Computer Science – Numerical Analysis
Scientific paper
2010-12-20
Comm. Comput. Phys. 11 p 415-434 (2012)
Computer Science
Numerical Analysis
Accepted in Communications in Computational Physics
Scientific paper
The Schr\"odinger equation defines the dynamics of quantum particles which has been an area of unabated interest in physics. We demonstrate how simple transformations of the Schr\"odinger 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 conjuction with suitable Krylov-subspace methods for solving the indefinite Helmholtz model problems. The aim of this study is to report the feasbility 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.
Reps Bram
Vanroose Wim
Zubair Hisham bin
No associations
LandOfFree
A preconditioned iterative solver for the scattering solutions of the Schrödinger equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A preconditioned iterative solver for the scattering solutions of the Schrödinger equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A preconditioned iterative solver for the scattering solutions of the Schrödinger equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-453907