant energy quadratization (IEQ) finite element methods (FEMs) [Chen et al. Numerical Algorithms, DOI: 10.1007/s11075-024-0191…
A posteriori error estimators for fourth order elliptic problems with concentrated loads
Huihui Cao, Yunqing Huang, Nianyu Yi +1
In this paper, we study two residual-based a posteriori error estimators for the interior penalty method in solving the biharmonic equation in a polygonal domain under a conc…
A structure-preserving relaxation Crank-Nicolson finite element method for the Schrödinger-Poisson equation
Huini Liu, Nianyu Yi, Peimeng Yin
In this paper, we propose a mass- and modified energy-conservative relaxation Crank-Nicolson finite element method for the Schrödinger-Poisson equation. Utilizing only a single aux…
Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation
Yaoyao Chen, Hailiang Liu, Nianyu Yi +1
In this paper, we present several unconditionally energy-stable invariant energy quadratization (IEQ) finite element methods (FEMs) with linear, first- and second-order accuracy fo…
A semi-implicit dynamical low-rank discontinuous Galerkin method for space homogeneous kinetic equations. Part I: emission and absorption
Peimeng Yin, Eirik Endeve, Cory D. Hauck +1
Dynamical low-rank approximation (DLRA) is an emerging tool for reducing computational costs and provides memory savings when solving high-dimensional problems. In this work, we pr…
Recovery type a posteriori error estimation of an adaptive finite element method for Cahn--Hilliard equation
Yaoyao Chen, Yunqing Huang, Nianyu Yi +1
In this paper, we derive a novel recovery type a posteriori error estimation of the Crank-Nicolson finite element method for the Cahn--Hilliard equation. To achieve this, we employ…
A finite element algorithm for the sixth order problem with simply supported boundary conditions
Hengguang Li, Peimeng Yin
In this paper, we investigate a sixth order elliptic equation with the simply supported boundary conditions in a polygonal domain. We propose a new method that decouples the sixth…
A finite element method for the biharmonic problem with Dirichlet boundary conditions in a polygonal domain
Hengguang Li, Charuka D. Wickramasinghe, Peimeng Yin
In this paper, we study the biharmonic equation with Dirichlet boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the fourth-o…
An adaptive finite element method for two-dimensional elliptic equations with line Dirac sources
Huihui Cao, Hengguang Li, Nianyu Yi +1
In this paper, we propose a novel adaptive finite element method for an elliptic equation with line Dirac delta functions as a source term. We first study the well-posedness and gl…
Positivity-preserving third order DG schemes for Poisson--Nernst--Planck equations
Hailiang Liu, Zhongming Wang, Peimeng Yin +1
In this paper, we design and analyze third order positivity-preserving discontinuous Galerkin (DG) schemes for solving the time-dependent system of Poisson--Nernst--Planck (PNP) eq…
Energy stable Runge-Kutta discontinuous Galerkin schemes for fourth order gradient flows
Hailiang Liu, Peimeng Yin
We present unconditionally energy stable Runge-Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows. Our algorithm is geared toward arb…
A finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain
Hengguang Li, Peimeng Yin, Zhimin Zhang
In this paper, we study the biharmonic equation with the Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-ord…
Regularity and finite element approximation for two-dimensional elliptic equations with line Dirac sources
Hengguang Li, Xiang Wan, Peimeng Yin +1
We study the elliptic equation with a line Dirac delta function as the source term subject to the Dirichlet boundary condition in a two-dimensional domain. Such a line Dirac measur…
On the SAV-DG method for a class of fourth order gradient flows
Hailiang Liu, Peimeng Yin
For a class of fourth order gradient flow problems, integration of the scalar auxiliary variable (SAV) time discretization with the penalty-free discontinuous Galerkin (DG) spatial…
Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation
Hailiang Liu, Peimeng Yin
In this paper, we introduce novel discontinuous Galerkin (DG) schemes for the Cahn-Hilliard equation, which arises in many applications. The method is designed by integrating the m…