Applied and Computational Mathematics (ACM)

Multirate

Highly integrated electric cicuits show a phenomenon called latency. That is, a processed signal causes activity only in a small subset of the whole circuit (imagine a central processing unit), whereas the other part of the system behaves almost constant over some time - is latent. Such an electric system can be described as coupled system, where the waveforms show different time scales, also refered to as multirate.

More generally, any coupled problem formulation due to coupled physical effects, may cause a multirate problem: image the simulation of car driving on the road, there you need a model for the wheel, the chassis, the dampers, the road,... (cf. co-simulation). Again each system is covered by their own time constant, which might vary over several orders of magnitude comparing different subsystems.

Classical methods cannot exploit this multirate potential, but resolve everything on the finest scale. This causes an over sampling of the latent components. In constrast, Co-simulation or especially dedicated multirate methods are designed to use the inherent step size to resolve the time-domain behaviour of each subystem with the required accuracy. This requires a time-stepping for each.

Group members working in that field

  • Andreas Bartel
  • Michael Günther

Former and ongoing Projects

Cooperations

Publications



1986

142.

Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.; Beardsworth, R.
The potential surface of X\verb=~=\(^{3}\)B\(_{1}\) methylene (CH\(_{2}\)) and the singlet-triplet splitting
The Journal of Chemical Physics, 85 (7) :3724-3731
1986

141.

Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.; Beardsworth, R.
The potential surface of X~3B1 methylene (CH2) and the singlet-triplet splitting
The Journal of Chemical Physics, 85 (7) :3724-3731
1986

140.

Vojt{í}k, Jan; Spirko, Vladim{í}r; Jensen, Per
Vibrational energies of H\(_{3}\)\(^{+}\) and Li\(_{3}\)\(^{+}\) based on the diatomics-in-molecules potentials
Collection of Czechoslovak Chemical Communications, 51 (10) :2057-2062
1986
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

139.

Vojt{í}k, Jan; Spirko, Vladim{í}r; Jensen, Per
Vibrational energies of H\(_{3}\)\(^{+}\) and Li\(_{3}\)\(^{+}\) based on the diatomics-in-molecules potentials
Collection of Czechoslovak Chemical Communications, 51 (10) :2057-2062
1986
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

138.

Vojtík, Jan; Spirko, Vladimír; Jensen, Per
Vibrational energies of H3+ and Li3+ based on the diatomics-in-molecules potentials
Collection of Czechoslovak Chemical Communications, 51 (10) :2057-2062
1986
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.
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
1985

136.

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
1985

135.

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
1985

134.

Tausch, Michael W.
Aktivierungsenergie - was ist das?
Praxis der Naturwissenschaften (Chemie), 34 :33
1985

133.

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
1985

132.

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
1985

131.

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
1985

130.

Kling, H.-W.; Hartkamp, H.; Buchholz, N.
Matrixunabhängige kontinuierliche Dampfraum-Gas-Chromatographie
Fresenius' Journal of Analytical Chemistry, 320 (4) :341--346
1985

129.

Winkler, R.
Path-following for two-point boundary value problems
, Seminarbericht 78 der Sektion MathematikBand78
Humboldt-Universität zu Berlin
1985

128.

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
1985

127.

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
1985

126.

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
1985

125.

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, Canada

123.

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, Canada

122.

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, Canada

121.

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
1984

120.

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
1984

119.

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
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
1984