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

1986

175.

Jensen, Per; Spirko, Vladimír
A new Morse-oscillator based Hamiltonian for H3+: Calculation of line strengths
Journal of Molecular Spectroscopy, 118 (1) :208-231
1986

DOI: 10.1016/0022-2852(86)90236-5

174.

Jensen, Per; Spirko, Vladimír; Bunker, Philip R.
A new Morse-oscillator based Hamiltonian for H3+: Extension to H2D+ and D2H+
Journal of Molecular Spectroscopy, 115 (2) :269-293
1986

DOI: 10.1016/0022-2852(86)90047-0

173.

Adams, Warren P; Sherali, Hanif D
A tight linearization and an algorithm for zero-one quadratic programming problems
Management Science, 32 (10) :1274--1290
1986
Herausgeber: INFORMS

172.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Ab initio rotation-vibration energies of HOC\(^{+}\) calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :40-49
1986

DOI: 10.1016/0022-2852(86)90221-3

171.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Ab initio rotation-vibration energies of HOC\(^{+}\) calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :40-49
1986

DOI: 10.1016/0022-2852(86)90221-3

170.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Ab initio rotation-vibration energies of HOC+ calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :40-49
1986

DOI: 10.1016/0022-2852(86)90221-3

169.

Kraemer, Wolfgang P.; Roos, B. O.; Bunker, Philip R.; Jensen, Per
An ab initio calculation of the rotation-vibration energies of the state of CCH using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 120 (1) :236-238
1986

DOI: 10.1016/0022-2852(86)90085-8

168.

Kraemer, Wolfgang P.; Roos, B. O.; Bunker, Philip R.; Jensen, Per
An ab initio calculation of the rotation-vibration energies of the state of CCH using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 120 (1) :236-238
1986

DOI: 10.1016/0022-2852(86)90085-8

167.

Kraemer, Wolfgang P.; Roos, B. O.; Bunker, Philip R.; Jensen, Per
An ab initio calculation of the rotation-vibration energies of the state of CCH using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 120 (1) :236-238
1986

DOI: 10.1016/0022-2852(86)90085-8

166.

Fink, Ewald H.; Kruse, H.; Ramsay, D. A.; Vervloet, M.
An electric quadrupole transition: the emission system of oxygen
Canadian Journal of Physics, 64 (3) :242-245
1986
Herausgeber: NRC Research Press Ottawa, Canada

DOI: 10.1139/p86-044

165.

Fink, Ewald H.; Kruse, H.; Ramsay, D. A.; Vervloet, M.
An electric quadrupole transition: the emission system of oxygen
Canadian Journal of Physics, 64 (3) :242-245
1986
Herausgeber: NRC Research Press Ottawa, Canada

DOI: 10.1139/p86-044

164.

Fink, Ewald H.; Kruse, H.; Ramsay, D. A.; Vervloet, M.
An electric quadrupole transition: the emission system of oxygen
Canadian Journal of Physics, 64 (3) :242-245
1986
Herausgeber: NRC Research Press Ottawa, Canada

DOI: 10.1139/p86-044

163.

Jensen, Per; Winnewisser, Manfred
Prediction of higher inversion energy levels for isocyanamide H\(_{2}\)NNC
Collection of Czechoslovak Chemical Communications, 51 (7) :1373-1381
1986
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19861373

162.

Jensen, Per; Winnewisser, Manfred
Prediction of higher inversion energy levels for isocyanamide H\(_{2}\)NNC
Collection of Czechoslovak Chemical Communications, 51 (7) :1373-1381
1986
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19861373

161.

Jensen, Per; Winnewisser, Manfred
Prediction of higher inversion energy levels for isocyanamide H2NNC
Collection of Czechoslovak Chemical Communications, 51 (7) :1373-1381
1986
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19861373

160.

Bielefeld, M.; Wildt, J{ü}rgen; Fink, Ewald H.
Rate constants of the near-resonant E-E energy exchange processes SeS(b0\(^{+}\)) + O\(_{2}\)(X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\)) ↔ SeS(X\(_{1}\)0\(^{+}\)) + O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))
Chemical Physics Letters, 126 (5) :421-426
1986

DOI: 10.1016/S0009-2614(86)80128-2

159.

Bielefeld, M.; Wildt, J{ü}rgen; Fink, Ewald H.
Rate constants of the near-resonant E-E energy exchange processes SeS(b0\(^{+}\)) + O\(_{2}\)(X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\)) ↔ SeS(X\(_{1}\)0\(^{+}\)) + O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))
Chemical Physics Letters, 126 (5) :421-426
1986

DOI: 10.1016/S0009-2614(86)80128-2

158.

Bielefeld, M.; Wildt, Jürgen; Fink, Ewald H.
Rate constants of the near-resonant E-E energy exchange processes SeS(b0+) + O2(X3Σg-) ↔ SeS(X10+) + O2(a1Δg)
Chemical Physics Letters, 126 (5) :421-426
1986

DOI: 10.1016/S0009-2614(86)80128-2

157.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Rotation-vibration energy levels of H\(_{2}\)O and C\(_{3}\) calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :50-63
1986

DOI: 10.1016/0022-2852(86)90222-5

156.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Rotation-vibration energy levels of H\(_{2}\)O and C\(_{3}\) calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :50-63
1986

DOI: 10.1016/0022-2852(86)90222-5

155.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Rotation-vibration energy levels of H2O and C3 calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :50-63
1986

DOI: 10.1016/0022-2852(86)90222-5

154.

Tausch, Michael W.
Silberfreie Photographie und Photochromie
Praxis der Naturwissenschaften (Chemie), 35 :19
1986

153.

Maten, E. J. W.
Splitting methods for fourth order parabolic partial differential equations
Computing, 37 (4) :335--350
Dezember 1986
Herausgeber: Springer Science and Business Media {LLC}

DOI: 10.1007/bf02251091

152.

Fink, Ewald H.; Kruse, H.; Ramsay, D. A.
The high-resolution emission spectrum of S\(_{2}\) in the near infrared: The b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) - X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) system
Journal of Molecular Spectroscopy, 119 (2) :377-387
1986

DOI: 10.1016/0022-2852(86)90032-9

151.

Fink, Ewald H.; Kruse, H.; Ramsay, D. A.
The high-resolution emission spectrum of S\(_{2}\) in the near infrared: The b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) - X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) system
Journal of Molecular Spectroscopy, 119 (2) :377-387
1986

DOI: 10.1016/0022-2852(86)90032-9