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
- 1985
137.
Holstein, K. J.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
A\verb=~=\(^{2}\)A' → X\verb=~=\(^{2}\)A'' emission spectrum of the HS\(_{2}\) radical
Chemical Physics Letters, 113 (1) :1-7
1985136.
Holstein, K. J.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
A\verb=~=\(^{2}\)A' → X\verb=~=\(^{2}\)A'' emission spectrum of the HS\(_{2}\) radical
Chemical Physics Letters, 113 (1) :1-7
1985135.
Holstein, K. J.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
A~2A' → X~2A" emission spectrum of the HS2 radical
Chemical Physics Letters, 113 (1) :1-7
1985134.
Tausch, Michael W.
Aktivierungsenergie - was ist das?
Praxis der Naturwissenschaften (Chemie), 34 :33
1985133.
Phillips, R.A.; Buenker, Robert J.; Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
An ab initio study of the rotation-vibration energy levels of GeH\(_{2}\) in the a\verb=~=\(^{3}\)B\(_{1}\) state
Chemical Physics Letters, 118 (1) :60-63
1985132.
Phillips, R.A.; Buenker, Robert J.; Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
An ab initio study of the rotation-vibration energy levels of GeH\(_{2}\) in the a\verb=~=\(^{3}\)B\(_{1}\) state
Chemical Physics Letters, 118 (1) :60-63
1985131.
Phillips, R.A.; Buenker, Robert J.; Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
An ab initio study of the rotation-vibration energy levels of GeH2 in the a~3B1 state
Chemical Physics Letters, 118 (1) :60-63
1985130.
Kling, H.-W.; Hartkamp, H.; Buchholz, N.
Matrixunabhängige kontinuierliche Dampfraum-Gas-Chromatographie
Fresenius' Journal of Analytical Chemistry, 320 (4) :341--346
1985129.
Winkler, R.
Path-following for two-point boundary value problems
, Seminarbericht 78 der Sektion MathematikBand78
Humboldt-Universität zu Berlin
1985128.
Spirko, Vladim{í}r; Jensen, Per; Bunker, Philip R.; Cejchan, A.
The development of a new Morse-oscillator based rotation-vibration Hamiltonian for H\(_{3}\)\(^{+}\)
Journal of Molecular Spectroscopy, 112 (1) :183-202
1985127.
Spirko, Vladim{í}r; Jensen, Per; Bunker, Philip R.; Cejchan, A.
The development of a new Morse-oscillator based rotation-vibration Hamiltonian for H\(_{3}\)\(^{+}\)
Journal of Molecular Spectroscopy, 112 (1) :183-202
1985126.
Spirko, Vladimír; Jensen, Per; Bunker, Philip R.; Cejchan, A.
The development of a new Morse-oscillator based rotation-vibration Hamiltonian for H3+
Journal of Molecular Spectroscopy, 112 (1) :183-202
1985125.
Lamour, R.; Hanke, M.; Winkler, R.
The program system ‘RWA’ (version 2) for the solution of TPBVP - fundamentals and algorithms
, Seminarbericht 67 der Sektion MathematikBand67
Humboldt-Universität zu Berlin
1985- 1984
124.
Morillon-Chapey, M.; Guelachvili, Guy; Jensen, Per
Analysis of the high resolution spectrum of the \(\nu\)\(_{2}\) and \(\nu\)\(_{5}\) absorption bands of methyl chloride
Canadian Journal of Physics, 62 (3) :247-253
1984
Herausgeber: NRC Research Press Ottawa, Canada123.
Morillon-Chapey, M.; Guelachvili, Guy; Jensen, Per
Analysis of the high resolution spectrum of the \(\nu\)\(_{2}\) and \(\nu\)\(_{5}\) absorption bands of methyl chloride
Canadian Journal of Physics, 62 (3) :247-253
1984
Herausgeber: NRC Research Press Ottawa, Canada122.
Morillon-Chapey, M.; Guelachvili, Guy; Jensen, Per
Analysis of the high resolution spectrum of the ν2 and ν5 absorption bands of methyl chloride
Canadian Journal of Physics, 62 (3) :247-253
1984
Herausgeber: NRC Research Press Ottawa, Canada121.
Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) Emissions from group V-VII diatomic molecules. b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)1 band systems of AsCl and AsBr
Chemical Physics Letters, 111 (1-2) :100-104
1984120.
Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) Emissions from group V-VII diatomic molecules. b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)1 band systems of AsCl and AsBr
Chemical Physics Letters, 111 (1-2) :100-104
1984119.
Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) Emissions from group V-VII diatomic molecules. b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)1 emissions of AsI and SbI
Chemical Physics Letters, 104 (4) :383-388
1984118.
Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) Emissions from group V-VII diatomic molecules. b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)1 emissions of AsI and SbI
Chemical Physics Letters, 104 (4) :383-388
1984117.
Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ Emissions from group V-VII diatomic molecules. b0+ → X10+, X21 band systems of AsCl and AsBr
Chemical Physics Letters, 111 (1-2) :100-104
1984116.
Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ Emissions from group V-VII diatomic molecules. b0+ → X10+, X21 emissions of AsI and SbI
Chemical Physics Letters, 104 (4) :383-388
1984115.
Jensen, Per
C\(_{3}\)O\(_{2}\) as a semirigid bender: The degenerate \(\nu\)\(_{5}\) state
Journal of Molecular Spectroscopy, 104 (1) :59-71
1984114.
Jensen, Per
C\(_{3}\)O\(_{2}\) as a semirigid bender: The degenerate \(\nu\)\(_{5}\) state
Journal of Molecular Spectroscopy, 104 (1) :59-71
1984113.
Jensen, Per
C3O2 as a semirigid bender: The degenerate ν5 state
Journal of Molecular Spectroscopy, 104 (1) :59-71
1984
