Applied and Computational Mathematics (ACM)

Multirate Partial Differential Algebraic Equations

In radio frequency (RF) applications, electric circuits produce signals exhibiting fast oscillations, whereas the amplitude and/or frequency change slowly in time. Thus, solving a system of differential algebraic equations (DAEs), which describes the circuit's transient behaviour, becomes inefficient, since the fast rate restricts the step sizes in time. A multivariate model is able to decouple the widely separated time scales of RF signals and provides an alternative approach. Consequently, a system of DAEs changes into a system of multirate partial differential algebraic equations (MPDAEs). The determination of multivariate solutions allows for the exact reconstruction of corresponding time-dependent signals. Hence, an efficient numerical simulation is obtained by exploiting the periodicities in fast time scales. On the one hand, the simulation of enveloppe-modulated signals requires the solution of initial-boundary value problems of the MPDAEs. On the other hand, the simulation of quasiperiodic signals implies multiperiodic boundary conditions only for the MPDAEs. In case of quasiperiodic signals, a method of characteristics solves the multirate model efficiently, since the system of partial differential algebraic equations exhibits a hyperbolic structure.

Publications

1992

413.

Maten, E. J. W.; Melissen, J. B. M.
Simulation of inductive heating
{IEEE} Transactions on Magnetics, 28 (2) :1287--1290
März 1992
Herausgeber: Institute of Electrical and Electronics Engineers ({IEEE})

DOI: 10.1109/20.123925

412.

Kraemer, Wolfgang P.; Jensen, Per; Roos, B. O.; Bunker, Philip R.
Ab initio rotation-vibration energies and intensities for the HNC\(^{+}\) molecule
Journal of Molecular Spectroscopy, 153 (1-2) :240-254
1992

DOI: 10.1016/0022-2852(92)90472-Z

411.

Kraemer, Wolfgang P.; Jensen, Per; Roos, B. O.; Bunker, Philip R.
Ab initio rotation-vibration energies and intensities for the HNC\(^{+}\) molecule
Journal of Molecular Spectroscopy, 153 (1-2) :240-254
1992

DOI: 10.1016/0022-2852(92)90472-Z

410.

Kraemer, Wolfgang P.; Jensen, Per; Roos, B. O.; Bunker, Philip R.
Ab initio rotation-vibration energies and intensities for the HNC+ molecule
Journal of Molecular Spectroscopy, 153 (1-2) :240-254
1992

DOI: 10.1016/0022-2852(92)90472-Z

409.

Jensen, Per; Bunker, Philip R.; Epa, V. C.; Karpfen, Alfred
An ab initio calculation of the fundamental and overtone HCl stretching vibrations for the HCl dimer
Journal of Molecular Spectroscopy, 151 (2) :384-395
1992

DOI: 10.1016/0022-2852(92)90574-8

408.

Jensen, Per; Bunker, Philip R.; Epa, V. C.; Karpfen, Alfred
An ab initio calculation of the fundamental and overtone HCl stretching vibrations for the HCl dimer
Journal of Molecular Spectroscopy, 151 (2) :384-395
1992

DOI: 10.1016/0022-2852(92)90574-8

407.

Jensen, Per; Bunker, Philip R.; Epa, V. C.; Karpfen, Alfred
An ab initio calculation of the fundamental and overtone HCl stretching vibrations for the HCl dimer
Journal of Molecular Spectroscopy, 151 (2) :384-395
1992

DOI: 10.1016/0022-2852(92)90574-8

406.

Jensen, Per; Rohlfing, Celeste Michael; Alml{ö}f, Jan
Calculation of the complete-active-space self-consistent-field potential-energy surface, the dipole moment surfaces, the rotation-vibration energies, and the vibrational transition moments for C\(_{3}\)(X\verb=~= \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\))
The Journal of Chemical Physics, 97 (5) :3399-3411
1992

DOI: 10.1063/1.462976

405.

Jensen, Per; Rohlfing, Celeste Michael; Alml{ö}f, Jan
Calculation of the complete-active-space self-consistent-field potential-energy surface, the dipole moment surfaces, the rotation-vibration energies, and the vibrational transition moments for C\(_{3}\)(X\verb=~= \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\))
The Journal of Chemical Physics, 97 (5) :3399-3411
1992

DOI: 10.1063/1.462976

404.

Jensen, Per; Rohlfing, Celeste Michael; Almlöf, Jan
Calculation of the complete-active-space self-consistent-field potential-energy surface, the dipole moment surfaces, the rotation-vibration energies, and the vibrational transition moments for C3(X~ 1Σg+)
The Journal of Chemical Physics, 97 (5) :3399-3411
1992

DOI: 10.1063/1.462976

403.

Wildt, J{ü}rgen; Fink, Ewald H.; Biggs, P.; Wayne, Richard P.; Vilesov, A. F.
Collision-induced emission of O\(_{2}\)(a \(^{1}\)\(\Delta\)\(_{g}\) → X \(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\)) in the gas phase
Chemical Physics, 159 (1) :127-140
1992

DOI: 10.1016/0301-0104(92)80065-4

402.

Wildt, J{ü}rgen; Fink, Ewald H.; Biggs, P.; Wayne, Richard P.; Vilesov, A. F.
Collision-induced emission of O\(_{2}\)(a \(^{1}\)\(\Delta\)\(_{g}\) → X \(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\)) in the gas phase
Chemical Physics, 159 (1) :127-140
1992

DOI: 10.1016/0301-0104(92)80065-4

401.

Wildt, Jürgen; Fink, Ewald H.; Biggs, P.; Wayne, Richard P.; Vilesov, A. F.
Collision-induced emission of O2(a 1Δg → X 3Σg-) in the gas phase
Chemical Physics, 159 (1) :127-140
1992

DOI: 10.1016/0301-0104(92)80065-4

400.

Heilmann, Margareta
Erhöhung der Konvergenzgeschwindigkeit bei der Approximation von Funktionen mit Hilfe von Linearkombinationen spezieller positiver linearer Operatoren
Universität Dortmund
1992

Download

399.

Tausch, Michael W.
Erzeugung und Desaktivierung von angeregten Zuständen
Mitteilungsblatt der FG Chemieunterricht der GDCh (17) :253
1992

398.

Becker, Karl Heinz; Kurtenbach, Ralf; Wiesen, Peter
Investigation of N\(_{2}\)O formation in the NCO+NO reaction by Fourier-transform infrared spectroscopy
Chemical Physics Letters, 198 (3-4) :424-428
1992

DOI: 10.1016/0009-2614(92)85076-M

397.

Becker, Karl Heinz; Kurtenbach, Ralf; Wiesen, Peter
Investigation of N\(_{2}\)O formation in the NCO+NO reaction by Fourier-transform infrared spectroscopy
Chemical Physics Letters, 198 (3-4) :424-428
1992

DOI: 10.1016/0009-2614(92)85076-M

396.

Becker, Karl Heinz; Kurtenbach, Ralf; Wiesen, Peter
Investigation of N2O formation in the NCO+NO reaction by Fourier-transform infrared spectroscopy
Chemical Physics Letters, 198 (3-4) :424-428
1992

DOI: 10.1016/0009-2614(92)85076-M

395.

Becker, Karl Heinz; K{ö}nig, R.; Meuser, R.; Wiesen, Peter; Bayes, Kyle D.
Kinetics of C\(_{2}\)O radicals formed in the photolysis of carbon suboxide at 308 and 248 nm
Journal of Photochemistry and Photobiology, A: Chemistry, 64 (1) :1-14
1992

DOI: 10.1016/1010-6030(92)85089-D

394.

Becker, Karl Heinz; K{ö}nig, R.; Meuser, R.; Wiesen, Peter; Bayes, Kyle D.
Kinetics of C\(_{2}\)O radicals formed in the photolysis of carbon suboxide at 308 and 248 nm
Journal of Photochemistry and Photobiology, A: Chemistry, 64 (1) :1-14
1992

DOI: 10.1016/1010-6030(92)85089-D

393.

Becker, Karl Heinz; König, R.; Meuser, R.; Wiesen, Peter; Bayes, Kyle D.
Kinetics of C2O radicals formed in the photolysis of carbon suboxide at 308 and 248 nm
Journal of Photochemistry and Photobiology, A: Chemistry, 64 (1) :1-14
1992

DOI: 10.1016/1010-6030(92)85089-D

392.

Tausch, Michael W.; Wachtendonk, M.; Deissenberger, H.; Porth, H.-R.; Weißenhorn, R.G.
Lehrerband mit didaktischen Hinweisen und Lösungen der Aufgaben zu STOFF-FORMEL-UMWELT, BAND 2: ORGANISCHE CHEMIE - ANGEWANDTE CHEMIE, Lehrbuch für die S II, (Grund- und Leistungskurse)
Herausgeber: C. C. Buchner, Bamberg
1992

391.

G\"unther, Michael
Multirate {Rosenbrock}-{Wanner} Verfahren zur Integration von elektrischen Schaltkreisen
Technische Universit\"at at M\"unchen
1992

390.

Shestakov, Oleg; Pravilov, A. M.; Demes, H.; Fink, Ewald H.
Radiative lifetime and quenching of the A \(^{2}\)\(\Sigma\)\(^{+}\) and X\(_{2}\) \(^{2}\)\(\Pi\)\(_{3/2}\) states of PbF
Chemical Physics, 165 (2-3) :415-427
1992

DOI: 10.1016/0301-0104(92)87056-F

389.

Shestakov, Oleg; Pravilov, A. M.; Demes, H.; Fink, Ewald H.
Radiative lifetime and quenching of the A \(^{2}\)\(\Sigma\)\(^{+}\) and X\(_{2}\) \(^{2}\)\(\Pi\)\(_{3/2}\) states of PbF
Chemical Physics, 165 (2-3) :415-427
1992

DOI: 10.1016/0301-0104(92)87056-F