scholarly journals Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

2003 ◽  
Vol 119 (24) ◽  
pp. 12729-12740 ◽  
Author(s):  
Terry J. Frankcombe ◽  
Sean C. Smith
Keyword(s):  
Master Equation ◽  
Diffusion Approximation ◽  
Iterative Solver ◽  
Equation Solution ◽  
Solution Algorithms ◽  
Time Propagation ◽  
Preconditioned Iterative

scholarly journals GPU-Based Fast Decoupled Power Flow With Preconditioned Iterative Solver and Inexact Newton Method

2017 ◽  
Vol 32 (4) ◽  
pp. 2695-2703 ◽  
Author(s):  
Xue Li ◽  
Fangxing Li ◽  
Haoyu Yuan ◽  
Hantao Cui ◽  
Qinran Hu
Keyword(s):  
Newton Method ◽  
Power Flow ◽  
Inexact Newton Method ◽  
Iterative Solver ◽  
Preconditioned Iterative

Master equation solution of Ornstein-Uhlenbeck processes

Physica ◽  
1960 ◽  
Vol 26 (7) ◽  
pp. 485-491 ◽  
Author(s):  
Julius I. Bowen) ◽  
Paul H.E. Meijer)
Keyword(s):  
Master Equation ◽  
Equation Solution

scholarly journals Accurate Chemical Master Equation Solution Using Multi-Finite Buffers

2016 ◽  
Vol 14 (2) ◽  
pp. 923-963 ◽  
Author(s):  
Youfang Cao ◽  
Anna Terebus ◽  
Jie Liang
Keyword(s):  
Master Equation ◽  
Chemical Master Equation ◽  
Finite Buffers ◽  
Equation Solution

scholarly journals A Preconditioned Iterative Solver for the Scattering Solutions of the Schrödinger Equation

2012 ◽  
Vol 11 (2) ◽  
pp. 415-434 ◽  
Author(s):  
Hisham bin Zubair ◽  
Bram Reps ◽  
Wim Vanroose
Keyword(s):  
Schrödinger Equation ◽  
High Frequency ◽  
Numerical Experiments ◽  
Schrodinger Equation ◽  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Iterative Solver ◽  
Quantum Particles ◽  
Helmholtz Problem ◽  
Preconditioned Iterative

AbstractThe Schrödinger equation defines the dynamics of quantum particles which has been an area of unabated interest in physics. We demonstrate how simple transformations of the Schrödinger equation leads to a coupled linear system, whereby each diagonal block is a high frequency Helmholtz problem. Based on this model, we derive indefinite Helmholtz model problems with strongly varying wavenumbers. We employ the iterative approach for their solution. In particular, we develop a preconditioner that has its spectrum restricted to a quadrant (of the complex plane) thereby making it easily invertible by multigrid methods with standard components. This multigrid preconditioner is used in conjunction with suitable Krylov-subspace methods for solving the indefinite Helmholtz model problems. The aim of this study is to report the feasibility of this preconditioner for the model problems. We compare this idea with the other prevalent preconditioning ideas, and discuss its merits. Results of numerical experiments are presented, which complement the proposed ideas, and show that this preconditioner may be used in an automatic setting.

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