scholarly journals Multilevel preconditioning technique for Schwarz waveform relaxation domain decomposition method for real- and imaginary-time nonlinear Schrödinger equation

2018 ◽  
Vol 336 ◽  
pp. 403-417 ◽  
Author(s):  
X. Antoine ◽  
E. Lorin
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Schrodinger Equation ◽  
Domain Decomposition Method ◽  
Nonlinear Schrodinger Equation ◽  
Waveform Relaxation ◽  
Imaginary Time ◽  
Schwarz Waveform Relaxation ◽  
Preconditioning Technique ◽  
Multilevel Preconditioning

scholarly journals Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Shu-Lin Wu
Keyword(s):  
Boundary Conditions ◽  
Domain Decomposition ◽  
Domain Decomposition Method ◽  
Linear Convergence ◽  
Decomposition Methods ◽  
Waveform Relaxation ◽  
Heat Equations ◽  
Nonlinear Dynamical ◽  
Schwarz Waveform Relaxation ◽  
Dynamical Boundary Conditions

We are interested in solving heat equations with nonlinear dynamical boundary conditions by using domain decomposition methods. In the classical framework, one first discretizes the time direction and then solves a sequence of state steady problems by the domain decomposition method. In this paper, we consider the heat equations at spacetime continuous level and study a Schwarz waveform relaxation algorithm for parallel computation purpose. We prove the linear convergence of the algorithm on long time intervals and show how the convergence rate depends on the size of overlap and the nonlinearity of the nonlinear boundary functions. Numerical experiments are presented to verify our theoretical conclusions.

scholarly journals A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics

2020 ◽  
Vol 369 ◽  
pp. 113223
Author(s):  
Alice Lieu ◽  
Philippe Marchner ◽  
Gwénaël Gabard ◽  
Hadrien Bériot ◽  
Xavier Antoine ◽  
...  
Keyword(s):  
Finite Elements ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
High Order ◽  
Overlapping Schwarz
Sign in / Sign up

Export Citation Format

Share Document