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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

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.

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

266.

Heilmann, Margareta
On simultaneous approximation by optimal algebraic polynomials
Results in Mathematics, 16 (1-2) :77-81
1989

DOI: 10.1007/BF03322645

265.

Heilmann, Margareta; Müller, Manfred
On simultaneous approximation by the method of Baskakov-Durrmeyer operators
Numerical Functional Analysis and Optimization, 10 (1-2) :127-138
1989

DOI: 10.1080/01630568908816295

264.

[german] Tausch, Michael W.; Wöhrle, D.
Photokatalyse
Praxis der Naturwissenschaften (Chemie), 38 :37
1989

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263.

Becker, Karl Heinz; Engelhardt, B.; Wiesen, Peter; Bayes, Kyle D.
Rate constants for CH(X\(^{2}\)\(\Pi\)) reactions at low total pressures
Chemical Physics Letters, 154 (4) :342-348
1989

DOI: 10.1016/0009-2614(89)85367-9

262.

Becker, Karl Heinz; Engelhardt, B.; Wiesen, Peter; Bayes, Kyle D.
Rate constants for CH(X\(^{2}\)\(\Pi\)) reactions at low total pressures
Chemical Physics Letters, 154 (4) :342-348
1989

DOI: 10.1016/0009-2614(89)85367-9

261.

Becker, Karl Heinz; Engelhardt, B.; Wiesen, Peter; Bayes, Kyle D.
Rate constants for CH(X2Π) reactions at low total pressures
Chemical Physics Letters, 154 (4) :342-348
1989

DOI: 10.1016/0009-2614(89)85367-9

260.

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

259.

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

258.

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

257.

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

256.

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

255.

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

254.

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

253.

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
Publisher: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19891209

252.

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
Publisher: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19891209

251.

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
Publisher: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19891209

250.

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

249.

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

248.

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

247.

Schönfeld, J; Loennecken, I; Gückel, C
Unilateral pulsating tinnitus: paraganglioma of the glomus jugulare with predominantly vascular extension
Medizinische Klinik (Munich, Germany: 1983), 84 (9) :445--449
1989

246.

Heilmann, Margareta; Müller, Manfred
Weighted simultaneous L_p-approximation by the method of Baskakov-Durrmeyer operators
Approximation Theory VI, Proc. 6th Int. Symp., College Station/TX USA1989Volume 1, Page 331-332
1989

DOI: 10.1007/s10474-011-0135-x

1988

245.

Jensen, Per; Kraemer, Wolfgang P.
A comparison of perturbative and variational rotation-vibration energies calculated for HOC\(^{+}\) and C\(_{3}\) using the nonrigid bender and MORBID Hamiltonians
Journal of Molecular Spectroscopy, 129 (1) :172-185
1988

DOI: 10.1016/0022-2852(88)90268-8

244.

Jensen, Per; Kraemer, Wolfgang P.
A comparison of perturbative and variational rotation-vibration energies calculated for HOC\(^{+}\) and C\(_{3}\) using the nonrigid bender and MORBID Hamiltonians
Journal of Molecular Spectroscopy, 129 (1) :172-185
1988

DOI: 10.1016/0022-2852(88)90268-8