Discrete transparent boundary conditions for the Schrödinger equation: Fast calculation, approximation, and stability

dc.contributor.authorArnold, Anton
dc.contributor.authorEhrhardt, Matthias
dc.contributor.authorSofronov, Ivan
dc.date.accessioned2022-05-11T12:11:45Z
dc.date.available2022-05-11T12:11:45Z
dc.date.issued2002-12-06
dc.description.abstractThis 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.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/16903
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-15681
dc.language.isoen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subject.ddc510 Mathematiken
dc.subject.otherSchrödinger equationen
dc.subject.othertransparent boundary conditionsen
dc.subject.otherdiscrete convolutionen
dc.subject.othersum of exponentialsen
dc.subject.otherPadé approximationsen
dc.subject.otherfinite difference schemesen
dc.titleDiscrete transparent boundary conditions for the Schrödinger equation: Fast calculation, approximation, and stabilityen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfree
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2002, 753en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200065M12 Stability and convergence of numerical methodsen
tub.subject.msc200035Q40 Equations from quantum mechanicsen
tub.subject.msc200045K05 Integro-partial differential equationsen
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