Discrete transparent boundary conditions for the Schrödinger equation: Fast calculation, approximation, and stability
dc.contributor.author | Arnold, Anton | |
dc.contributor.author | Ehrhardt, Matthias | |
dc.contributor.author | Sofronov, Ivan | |
dc.date.accessioned | 2022-05-11T12:11:45Z | |
dc.date.available | 2022-05-11T12:11:45Z | |
dc.date.issued | 2002-12-06 | |
dc.description.abstract | This paper is concerned with transparent boundary conditions (TBCs) for the time-dependent Schrödinger equation in one and two dimensions. Discrete TBCs are introduced in the numerical simulations of whole space problems in order to reduce the computational domain to a finite region. Since the discrete TBC for the Schrödinger equation includes a convolution w.r.t. time with a weakly decaying kernel, its numerical evaluation becomes very costly for large-time simulations. As a remedy we construct approximate TBCs with a kernel having the form of a finite sum-of-exponentials, which can be evaluated in a very efficient recursion. We prove stability of the resulting initial-boundary value scheme, give error estimates for the considered approximation of the boundary condition, and illustrate the efficiency of the proposed method on several examples. | en |
dc.identifier.issn | 2197-8085 | |
dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/16903 | |
dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-15681 | |
dc.language.iso | en | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject.ddc | 510 Mathematik | en |
dc.subject.other | Schrödinger equation | en |
dc.subject.other | transparent boundary conditions | en |
dc.subject.other | discrete convolution | en |
dc.subject.other | sum of exponentials | en |
dc.subject.other | Padé approximations | en |
dc.subject.other | finite difference schemes | en |
dc.title | Discrete transparent boundary conditions for the Schrödinger equation: Fast calculation, approximation, and stability | en |
dc.type | Research Paper | en |
dc.type.version | submittedVersion | en |
tub.accessrights.dnb | free | |
tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
tub.affiliation.institute | Inst. Mathematik | de |
tub.publisher.universityorinstitution | Technische Universität Berlin | en |
tub.series.issuenumber | 2002, 753 | en |
tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
tub.subject.msc2000 | 65M12 Stability and convergence of numerical methods | en |
tub.subject.msc2000 | 35Q40 Equations from quantum mechanics | en |
tub.subject.msc2000 | 45K05 Integro-partial differential equations | en |
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