Optimized Schwarz Waveform Relaxation: Roots, Blossoms and Fruits

2009 ◽  
pp. 225-232 ◽  
Author(s):  
Laurence Halpern
Keyword(s):  
Waveform Relaxation ◽  
Schwarz Waveform Relaxation

scholarly journals Asymptotic estimates of the convergence of classical Schwarz waveform relaxation domain decomposition methods for two-dimensional stationary quantum waves

2018 ◽  
Vol 52 (4) ◽  
pp. 1569-1596 ◽  
Author(s):  
Xavier Antoine ◽  
Fengji Hou ◽  
Emmanuel Lorin
Keyword(s):  
Domain Decomposition ◽  
Decomposition Methods ◽  
Nonlinear Schrödinger Equations ◽  
Waveform Relaxation ◽  
Schrödinger Equations ◽  
Two Dimensional ◽  
Domain Decomposition Methods ◽  
Schwarz Waveform Relaxation ◽  
Nonlinear Schrodinger Equations ◽  
Linear And Nonlinear

This paper is devoted to the analysis of convergence of Schwarz Waveform Relaxation (SWR) domain decomposition methods (DDM) for solving the stationary linear and nonlinear Schrödinger equations by the imaginary-time method. Although SWR are extensively used for numerically solving high-dimensional quantum and classical wave equations, the analysis of convergence and of the rate of convergence is still largely open for linear equations with variable coefficients and nonlinear equations. The aim of this paper is to tackle this problem for both the linear and nonlinear Schrödinger equations in the two-dimensional setting. By extending ideas and concepts presented earlier [X. Antoine and E. Lorin, Numer. Math. 137 (2017) 923–958] and by using pseudodifferential calculus, we prove the convergence and determine some approximate rates of convergence of the two-dimensional Classical SWR method for two subdomains with smooth boundary. Some numerical experiments are also proposed to validate the analysis.

scholarly journals Nonoverlapping Schwarz Waveform Relaxation and Numerical Recovery for Non-Fickian Problems With Time-Delay

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 11754-11762
Author(s):  
Zhiyong Wang ◽  
ShuLin Wu ◽  
Dan Zhang ◽  
Di Liu
Keyword(s):  
Time Delay ◽  
Waveform Relaxation ◽  
Schwarz Waveform Relaxation
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