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



1988

265.

Becker, Karl Heinz; Brockmann, Klaus Josef; Wiesen, Peter
Spectroscopic identification of C(\(^{3}\)P) atoms in halogenomethane + H flame systems and measurements of C(\(^{3}\)P) reaction rate constants by two-photon laser-induced fluorescence
Journal of the Chemical Society, Faraday Transactions 2, 84 (5) :455-461
1988

264.

Becker, Karl Heinz; Brockmann, Klaus Josef; Wiesen, Peter
Spectroscopic identification of C(3P) atoms in halogenomethane + H flame systems and measurements of C(3P) reaction rate constants by two-photon laser-induced fluorescence
Journal of the Chemical Society, Faraday Transactions 2, 84 (5) :455-461
1988

263.

Fink, Ewald H.; Setzer, Klaus-Dieter; Kottsieper, U.; Ramsay, D. A.; Vervloet, M.
The a\(^{1}\)\(\Delta\)(a2)-X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{2}\)1) electronic band system of selenium monoxide
Journal of Molecular Spectroscopy, 131 (1) :127-132
1988

262.

Fink, Ewald H.; Setzer, Klaus-Dieter; Kottsieper, U.; Ramsay, D. A.; Vervloet, M.
The a\(^{1}\)\(\Delta\)(a2)-X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{2}\)1) electronic band system of selenium monoxide
Journal of Molecular Spectroscopy, 131 (1) :127-132
1988

261.

Fink, Ewald H.; Setzer, Klaus-Dieter; Kottsieper, U.; Ramsay, D. A.; Vervloet, M.
The a1Δ(a2)-X3Σ-(X21) electronic band system of selenium monoxide
Journal of Molecular Spectroscopy, 131 (1) :127-132
1988

260.

Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X\verb=~=\(^{3}\)B\(_{1}\) methylene (CH\(_{2}\)) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988

259.

Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X\verb=~=\(^{3}\)B\(_{1}\) methylene (CH\(_{2}\)) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988

258.

Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X~3B1 methylene (CH2) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988

257.

[german] Tausch, Michael W.; Paterkiewicz, D.
Fluoreszenz und Phosphoreszenz
Praxis der Naturwissenschaften (Chemie), 36 :14
1988

256.

Weinmüller, E.; Winkler, E.
Path-following Algorithm for Singular Boundary Value Problems
ZAMM, 68 :527--537
1988

255.

Jensen, Per
Calculation of rotation-vibration linestrengths for triatomic molecules using a variational approach
Journal of Molecular Spectroscopy, 132 (2) :429-457
1988

254.

Jensen, Per; Kraemer, Wolfgang P.
A variational calculation of the rotation-vibration energies for CNC\(^{+}\) and CCN\(^{+}\)
Journal of Molecular Spectroscopy, 129 (1) :216-222
1988

253.

Jensen, Per
Calculation of rotation-vibration linestrengths for triatomic molecules using a variational approach
Journal of Molecular Spectroscopy, 132 (2) :429-457
1988

252.

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

251.

Jensen, Per; Kraemer, Wolfgang P.
A comparison of perturbative and variational rotation-vibration energies calculated for HOC+ and C3 using the nonrigid bender and MORBID Hamiltonians
Journal of Molecular Spectroscopy, 129 (1) :172-185
1988

250.

Rahman, M. M.; Becker, Eilhard; Benter, Thorsten; Schindler, Ralph N.
A Gasphase Kinetic Investigation of the System F + HNO\(_{3}\) and the Determination of Absolute Rate Constants for the Reaction of the NO\(_{3}\) Radical with CH\(_{3}\)SH, 2-Methylpropene, 1,3-Butadiene and 2,3-Dimethyl-2-Butene
Berichte der Bunsengesellschaft für physikalische Chemie, 92 (1) :91-100
1988

249.

Rahman, M. M.; Becker, Eilhard; Benter, Thorsten; Schindler, Ralph N.
A Gasphase Kinetic Investigation of the System F + HNO\(_{3}\) and the Determination of Absolute Rate Constants for the Reaction of the NO\(_{3}\) Radical with CH\(_{3}\)SH, 2-Methylpropene, 1,3-Butadiene and 2,3-Dimethyl-2-Butene
Berichte der Bunsengesellschaft für physikalische Chemie, 92 (1) :91-100
1988

248.

Rahman, M. M.; Becker, Eilhard; Benter, Thorsten; Schindler, Ralph N.
A Gasphase Kinetic Investigation of the System F + HNO3 and the Determination of Absolute Rate Constants for the Reaction of the NO3 Radical with CH3SH, 2-Methylpropene, 1,3-Butadiene and 2,3-Dimethyl-2-Butene
Berichte der Bunsengesellschaft für physikalische Chemie, 92 (1) :91-100
1988

247.

Jensen, Per
A new morse oscillator-rigid bender internal dynamics (MORBID) Hamiltonian for triatomic molecules
Journal of Molecular Spectroscopy, 128 (2) :478-501
1988

246.

Jensen, Per
A new morse oscillator-rigid bender internal dynamics (MORBID) Hamiltonian for triatomic molecules
Journal of Molecular Spectroscopy, 128 (2) :478-501
1988

245.

Jensen, Per
A new morse oscillator-rigid bender internal dynamics (MORBID) Hamiltonian for triatomic molecules
Journal of Molecular Spectroscopy, 128 (2) :478-501
1988

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

243.

Jensen, Per; Kraemer, Wolfgang P.
A variational calculation of the rotation-vibration energies for CNC\(^{+}\) and CCN\(^{+}\)
Journal of Molecular Spectroscopy, 129 (1) :216-222
1988

242.

Benter, Thorsten; Schindler, Ralph N.
Absolute rate coefficients for the reaction of NO\(_{3}\) radicals with simple dienes
Chemical Physics Letters, 145 (1) :67-70
1988

241.

Benter, Thorsten; Schindler, Ralph N.
Absolute rate coefficients for the reaction of NO3 radicals with simple dienes
Chemical Physics Letters, 145 (1) :67-70
1988

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