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

1990

303.

Jensen, Per; Buenker, Robert J.; Hirsch, Gerhard; Rai, Sachchida N.
An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH2
Molecular Physics, 70 (3) :443-454
1990

DOI: 10.1080/00268979000101111

302.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990

DOI: 10.1063/1.458229

301.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990

DOI: 10.1063/1.458229

300.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990

DOI: 10.1063/1.458229

299.

Heilmann, Margareta; Müller, Manfred
Direct and converse results on simultaneous approximation by the method of Bernstein-Durrmeyer operators
Algorithms for approximation II, Proc. 2nd Int. Conf., Shrivenham/UK 1988, Seite 107-116
1990

DOI: 10.1007/978-1-4899-3442-0_11

298.

Fink, Ewald H.; Kruse, H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High resolution Fourier-transform spectra of the a\(^{1}\)\(\Delta\)\(_{g}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\), b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) and X\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\) systems of O\(_{2}\), SO, S\(_{2}\) and isoe
Acta Physica Hungarica, 67 (1-2) :67-72
1990

DOI: 10.1007/BF03054252

297.

Fink, Ewald H.; Kruse, H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High resolution Fourier-transform spectra of the a\(^{1}\)\(\Delta\)\(_{g}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\), b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) and X\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\) systems of O\(_{2}\), SO, S\(_{2}\) and isoe
Acta Physica Hungarica, 67 (1-2) :67-72
1990

DOI: 10.1007/BF03054252

296.

Fink, Ewald H.; Kruse, H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High resolution Fourier-transform spectra of the a1Δg → X3Σg-, b1Σg+ → X3Σg- and X1Σg+ → a1Δg systems of O2, SO, S2 and isoe
Acta Physica Hungarica, 67 (1-2) :67-72
1990

DOI: 10.1007/BF03054252

295.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Brown, John M.
High-resolution study of the A 1-X 0\(^{+}\) emission system of bismuth hydride
Journal of Molecular Spectroscopy, 142 (1) :108-116
1990

DOI: 10.1016/0022-2852(90)90294-Z

294.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Brown, John M.
High-resolution study of the A 1-X 0\(^{+}\) emission system of bismuth hydride
Journal of Molecular Spectroscopy, 142 (1) :108-116
1990

DOI: 10.1016/0022-2852(90)90294-Z

293.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Brown, John M.
High-resolution study of the A 1-X 0+ emission system of bismuth hydride
Journal of Molecular Spectroscopy, 142 (1) :108-116
1990

DOI: 10.1016/0022-2852(90)90294-Z

292.

Tausch, Michael W.; Deissenberger, H.; Fischer, W.; Hoffmann, W.; Jakob, O.; Riedl, A.; Schallies, M.; Wachtendonk, M.
Lehrerband mit didaktischen Hinweisen und Lösungen der Aufgaben zu STOFF UND FORMEL II, Lehrbuch für die S II (Grundkurse)
Herausgeber: C. C. Buchner, Bamberg
1990

291.

Tausch, Michael W.; Deissenberger, H.; Fischer, W.; Hoffmann, W.; Jakob, O.; Riedl, A.; Schallies, M.; Wachtendonk, M.
STOFF UND FORMEL II, Lehrbuch für die S II (Grundkurse), 325 Seiten
Herausgeber: C. C. Buchner, Bamberg
1990

290.


Technische Universität Berlin Wintersemester 06/07 Fakultät II--Institut für Mathematik
SIAM J. Appl. Math, 50 :1442--1456
1990
1989

289.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Lischka, Hans
A theoretical calculation of the rotation-vibration energies for lithium hydroxide, LiOH
Journal of Molecular Spectroscopy, 135 (1) :89-104
1989

DOI: 10.1016/0022-2852(89)90357-3

288.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Lischka, Hans
A theoretical calculation of the rotation-vibration energies for lithium hydroxide, LiOH
Journal of Molecular Spectroscopy, 135 (1) :89-104
1989

DOI: 10.1016/0022-2852(89)90357-3

287.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Lischka, Hans
A theoretical calculation of the rotation-vibration energies for lithium hydroxide, LiOH
Journal of Molecular Spectroscopy, 135 (1) :89-104
1989

DOI: 10.1016/0022-2852(89)90357-3

286.

Comeau, Donald C.; Shavitt, Isaiah; Jensen, Per; Bunker, Philip R.
An ab initio determination of the potential-energy surfaces and rotation-vibration energy levels of methylene in the lowest triplet and singlet states and the singlet-triplet splitting
The Journal of Chemical Physics, 90 (11) :6491-6500
1989

DOI: 10.1063/1.456315

285.

Comeau, Donald C.; Shavitt, Isaiah; Jensen, Per; Bunker, Philip R.
An ab initio determination of the potential-energy surfaces and rotation-vibration energy levels of methylene in the lowest triplet and singlet states and the singlet-triplet splitting
The Journal of Chemical Physics, 90 (11) :6491-6500
1989

DOI: 10.1063/1.456315

284.

Comeau, Donald C.; Shavitt, Isaiah; Jensen, Per; Bunker, Philip R.
An ab initio determination of the potential-energy surfaces and rotation-vibration energy levels of methylene in the lowest triplet and singlet states and the singlet-triplet splitting
The Journal of Chemical Physics, 90 (11) :6491-6500
1989

DOI: 10.1063/1.456315

283.

Civis, S.; Blom, C. E.; Jensen, Per
Diode laser infrared spectra and potential energy curve for SH\(^{+}\)
Journal of Molecular Spectroscopy, 138 (1) :69-78
1989

DOI: 10.1016/0022-2852(89)90099-4

282.

Civis, S.; Blom, C. E.; Jensen, Per
Diode laser infrared spectra and potential energy curve for SH\(^{+}\)
Journal of Molecular Spectroscopy, 138 (1) :69-78
1989

DOI: 10.1016/0022-2852(89)90099-4

281.

Civis, S.; Blom, C. E.; Jensen, Per
Diode laser infrared spectra and potential energy curve for SH+
Journal of Molecular Spectroscopy, 138 (1) :69-78
1989

DOI: 10.1016/0022-2852(89)90099-4

280.

Heilmann, Margareta
Direct and converse results for operators of Baskakov-Durrmeyer type
Approximation Theory Appl., 5 (1) :105-127
1989

DOI: 10.1007/BF02836120

279.

Heilmann, Margareta; Müller, Manfred
Direct and converse results on weighted simultaneous approximation by the method of operators of Baskakov-Durrmeyer type
Results in Mathematics, 16 (3-4) :228-242
1989

DOI: 10.1007/BF03322474