Dynamic Iteration Schemes
Standard time-integration methods solve transient problems all at once. This may become very inefficient or impossible for large systems of equations. Imaging that such large systems often stem from a coupled problem formulation, where different physical phenomena interact and need to be coupled in order to produce a precise mathematical model.
E.g. highly integrated electric circuits (as in memory chips or CPUs) produce heat, which effects in turn their behavior as electrical system; thus one needs to couple electric and thermal subproblem descriptions. On the one hand, this creates multiple time scales due to different physical phenomena, which demands an efficient treatment, see multirate. On the other hand, in a professional environment one usually has dedicated solvers for the subproblems, which need to be used, and an overall problem formulation is not feasible for any of the involved tools.
For those partitioned problems a dynamic iteration method becomes beneficial or even the sole way-out: it keeps the subproblems separate, solves subproblems sequentially (or in parallel) and iterates until convergence (fixed-point interation). Thus the subproblem's structure can be exploited in the respective integration.
To guarantee or to speed up convergence the time interval of interest is split into a series of windows. Then the time-integration of the windows is applied sequentially and in each window the subproblems are solved iteratively by your favoured method.
Group members working on that field
- Andreas Bartel
- Michael Günther
Former and ongoing Projects
Cooperation
- Herbert De Gersem, Katholieke Universiteit Leuven
Publications
- 1989
255.
Becker, Karl Heinz; Wiesen, Peter
Measurements on the CH*(A\(^{2}\)\(\Delta\) → X\(^{2}\)\(\Pi\)) Chemiluminescence in the C\(_{2}\)H\(_{2}\) + O Flame and Quenching Rate Constants for Different Reactants at 297 K
Zeitschrift für Physikalische Chemie, 161 (Part_1_2) :131-144
1989254.
Heilmann, Margareta; Müller, Manfred
Direct and converse results on weighted simultaneous approximation by the method of operators of Baskakov-Durrmeyer type
Results in Mathematics, 16 (3-4) :228-242
1989253.
Tausch, Michael W.; Wöhrle, D.
Katalytische Wasserphotolyse
Praxis der Naturwissenschaften (Chemie), 38 :46
1989252.
Tausch, Michael W.
Kritische Überlegungen zur Teilchenzahl als eigenständige Größe im Größenkalkül
Der mathematische und naturwissenschaftliche Unterricht (MNU), 42 :438
1989251.
Tausch, Michael W.; Wachtendonk, M.
Lehrerband mit didaktischen Hinweisen und Lösungen der Aufgaben zu STOFF-FORMEL-UMWELT, BAND 1: CHEMISCHE GLEICHGEWICHTE - ELEKTROCHEMIE, Lehrbuch für die S II (Grund- und Leistungskurse), 172 Seiten
Herausgeber: C. C. Buchner, Bamberg
1989250.
Heilmann, Margareta; Müller, Manfred
Weighted simultaneous L_p-approximation by the method of Baskakov-Durrmeyer operators
Approximation Theory VI, Proc. 6th Int. Symp., College Station/TX USA1989Band 1, Seite 331-332
1989249.
Bauer, W.; Engelhardt, B.; Wiesen, Peter; Becker, Karl Heinz
Lifetime measurements of GeH and CH in the A\(^{2}\)\(\Delta\), v'=0 state by laser-induced fluorescence
Chemical Physics Letters, 158 (3-4) :321-324
1989248.
Bauer, W.; Engelhardt, B.; Wiesen, Peter; Becker, Karl Heinz
Lifetime measurements of GeH and CH in the A2Δ, v'=0 state by laser-induced fluorescence
Chemical Physics Letters, 158 (3-4) :321-324
1989247.
Becker, Karl Heinz; Wiesen, Peter
Measurements on the CH*(A\(^{2}\)\(\Delta\) → X\(^{2}\)\(\Pi\)) Chemiluminescence in the C\(_{2}\)H\(_{2}\) + O Flame and Quenching Rate Constants for Different Reactants at 297 K
Zeitschrift für Physikalische Chemie, 161 (Part_1_2) :131-144
1989246.
Jensen, Per
The potential energy surface for the electronic ground state of the water molecule determined from experimental data using a variational approach
Journal of Molecular Spectroscopy, 133 (2) :438-460
1989245.
Jensen, Per
The potential energy surface for the electronic ground state of the water molecule determined from experimental data using a variational approach
Journal of Molecular Spectroscopy, 133 (2) :438-460
1989- 1988
244.
Weinmüller, E.; Winkler, E.
Path-following Algorithm for Singular Boundary Value Problems
ZAMM, 68 :527--537
1988243.
Becker, Karl Heinz; Brockmann, Klaus Josef; Wiesen, Peter
Spectroscopic identification of C(\(^{3}\)P) atoms in halogenomethane + H flame systems and measurements of C(\(^{3}\)P) reaction rate constants by two-photon laser-induced fluorescence
Journal of the Chemical Society, Faraday Transactions 2, 84 (5) :455-461
1988242.
Becker, Karl Heinz; Brockmann, Klaus Josef; Wiesen, Peter
Spectroscopic identification of C(3P) atoms in halogenomethane + H flame systems and measurements of C(3P) reaction rate constants by two-photon laser-induced fluorescence
Journal of the Chemical Society, Faraday Transactions 2, 84 (5) :455-461
1988241.
Jensen, Per
Calculation of rotation-vibration linestrengths for triatomic molecules using a variational approach
Journal of Molecular Spectroscopy, 132 (2) :429-457
1988240.
Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X~3B1 methylene (CH2) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988239.
Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X\verb=~=\(^{3}\)B\(_{1}\) methylene (CH\(_{2}\)) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988238.
Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X\verb=~=\(^{3}\)B\(_{1}\) methylene (CH\(_{2}\)) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988237.
Fink, Ewald H.; Setzer, Klaus-Dieter; Kottsieper, U.; Ramsay, D. A.; Vervloet, M.
The a1Δ(a2)-X3Σ-(X21) electronic band system of selenium monoxide
Journal of Molecular Spectroscopy, 131 (1) :127-132
1988236.
Fink, Ewald H.; Setzer, Klaus-Dieter; Kottsieper, U.; Ramsay, D. A.; Vervloet, M.
The a\(^{1}\)\(\Delta\)(a2)-X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{2}\)1) electronic band system of selenium monoxide
Journal of Molecular Spectroscopy, 131 (1) :127-132
1988235.
Fink, Ewald H.; Setzer, Klaus-Dieter; Kottsieper, U.; Ramsay, D. A.; Vervloet, M.
The a\(^{1}\)\(\Delta\)(a2)-X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{2}\)1) electronic band system of selenium monoxide
Journal of Molecular Spectroscopy, 131 (1) :127-132
1988234.
Becker, Karl Heinz; Brockmann, Klaus Josef; Wiesen, Peter
Spectroscopic identification of C(\(^{3}\)P) atoms in halogenomethane + H flame systems and measurements of C(\(^{3}\)P) reaction rate constants by two-photon laser-induced fluorescence
Journal of the Chemical Society, Faraday Transactions 2, 84 (5) :455-461
1988233.
Jensen, Per
Calculation of rotation-vibration linestrengths for triatomic molecules using a variational approach
Journal of Molecular Spectroscopy, 132 (2) :429-457
1988232.
Heilmann, Margareta
Commutativity of operators from Baskakov-Durrmeyer type
Constructive Theory of Functions - Proceedings of the International Conference, Varna, Bulgaria, 1987, Seite 197-206
1988231.
Wildt, Jürgen; Bednarek, G.; Fink, Ewald H.; Wayne, Richard P.
Laser excitation of O2(b1Σg+, v'=0,1,2) - rates and channels of energy transfer and quenching
Chemical Physics, 122 (3) :463-470
1988