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
- 1983
100.
Bunker, Philip R.; Jensen, Per
A refined potential surface for the X\verb=~=\(^{3}\)B\(_{1}\) electronic state of methylene CH\(_{2}\)
The Journal of Chemical Physics, 79 (3) :1224-1228
198399.
Bunker, Philip R.; Jensen, Per
A refined potential surface for the X\verb=~=\(^{3}\)B\(_{1}\) electronic state of methylene CH\(_{2}\)
The Journal of Chemical Physics, 79 (3) :1224-1228
198398.
Bunker, Philip R.; Jensen, Per
A refined potential surface for the X~3B1 electronic state of methylene CH2
The Journal of Chemical Physics, 79 (3) :1224-1228
198397.
Winter, R.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) and a\(^{1}\)\(\Delta\) emissions from group VI-VI diatomic molecules: b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)1 emissions of TeSe
Chemical Physics Letters, 94 (3) :335-338
198396.
Winter, R.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) and a\(^{1}\)\(\Delta\) emissions from group VI-VI diatomic molecules: b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)1 emissions of TeSe
Chemical Physics Letters, 94 (3) :335-338
198395.
Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, J{ü}rgen
b\(^{1}\)\(\Sigma\)\(^{+}\) Emissions from group V-VII diatomic molecules: b0\(^{+}\) → X\(_{1}\)0\(^{+}\) emission of Pl
Chemical Physics Letters, 102 (5) :404-408
198394.
Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, J{ü}rgen
b\(^{1}\)\(\Sigma\)\(^{+}\) Emissions from group V-VII diatomic molecules: b0\(^{+}\) → X\(_{1}\)0\(^{+}\) emission of Pl
Chemical Physics Letters, 102 (5) :404-408
198393.
Winter, R.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ and a1Δ emissions from group VI-VI diatomic molecules: b0+ → X10+, X21 emissions of TeSe
Chemical Physics Letters, 94 (3) :335-338
198392.
Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, Jürgen
b1Σ+ Emissions from group V-VII diatomic molecules: b0+ → X10+ emission of Pl
Chemical Physics Letters, 102 (5) :404-408
198391.
Tausch, Michael W.
Chemische Solarenergiespeicherung in Valenzisomeren
Praxis der Naturwissenschaften (Chemie), 32 :79
198390.
Tausch, Michael W.
DER UV-TAUCHLAMPENREAKTOR FÜR PHOTOCHEMISCHE SCHULVERSUCHE, Monographie mit Versuchsanleitungen und didaktischen Hinweisen
Herausgeber: SCS Jürgens\&Co KG, Bremen
198389.
Jensen, Per
HCNO as a semirigid bender: The degenerate \(\nu\)\(_{4}\) state
Journal of Molecular Spectroscopy, 101 (2) :422-439
198388.
Jensen, Per
HCNO as a semirigid bender: The degenerate \(\nu\)\(_{4}\) state
Journal of Molecular Spectroscopy, 101 (2) :422-439
198387.
Jensen, Per
HCNO as a semirigid bender: The degenerate ν4 state
Journal of Molecular Spectroscopy, 101 (2) :422-439
198386.
Holstein, K. J.; Fink, Ewald H.; Wildt, J{ü}rgen; Winter, R.; Zabel, Friedhelm
Mechanisms of perhydroxyl HO\(_{2}\)(A\(^{2}\)A') excitation in various chemical systems
The Journal of Physical Chemistry, 87 (20) :3943-3948
198385.
Holstein, K. J.; Fink, Ewald H.; Wildt, J{ü}rgen; Winter, R.; Zabel, Friedhelm
Mechanisms of perhydroxyl HO\(_{2}\)(A\(^{2}\)A') excitation in various chemical systems
The Journal of Physical Chemistry, 87 (20) :3943-3948
198384.
Holstein, K. J.; Fink, Ewald H.; Wildt, Jürgen; Winter, R.; Zabel, Friedhelm
Mechanisms of perhydroxyl HO2(A2A') excitation in various chemical systems
The Journal of Physical Chemistry, 87 (20) :3943-3948
198383.
Wildt, J{ü}rgen; Fink, Ewald H.; Winter, R.; Zabel, Friedhelm
Radiative lifetime and quenching of SO(b\(^{1}\)\(\Sigma\)\(^{+}\),\(\nu\)'=0)
Chemical Physics, 80 (1-2) :167-175
198382.
Wildt, J{ü}rgen; Fink, Ewald H.; Winter, R.; Zabel, Friedhelm
Radiative lifetime and quenching of SO(b\(^{1}\)\(\Sigma\)\(^{+}\),\(\nu\)'=0)
Chemical Physics, 80 (1-2) :167-175
198381.
Wildt, Jürgen; Fink, Ewald H.; Winter, R.; Zabel, Friedhelm
Radiative lifetime and quenching of SO(b1Σ+,ν'=0)
Chemical Physics, 80 (1-2) :167-175
198380.
Wildt, J{ü}rgen; Bielefeld, M.; Fink, Ewald H.; Winter, R.; Zabel, Friedhelm
Radiative livetimes of the metastable b\(^{1}\)\(\Sigma\) states of SO, SeO, PCl and PBr
Bulletin des Sociétés Chimiques Belges, 92 (6-7) :523-524
198379.
Wildt, J{ü}rgen; Bielefeld, M.; Fink, Ewald H.; Winter, R.; Zabel, Friedhelm
Radiative livetimes of the metastable b\(^{1}\)\(\Sigma\) states of SO, SeO, PCl and PBr
Bulletin des Sociétés Chimiques Belges, 92 (6-7) :523-524
198378.
Wildt, Jürgen; Bielefeld, M.; Fink, Ewald H.; Winter, R.; Zabel, Friedhelm
Radiative livetimes of the metastable b1Σ states of SO, SeO, PCl and PBr
Bulletin des Sociétés Chimiques Belges, 92 (6-7) :523-524
198377.
[german] Tausch, Michael W.
Strukturaufklärung in der organischen Chemie - Ermittlung der Strukturformeln von Maleinsäure und Fumarsäure
Praxis der Naturwissenschaften (Chemie), 32 :44
198376.
Holstein, K. J.; Fink, Ewald H.; Zabel, Friedhelm
The \(\nu\)\(_{3}\) vibration of electronically excited HO\(_{2}\)(A\(^{2}\)A')
Journal of Molecular Spectroscopy, 99 (1) :231-234
1983
