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
- 1984
118.
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
1984112.
Kreglewski, Marek; Jensen, Per
Determination of the skeletal bending potential function for SiH\(_{3}\)NCO from the microwave spectrum
Journal of Molecular Spectroscopy, 103 (2) :312-320
1984111.
Kreglewski, Marek; Jensen, Per
Determination of the skeletal bending potential function for SiH\(_{3}\)NCO from the microwave spectrum
Journal of Molecular Spectroscopy, 103 (2) :312-320
1984110.
Kreglewski, Marek; Jensen, Per
Determination of the skeletal bending potential function for SiH3NCO from the microwave spectrum
Journal of Molecular Spectroscopy, 103 (2) :312-320
1984109.
Glöckner, W.; Tausch, Michael W.; Autorenteam
MATERIALIEN FÜR DER KURSUNTERRICHT CHEMIE, Aufgabensammlung mit Klausur- und Abituraufgaben aus allen Bereichen der Schulchemie, 3 Bände
Herausgeber: Aulis Deubner\&Co KG, Köln
1984108.
Winkler, R.
Numerische Behandlung von parameterabhängigen Zwei-Punkt-Randwertaufgaben unter Berücksichtigung von Verzweigungsproblemen
Humboldt-Universität zu Berlin
1984107.
Bielefeld, M.; Elfers, G.; Fink, Ewald H.; Kruse, H.; Wildt, J{ü}rgen; Winter, R.; Zabel, Friedhelm
O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))-sensitized chemiluminescence of a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) and b\(^{1}\)\(\Sigma\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(^{-}\) transitions of group VI-group VI and group V-group VII diatomic molecules
Journal of Photochemistry, 25 (2-4) :419-438
1984106.
Bielefeld, M.; Elfers, G.; Fink, Ewald H.; Kruse, H.; Wildt, J{ü}rgen; Winter, R.; Zabel, Friedhelm
O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))-sensitized chemiluminescence of a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) and b\(^{1}\)\(\Sigma\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(^{-}\) transitions of group VI-group VI and group V-group VII diatomic molecules
Journal of Photochemistry, 25 (2-4) :419-438
1984105.
Bielefeld, M.; Elfers, G.; Fink, Ewald H.; Kruse, H.; Wildt, Jürgen; Winter, R.; Zabel, Friedhelm
O2(a1Δg)-sensitized chemiluminescence of a1Δ → X3Σ- and b1Σ+ → X3Σ- transitions of group VI-group VI and group V-group VII diatomic molecules
Journal of Photochemistry, 25 (2-4) :419-438
1984104.
Maten, E. J. W.
Stability analysis of finite difference methods for fourth order parabolic partial differential equations
Rijksuniversiteit Utrecht
1984103.
Becker, Karl Heinz; Horie, O.; Wiesen, Peter
The formation of CH radicals during the photolysis of CH\(_{2}\)N\(_{2}\) in the presence of hydrogen and oxygen atoms
Journal of Photochemistry, 24 (3) :293-297
1984102.
Becker, Karl Heinz; Horie, O.; Wiesen, Peter
The formation of CH radicals during the photolysis of CH\(_{2}\)N\(_{2}\) in the presence of hydrogen and oxygen atoms
Journal of Photochemistry, 24 (3) :293-297
1984101.
Becker, Karl Heinz; Horie, O.; Wiesen, Peter
The formation of CH radicals during the photolysis of CH2N2 in the presence of hydrogen and oxygen atoms
Journal of Photochemistry, 24 (3) :293-297
1984- 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
1983
