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

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 USA1989Band 1, Seite 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

243.

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

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

242.

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

DOI: 10.1002/bbpc.198800018

241.

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

DOI: 10.1002/bbpc.198800018

240.

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

DOI: 10.1002/bbpc.198800018

239.

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

DOI: 10.1016/0022-2852(88)90164-6

238.

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

DOI: 10.1016/0022-2852(88)90164-6

237.

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

DOI: 10.1016/0022-2852(88)90164-6

236.

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

DOI: 10.1016/0022-2852(88)90271-8

235.

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

DOI: 10.1016/0022-2852(88)90271-8

234.

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

DOI: 10.1016/0022-2852(88)90271-8

233.

Jensen, Per
A variational calculation of the rotation-vibration energies for H\(_{2}\)O from Ab initio data
Journal of Molecular Structure, 190 :149-161
1988

DOI: 10.1016/0022-2860(88)80280-1

232.

Jensen, Per
A variational calculation of the rotation-vibration energies for H\(_{2}\)O from Ab initio data
Journal of Molecular Structure, 190 :149-161
1988

DOI: 10.1016/0022-2860(88)80280-1

231.

Jensen, Per
A variational calculation of the rotation-vibration energies for H2O from Ab initio data
Journal of Molecular Structure, 190 :149-161
1988

DOI: 10.1016/0022-2860(88)80280-1

230.

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

DOI: 10.1016/0009-2614(88)85134-0

229.

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

DOI: 10.1016/0009-2614(88)85134-0

228.

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

DOI: 10.1016/0009-2614(88)85134-0

227.

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

DOI: 10.1016/0022-2852(88)90338-4

226.

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

DOI: 10.1016/0022-2852(88)90338-4