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

1989

280.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Xu, G. Z.
Rotational analysis of the 0-0 band of the b0\(^{+}\) → X\(_{1}\)0\(^{+}\) system of \(^{130}\)Te\(^{80}\)Se
Journal of Molecular Spectroscopy, 136 (1) :218-221
1989

DOI: 10.1016/0022-2852(89)90236-1

279.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Xu, G. Z.
Rotational analysis of the 0-0 band of the b0\(^{+}\) → X\(_{1}\)0\(^{+}\) system of \(^{130}\)Te\(^{80}\)Se
Journal of Molecular Spectroscopy, 136 (1) :218-221
1989

DOI: 10.1016/0022-2852(89)90236-1

278.

Jensen, Per
The potential energy surface for the C\(_{3}\) molecule determined from experimental data. Evidence for a bent equilibrium structure
Collection of Czechoslovak Chemical Communications, 54 (5) :1209-1218
1989
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19891209

277.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Xu, G. Z.
Rotational analysis of the 0-0 band of the b0+ → X10+ system of 130Te80Se
Journal of Molecular Spectroscopy, 136 (1) :218-221
1989

DOI: 10.1016/0022-2852(89)90236-1

276.

Tausch, Michael W.; Wachtendonk, M.
STOFF-FORMEL-UMWELT, BAND 1: CHEMISCHE GLEICHGEWICHTE - ELEKTROCHEMIE, Lehrbuch für die S II (Grund- und Leistungskurse), 172 Seiten
Herausgeber: C. C. Buchner, Bamberg
1989

275.

Wildt, J{ü}rgen; Fink, Ewald H.; Biggs, P.; Wayne, Richard P.
The collision-induced radiation of O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))
Chemical Physics, 139 (2-3) :401-407
1989

DOI: 10.1016/0301-0104(89)80152-1

274.

Wildt, J{ü}rgen; Fink, Ewald H.; Biggs, P.; Wayne, Richard P.
The collision-induced radiation of O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))
Chemical Physics, 139 (2-3) :401-407
1989

DOI: 10.1016/0301-0104(89)80152-1

273.

Wildt, Jürgen; Fink, Ewald H.; Biggs, P.; Wayne, Richard P.
The collision-induced radiation of O2(a1Δg)
Chemical Physics, 139 (2-3) :401-407
1989

DOI: 10.1016/0301-0104(89)80152-1

272.

Jensen, Per
The potential energy surface for the C\(_{3}\) molecule determined from experimental data. Evidence for a bent equilibrium structure
Collection of Czechoslovak Chemical Communications, 54 (5) :1209-1218
1989
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19891209

271.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
Near-infrared emission bands of TeH and TeD
Journal of Molecular Spectroscopy, 138 (1) :19-28
1989

DOI: 10.1016/0022-2852(89)90094-5

270.

Jensen, Per
The potential energy surface for the C3 molecule determined from experimental data. Evidence for a bent equilibrium structure
Collection of Czechoslovak Chemical Communications, 54 (5) :1209-1218
1989
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19891209

269.

Jensen, Per
The potential energy surface for the electronic ground state of the water molecule determined from experimental data using a variational approach
Journal of Molecular Spectroscopy, 133 (2) :438-460
1989

DOI: 10.1016/0022-2852(89)90203-8

268.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
Near-infrared emission bands of TeH and TeD
Journal of Molecular Spectroscopy, 138 (1) :19-28
1989

DOI: 10.1016/0022-2852(89)90094-5

267.

Bauer, W.; Engelhardt, B.; Wiesen, Peter; Becker, Karl Heinz
Lifetime measurements of GeH and CH in the A\(^{2}\)\(\Delta\), v'=0 state by laser-induced fluorescence
Chemical Physics Letters, 158 (3-4) :321-324
1989

DOI: 10.1016/0009-2614(89)87344-0

266.

Becker, Karl Heinz; Wiesen, Peter
Measurements on the CH*(A2Δ → X2Π) Chemiluminescence in the C2H2 + O Flame and Quenching Rate Constants for Different Reactants at 297 K
Zeitschrift für Physikalische Chemie, 161 (Part_1_2) :131-144
1989

DOI: 10.1524/zpch.1989.161.Part_1_2.131

265.

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

264.

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

263.

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

262.

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

261.

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

260.

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

259.

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

258.

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

257.

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

256.

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

DOI: 10.1007/BF02836120

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