MPDAE

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

1981: 30.
Barnes, Ian; Bastian, V.; Becker, Karl Heinz; Fink, Ewald H.; Zabel, Friedhelm
Rate constant of the reaction of OH with HO2NO2
Chemical Physics Letters, 83 (3) :459-464
1981
DOI: 10.1016/0009-2614(81)85501-7
1980: 29.
Kauppinen, Jyrki; Jensen, Per; Brodersen, Svend
Determination of the B\(_{0}\) constant of C\(_{6}\)H\(_{6}\)
Journal of Molecular Spectroscopy, 83 (1) :161-174
1980
DOI: 10.1016/0022-2852(80)90318-5; 28.
Kauppinen, Jyrki; Jensen, Per; Brodersen, Svend
Determination of the B0 constant of C6H6
Journal of Molecular Spectroscopy, 83 (1) :161-174
1980
DOI: 10.1016/0022-2852(80)90318-5; 27.
Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(^{-}\) Emissions of SeO, SeS, and Se\(_{2}\) in the near infrared
Chemical Physics Letters, 73 (2) :297-303
1980
DOI: 10.1016/0009-2614(80)80376-9; 26.
Kauppinen, Jyrki; Jensen, Per; Brodersen, Svend
Determination of the B\(_{0}\) constant of C\(_{6}\)H\(_{6}\)
Journal of Molecular Spectroscopy, 83 (1) :161-174
1980
DOI: 10.1016/0022-2852(80)90318-5; 25.
Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ → X3Σ- Emissions of SeO, SeS, and Se2 in the near infrared
Chemical Physics Letters, 73 (2) :297-303
1980
DOI: 10.1016/0009-2614(80)80376-9; 24.
Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(^{-}\) Emissions of SeO, SeS, and Se\(_{2}\) in the near infrared
Chemical Physics Letters, 73 (2) :297-303
1980
DOI: 10.1016/0009-2614(80)80376-9
1979: 23.
Glaschick-Schimpf, I.; Leiss, A.; Monkhouse, Penelope B.; Schurath, Ulrich; Becker, Karl Heinz; Fink, Ewald H.
A kinetic study of the reactions of HO\(_{2}\)/DO\(_{2}\) radicals with nitric oxide using near-infrared chemiluminescence detection
Chemical Physics Letters, 67 (2-3) :318-323
1979
DOI: 10.1016/0009-2614(79)85170-2; 22.
Glaschick-Schimpf, I.; Leiss, A.; Monkhouse, Penelope B.; Schurath, Ulrich; Becker, Karl Heinz; Fink, Ewald H.
A kinetic study of the reactions of HO\(_{2}\)/DO\(_{2}\) radicals with nitric oxide using near-infrared chemiluminescence detection
Chemical Physics Letters, 67 (2-3) :318-323
1979
DOI: 10.1016/0009-2614(79)85170-2; 21.
Glaschick-Schimpf, I.; Leiss, A.; Monkhouse, Penelope B.; Schurath, Ulrich; Becker, Karl Heinz; Fink, Ewald H.
A kinetic study of the reactions of HO2/DO2 radicals with nitric oxide using near-infrared chemiluminescence detection
Chemical Physics Letters, 67 (2-3) :318-323
1979
DOI: 10.1016/0009-2614(79)85170-2; 20.
Tausch, Michael W.; C. Ha{ßs}, E.; J. Plath, P.
Beschreibung von Valenzisomerisierungen durch Strukturvariation auf vollständigen Graphen
Informal Communications in Mathematical Chemistry (MatCh), 7 :289
1979; 19.
Barnes, Ian; Becker, Karl Heinz; Fink, Ewald H.
Chemiluminescence of SO(\(^{1}\)\(\Delta\)\(_{g}\),\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\)) sensitized by O\(_{2}\)(\(^{1}\)\(\Delta\)\(_{g}\))
Chemical Physics Letters, 67 (2-3) :310-313
1979
DOI: 10.1016/0009-2614(79)85168-4; 18.
Barnes, Ian; Becker, Karl Heinz; Fink, Ewald H.
Chemiluminescence of SO(\(^{1}\)\(\Delta\)\(_{g}\),\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\)) sensitized by O\(_{2}\)(\(^{1}\)\(\Delta\)\(_{g}\))
Chemical Physics Letters, 67 (2-3) :310-313
1979
DOI: 10.1016/0009-2614(79)85168-4; 17.
Barnes, Ian; Becker, Karl Heinz; Fink, Ewald H.
Chemiluminescence of SO(1Δg,1Σg+) sensitized by O2(1Δg)
Chemical Physics Letters, 67 (2-3) :310-313
1979
DOI: 10.1016/0009-2614(79)85168-4; 16.
Barnes, Ian; Becker, Karl Heinz; Fink, Ewald H.
Near-infrared emissions from the \(^{1}\)\(\Delta\)\(_{g}\) and \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) states of S\(_{2}\)
Chemical Physics Letters, 67 (2-3) :314-317
1979
DOI: 10.1016/0009-2614(79)85169-6; 15.
Barnes, Ian; Becker, Karl Heinz; Fink, Ewald H.
Near-infrared emissions from the 1Δg and 1Σg+ states of S2
Chemical Physics Letters, 67 (2-3) :314-317
1979
DOI: 10.1016/0009-2614(79)85169-6; 14.
Tausch, Michael W.
Vorschlag für den Aufbau und die Bewertung einer Klausur zum Kurs ''Bindung und Struktur''
Praxis der Naturwissenschaften (Chemie), 28 :304
1979; 13.
Barnes, Ian; Becker, Karl Heinz; Fink, Ewald H.
Near-infrared emissions from the \(^{1}\)\(\Delta\)\(_{g}\) and \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) states of S\(_{2}\)
Chemical Physics Letters, 67 (2-3) :314-317
1979
DOI: 10.1016/0009-2614(79)85169-6
1978: 12.
Tausch, Michael W.; C. Hass, E.; J. Plath, P.
Eine graphentheoretische Bezugsstruktur für die Eigenwertsumme konjugierter Kohlenwasserstoffe
Bremer Briefe zur Chemie, 2 (30)
1978; 11.
Leiss, A.; Schurath, Ulrich; Becker, Karl Heinz; Fink, Ewald H.
Revised quenching rate constants for metastable oxygen molecules O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))
Journal of Photochemistry, 8 (2) :211-214
1978
DOI: 10.1016/0047-2670(78)80021-5; 10.
Leiss, A.; Schurath, Ulrich; Becker, Karl Heinz; Fink, Ewald H.
Revised quenching rate constants for metastable oxygen molecules O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))
Journal of Photochemistry, 8 (2) :211-214
1978
DOI: 10.1016/0047-2670(78)80021-5; 9.
Leiss, A.; Schurath, Ulrich; Becker, Karl Heinz; Fink, Ewald H.
Revised quenching rate constants for metastable oxygen molecules O2(a1Δg)
Journal of Photochemistry, 8 (2) :211-214
1978
DOI: 10.1016/0047-2670(78)80021-5
1977: 8.
[german] Tausch, Michael W.; Elian, Mihai; Bucur, Aurora; Cior{{\^a}}nescu, Ecaterina
Über das photochemische Verhalten von zwei Tribenzo-(CH)12-Valenzisomeren
Chemische Berichte, 110 (5) :1744-1747
1977
Herausgeber: Wiley
DOI: 10.1002/cber.19771100518
1974: 7.
Mihail, R.; Tausch, Michael W.
Homogene Reaktionen in einem Rohrreaktor mit nicht-Newtonscher Strömung
The Chemical Engineering Journal, 7 (1) :53--60
1974
Herausgeber: Elsevier {BV}
DOI: 10.1016/0300-9467(74)80025-0; 6.
Becker, Karl Heinz; Fink, Ewald H.; Langen, P.; Schurath, Ulrich
Near infrared emission bands of the HO\(_{2}\) radical
The Journal of Chemical Physics, 60 (11) :4623-4625
1974
DOI: 10.1063/1.1680950

Multirate Partial Differential Algebraic Equations

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