A quasiresonant smoothing algorithm for solving large highly oscillatory differential equations from quantum chemistry
Abstract: "In Quantum Chemistry the field of 'Laser-Assisted Molecular Control' has received a considerable amount of attention recently. One key problem in this new field is the simulation of the dynamical reaction of a molecule subjected to external radiation. This problem is descri...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Berlin-Wilmersdorf
Konrad-Zuse-Zentrum für Informationstechnik Berlin
1994
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| Schriftenreihe: | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Technical report
1994,4 |
| Schlagworte: |
Mathematisches Modell
> Differential equations
> Lasers in chemistry
> Computer simulation
> Matematical models
> Quantum chemistry
> Mathematical models
> Smoothing (Numerical analysis)
> Algorithms
> Glättung
> Molekül
> Schwingungsanregung
> Gewöhnliche Differentialgleichung
> Ultrakurzer Lichtimpuls
> Hochschulschrift
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Tag hinzufügen | Zusammenfassung: | Abstract: "In Quantum Chemistry the field of 'Laser-Assisted Molecular Control' has received a considerable amount of attention recently. One key problem in this new field is the simulation of the dynamical reaction of a molecule subjected to external radiation. This problem is described by the Schrödinger equation, which, after eigenfunction expansion, can be written in the form of a large system of ordinary differential equations, the solutions of which show a highly oscillatory behaviour. The oscillations with high frequencies and small amplitudes confine the stepsizes of any numerical integrator -- an effect, which, in turn, blows up the simulation time. Larger stepsizes can be expected by averaging these fast oscillations, thus smoothing the trajectories. Standard smoothing techniques (averaging, filtering) would kill the whole process and thus, lead to wrong numerical results. To avoid this unwanted effect and nevertheless speed up computations, this paper presents a quasiresonant smoothing algorithm (QRS). In QRS, a natural splitting parameter [delta] controls the smoothing properties. An adaptive QRS-version (AQRS) is presented which includes an error estimation scheme for choosing this parameter [delta] in order to meet a given accuracy requirement. In AQRS [delta] is permanently adapted to the solution properties for computing the 'chemically necessary information' only. The performance of AQRS is demonstrated in several test problems from the field 'Laser-Assisted Selective Excitation of Molecules' in which the external radiation is a picosecond laser pulse. In comparison with standard methods speedup factors of the order of 10² are observed." |
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| Beschreibung: | Zugl.: Berlin, Techn. Univ., Diss., 1994 |
| Beschreibung: | 122 S. graph. Darst. |