[图书][B] Splitting methods in communication, imaging, science, and engineering

R Glowinski, SJ Osher, W Yin - 2017 - books.google.com
This book is about computational methods based on operator splitting. It consists of twenty-
three chapters written by recognized splitting method contributors and practitioners, and …

Operator splitting

S MacNamara, G Strang - Splitting methods in communication, imaging …, 2016 - Springer
Operator splitting is a numerical method of computing the solution to a differential equation.
The splitting method separates the original equation into two parts over a time step …

A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance

C Liu, C Wang, Y Wang - Journal of Computational Physics, 2021 - Elsevier
In this paper, we propose and analyze a positivity-preserving, energy stable numerical
scheme for a certain type of reaction-diffusion systems involving the Law of Mass Action with …

Order estimates in time of splitting methods for the nonlinear Schrödinger equation

C Besse, B Bidégaray, S Descombes - SIAM Journal on Numerical Analysis, 2002 - SIAM
In this paper, we consider the nonlinear Schrödinger equation u_t+iΔu-F(u)=0 in two
dimensions. We show, by an operator-theoretic proof, that the well-known Lie and Strang …

Convergence analysis of the variational operator splitting scheme for a reaction-diffusion system with detailed balance

C Liu, C Wang, Y Wang, SM Wise - SIAM journal on numerical analysis, 2022 - SIAM
We present a detailed convergence analysis for an operator splitting scheme proposed in
[C. Liu, C. Wang, and Y. Wang, J. Comput. Phys., 436 (2021), 110253] for a reaction …

Splitting methods with complex times for parabolic equations

F Castella, P Chartier, S Descombes… - BIT Numerical …, 2009 - Springer
Using composition procedures, we build up high order splitting methods to solve evolution
equations posed in finite or infinite dimensional spaces. Since high-order splitting methods …

Stability and convergence of Strang splitting. Part I: scalar Allen-Cahn equation

D Li, C Quan, J Xu - Journal of Computational Physics, 2022 - Elsevier
We consider a class of second-order Strang splitting methods for Allen-Cahn equations with
polynomial or logarithmic nonlinearities. For the polynomial case both the linear and the …

Some facts about operator-splitting and alternating direction methods

R Glowinski, TW Pan, XC Tai - Splitting Methods in Communication …, 2016 - Springer
The main goal of this chapter is to give the reader a (relatively) brief overview of operator-
splitting, augmented Lagrangian and ADMM methods and algorithms. Following a general …

A second-order accurate, operator splitting scheme for reaction-diffusion systems in an energetic variational formulation

C Liu, C Wang, Y Wang - SIAM Journal on Scientific Computing, 2022 - SIAM
A second-order accurate in time, positivity-preserving, and unconditionally energy stable
operator splitting scheme is proposed and analyzed for reaction-diffusion systems with the …

Operator splitting for nonlinear reaction-diffusion systems with an entropic structure: singular perturbation and order reduction

S Descombes, M Massot - Numerische Mathematik, 2004 - Springer
In this paper, we perform the numerical analysis of operator splitting techniques for
nonlinear reaction-diffusion systems with an entropic structure in the presence of fast scales …