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A fast method to implement non‐local discrete transparent boundary conditions for the Schrödinger equation
Author(s) -
Arnold A.,
Ehrhardt M.,
Sofronov I.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310196
Subject(s) - recursion (computer science) , kernel (algebra) , boundary (topology) , boundary value problem , mathematics , domain (mathematical analysis) , convolution (computer science) , order (exchange) , exponential function , mathematical analysis , computer science , algorithm , discrete mathematics , machine learning , artificial neural network , finance , economics
Discrete transparent boundary conditions (DTBCs) for the time‐dependent Schrödinger equation were introduced in the numerical simulations of whole space problems in order to reduce the computational domain to a finite region. They include a convolution w.r.t. time with a weakly decaying kernel that leads to very costly numerical evaluation for large‐time simulations. As a remedy we construct approximate DTBCs with a kernel having the form of a finite sum‐of‐exponentials, which can be evaluated in an efficient recursion.