B-ITO: A MATLAB toolbox for isogeometric topology optimization with Bézier extraction of NURBS
The Bézier extraction can decompose the NURBS-based isogeometric analysis (IGA)
elements into a series of Bézier elements with C 0 continuity, which is considered into …
elements into a series of Bézier elements with C 0 continuity, which is considered into …
New proper orthogonal decomposition approximation theory for PDE solution data
S Locke, J Singler - SIAM Journal on Numerical Analysis, 2020 - SIAM
In our previous work [JR Singler, SIAM J. Numer. Anal., 52 (2014), pp. 852--876], we
considered the proper orthogonal decomposition (POD) of time varying PDE solution data …
considered the proper orthogonal decomposition (POD) of time varying PDE solution data …
A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
In this paper, we propose to improve the stabilized POD-ROM introduced in [48] to deal with
the numerical simulation of advection-dominated advection-diffusion-reaction equations. In …
the numerical simulation of advection-dominated advection-diffusion-reaction equations. In …
Two-grid reduced-order method based on POD for a nonlinear poroelasticity model
H Li, H Rui, M Gao - Journal of Computational and Applied Mathematics, 2024 - Elsevier
In this paper, we consider a two-field nonlinear poroelasticity model, in which the unknown
variables are the solid displacement and the pore pressure, and the permeability of the …
variables are the solid displacement and the pore pressure, and the permeability of the …
Space–Time Methods Based on Isogeometric Analysis for Time-fractional Schrödinger Equation
In this paper, we propose a time discontinuous Galerkin scheme for solving the nonlinear
time-fractional Schrödinger equation using B-splines in time and Non-Uniform Rational B …
time-fractional Schrödinger equation using B-splines in time and Non-Uniform Rational B …
The Convergence Analysis of a Class of Stabilized Semi-Implicit Isogeometric Methods for the Cahn-Hilliard Equation
X Meng, Y Qin, G Hu - Journal of Scientific Computing, 2025 - Springer
Isogeometric analysis (IGA) has been widely used as a spatial discretization method for
phase field models since the seminal work of Gómez et al.(Comput. Methods Appl. Mech …
phase field models since the seminal work of Gómez et al.(Comput. Methods Appl. Mech …
Artificial neural network-augmented stabilized finite element method
An artificial neural network-augmented Streamline Upwind/Petrov-Galerkin finite element
scheme (SPDE-NetII) is proposed for solving singularly perturbed partial differential …
scheme (SPDE-NetII) is proposed for solving singularly perturbed partial differential …
A numerical B-spline Galerkin method with proper generalized decomposition for reduced order modeling of partial differential equations
R Li, Q Wu, S Zhu - Communications in Nonlinear Science and Numerical …, 2024 - Elsevier
A numerical study is presented on reduced order modeling of low and high-dimensional
partial differential equations using a new B-spline Galerkin proper generalized …
partial differential equations using a new B-spline Galerkin proper generalized …
AI-augmented stabilized finite element method
An artificial intelligence-augmented Streamline Upwind/Petrov-Galerkin finite element
scheme (AiStab-FEM) is proposed for solving singularly perturbed partial differential …
scheme (AiStab-FEM) is proposed for solving singularly perturbed partial differential …
Isogeometric analysis for time-fractional partial differential equations
X Hu, S Zhu - Numerical Algorithms, 2020 - Springer
We consider isogeometric analysis to solve the time-fractional partial differential equations:
fractional diffusion and diffusion-wave equations. Traditional spatial discretization for time …
fractional diffusion and diffusion-wave equations. Traditional spatial discretization for time …