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



1983

70.

Winnewisser, Brenda P.; Jensen, Per
The infrared spectrum of fulminic acid, HCNO, in the \(\nu\)\(_{4}\) fundamental region
Journal of Molecular Spectroscopy, 101 (2) :408-421
1983

69.

Winnewisser, Brenda P.; Jensen, Per
The infrared spectrum of fulminic acid, HCNO, in the ν4 fundamental region
Journal of Molecular Spectroscopy, 101 (2) :408-421
1983

68.

Jensen, Per
The nonrigid bender Hamiltonian for calculating the rotation-vibration energy levels of a triatomic molecule
Computer Physics Reports, 1 (1) :1-55
1983

67.

Jensen, Per
The nonrigid bender Hamiltonian for calculating the rotation-vibration energy levels of a triatomic molecule
Computer Physics Reports, 1 (1) :1-55
1983

66.

Jensen, Per
The nonrigid bender Hamiltonian for calculating the rotation-vibration energy levels of a triatomic molecule
Computer Physics Reports, 1 (1) :1-55
1983

65.

Holstein, K. J.; Fink, Ewald H.; Zabel, Friedhelm
The ν3 vibration of electronically excited HO2(A2A')
Journal of Molecular Spectroscopy, 99 (1) :231-234
1983
1982

64.

Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) and a\(^{1}\)\(\Delta\) emissions from group VI-VI diatomic molecules b0\(_{g}\)\(^{+}\) → X\(^{2}\)1\(_{g}\) emissions of Se\(_{2}\) and Te\(_{2}\)
Chemical Physics Letters, 86 (2) :118-122
1982

63.

Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) and a\(^{1}\)\(\Delta\) emissions from group VI-VI diatomic molecules b0\(_{g}\)\(^{+}\) → X\(^{2}\)1\(_{g}\) emissions of Se\(_{2}\) and Te\(_{2}\)
Chemical Physics Letters, 86 (2) :118-122
1982

62.

Winter, R.; Barnes, Ian; 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 TeO and TeS
Journal of Molecular Structure, 80 :75-82
1982

61.

Winter, R.; Barnes, Ian; 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 TeO and TeS
Journal of Molecular Structure, 80 :75-82
1982

60.

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\(_{2}\)0\(^{+}\) emissions of SbBr
Chemical Physics Letters, 93 (5) :475-479
1982

59.

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\(_{2}\)0\(^{+}\) emissions of SbBr
Chemical Physics Letters, 93 (5) :475-479
1982

58.

Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ and a1Δ emissions from group VI-VI diatomic molecules b0g+ → X21g emissions of Se2 and Te2
Chemical Physics Letters, 86 (2) :118-122
1982

57.

Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ and a1Δ emissions from group VI-VI diatomic molecules: b0+ → X10+, X21 emissions of TeO and TeS
Journal of Molecular Structure, 80 :75-82
1982

56.

Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ emissions from group V-VII diatomic molecules: b0+ → X10+, X20+ emissions of SbBr
Chemical Physics Letters, 93 (5) :475-479
1982

55.

Tausch, Michael W.
Modelle im Chemieunterricht
Der mathematische und naturwissenschaftliche Unterricht (MNU), 35 :226
1982

54.

Becker, Karl Heinz; Horie, O.; Schmidt, V. H.; Wiesen, Peter
Spectroscopic identification of C\(_{2}\)O radicals in the C\(_{3}\)O\(_{2}\) + O flame system by laser-induced fluorescence
Chemical Physics Letters, 90 (1) :64-68
1982

53.

Becker, Karl Heinz; Horie, O.; Schmidt, V. H.; Wiesen, Peter
Spectroscopic identification of C\(_{2}\)O radicals in the C\(_{3}\)O\(_{2}\) + O flame system by laser-induced fluorescence
Chemical Physics Letters, 90 (1) :64-68
1982

52.

Becker, Karl Heinz; Horie, O.; Schmidt, V. H.; Wiesen, Peter
Spectroscopic identification of C2O radicals in the C3O2 + O flame system by laser-induced fluorescence
Chemical Physics Letters, 90 (1) :64-68
1982

51.

Jensen, Per; Brodersen, Svend
The \(\nu\)\(_{5}\) Raman band of CH\(_{3}\)CD\(_{3}\)
Journal of Raman Spectroscopy, 12 (3) :295-299
1982

50.

Jensen, Per; Brodersen, Svend
The \(\nu\)\(_{5}\) Raman band of CH\(_{3}\)CD\(_{3}\)
Journal of Raman Spectroscopy, 12 (3) :295-299
1982

49.

Jensen, Per; Bunker, Philip R.; Hoy, A. R.
The equilibrium geometry, potential function, and rotation?vibration energies of CH\(_{2}\) in the X\verb=~=\(^{3}\)B\(_{1}\) ground state
The Journal of Chemical Physics, 77 (11) :5370-5374
1982

48.

Jensen, Per; Bunker, Philip R.; Hoy, A. R.
The equilibrium geometry, potential function, and rotation?vibration energies of CH\(_{2}\) in the X\verb=~=\(^{3}\)B\(_{1}\) ground state
The Journal of Chemical Physics, 77 (11) :5370-5374
1982

47.

Jensen, Per; Bunker, Philip R.; Hoy, A. R.
The equilibrium geometry, potential function, and rotation?vibration energies of CH2 in the X~3B1 ground state
The Journal of Chemical Physics, 77 (11) :5370-5374
1982

46.

Jensen, Per; Bunker, Philip R.
The geometry and the inversion potential function of formaldehyde in the and electronic states
Journal of Molecular Spectroscopy, 94 (1) :114-125
1982