TY - GEN

T1 - Scaling invariant interpolation for singularly perturbed vector fields (SPVF)

AU - Bykov, Viatcheslav

AU - Gol'Dshtein, Vladimir

AU - Maas, Ulrich

N1 - Funding Information:
This research was supported by the Deutsche Forschungsgemeinschaft (DFG). Bykov thanks the Centre for Advanced Studies in Mathematics at the Ben-Gurion University of the Negev (BGU) for financial support of his stay at the BGU during spring 2009.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - The problem of modelling, numerical simulations and interpretation of the simulations results of complex systems arising in reacting flows requires more and more sophisticated methods of qualitative system analysis. Recently, the concept of invariant, slow/fast, attractive manifolds has proven to be an efficient tool for such an analysis. In particular, it allows us to study main properties of detailed models describing the reacting flow by considering appropriate low dimensional manifolds, which appear naturally in the system state/composition space as a manifestation of a restricted number of real degrees of freedom exhibited by the system.In order to answer the question of what are the minimal number of the real degrees of freedom (real system dimension) and to approximate low dimensional manifolds (i.e., reduced system's phase spaces) the concept of Singularly Perturbed Vector Fields (SPVF) has been suggested lately [1]. In the current work a scales invariant version of the SPVF will be presented and discussed.

AB - The problem of modelling, numerical simulations and interpretation of the simulations results of complex systems arising in reacting flows requires more and more sophisticated methods of qualitative system analysis. Recently, the concept of invariant, slow/fast, attractive manifolds has proven to be an efficient tool for such an analysis. In particular, it allows us to study main properties of detailed models describing the reacting flow by considering appropriate low dimensional manifolds, which appear naturally in the system state/composition space as a manifestation of a restricted number of real degrees of freedom exhibited by the system.In order to answer the question of what are the minimal number of the real degrees of freedom (real system dimension) and to approximate low dimensional manifolds (i.e., reduced system's phase spaces) the concept of Singularly Perturbed Vector Fields (SPVF) has been suggested lately [1]. In the current work a scales invariant version of the SPVF will be presented and discussed.

UR - http://www.scopus.com/inward/record.url?scp=78651591539&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-14941-2_5

DO - 10.1007/978-3-642-14941-2_5

M3 - Conference contribution

AN - SCOPUS:78651591539

SN - 9783642149405

T3 - Lecture Notes in Computational Science and Engineering

SP - 91

EP - 111

BT - Coping with Complexity

T2 - International Research Workshop: Coping with Complexity: Model Reduction and Data Analysis

Y2 - 31 August 2009 through 4 September 2009

ER -