Abstract
Multidimensional scattering wavefunctions are calculated using a new fully distributed parallel solver for the Helmholtz/Schroedinger equations. The solver is based on a parallel preconditioner which is derived from the generic structure of the Helmholtz/Schroedinger partial differential equations with scattering boundary conditions. The approach is useful for a broad range of scientific applications, e.g. in nano-electronics, fiber optics and multidimensional quantum scattering calculations. With minor changes, the solver can be applied as an exponential propagator for time-dependent Helmholtz/Schroedinger initial value problems. Examples are given for 3D models of a wave propagation in a discontinuous waveguide and of electron transmission through a water barrier.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Peskin U. and Miller W. H.: Reactive scattering theory for field induced transition. J. Chem. Phys. 102, (1995) 4084.
Peskin U., Miller W. H. and Edlund Å.: Quantum time-evolution in time-dependent fields and time-independent reactive-scattering calculations via an efficient Fourier grid preconditioner. J. Chem. Phys. 103, (1995) 10030.
Vorobeichik I., Moiseyev, N., Neuhauser D., Orenstein M. and Peskin U. Calculation of light distribution in optical devices by a global solution of an inhomogeneous scalar wave equation. IEEE J. Quant. Elec. 33 (1997) 1236.
Edlund Å., Vorobeichik I. and Peskin U.: High order perturbation theory for Helmholtz/Schrödinger equations via a separable preconditioner. J. Comput. Phys. 138 (1997) 788–800.
Edlund Å. and Peskin U.: A parallel Green’s operator for multidimensional quantum scattering calculations”. Int. J. of Quant. Chem. (to appear).
Bar-On I., Edlund Å. and Peskin U.: A fully distributed parallel solver for multi-dimensional Helmholtz/Schrödinger equations. (submitted).
Neuhauser D.: State-to-state reactive scattering amplitudes from single-arrangement propagation with absorbing potentials. Chem. Phys. Lett. 200 (1990) 7836.
Seideman T. and Miller W. H.: Calculation of the cumulative reaction probability via a discrete representation with absorbing boundary conditions. J. Chem. Phys. 96 (1992) 4412.
Colbert D. T. and Miller W. H.: A novel discrete variable representation for quantum mechanical reactive scattering via the S-matrix Kohn method. J. Chem. Phys. 96 (1992) 1982.
Kosloff R.: in Numerical Grid Methods and Their Application to Schrödinger’s Equation. NATO ASI Series C 412, edited by C. Cerjan (Kluwer, Academic, 1993).
Saad Y.: Iterative methods for sparse linear systems. PWS Publishing, (1996).
Ratowsky R. P., Fleck Jr. J. A., and Feit M. D.: Helmholtz beam propagation in rib waveguides and couplers by iterative Lanczos reduction. Opt. Soc. Am. A. 9 (1992) 265.
Freund R. W., Golub G. H. and Nachtigal N.: Iterative Solution of linear systems. Acta Numerica, 1–44, (1992).
Bar-On I. and Ryaboy V.: Fast Diagonalization of Large and Dense Complex Symmetric Matrices, with Applications to Quantum Reaction Dynamics. SIAM J. of Scientific and Stat. Comp. 28 (1997), 5.
G. H. Golub and C. f. Van Loan Matrix Computations (The John Hopkins University Press, 1989).
Mosyak A., Graf P., Benjamin I. and Nitzan A., J. Phys. Chem. (to appear).
Benjamin I., Evans D. and Nitzan A. Electron tunneling through water layers: Effect of layer structure and thickness. J. Chem. Phys. 106 (1997), 6647–6654.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Edlund, Å., Bar-On, I., Peskin, U. (1998). Parallel computation of multidimensional scattering wavefunctions for Helmholtz/Schroedinger equations. In: Kågström, B., Dongarra, J., Elmroth, E., Waśniewski, J. (eds) Applied Parallel Computing Large Scale Scientific and Industrial Problems. PARA 1998. Lecture Notes in Computer Science, vol 1541. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0095327
Download citation
DOI: https://doi.org/10.1007/BFb0095327
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65414-8
Online ISBN: 978-3-540-49261-0
eBook Packages: Springer Book Archive