The partition of unity finite element approach to the stationary fokker-planck equation

Mrinal Kumar, Puneet Singla, Suman Chakravorty, John L. Junkins

Research output: Chapter in Book/Report/Conference proceedingConference contribution

21 Scopus citations

Abstract

The stationary Fokker-Planck Equation (FPE) is solved for nonlinear dynamic systems using a local numerical technique based on the meshless Partition of Unity Finite Element Method (PUFEM). The method is applied to the FPE for two-dimensional dynamical systems, and argued to be an excellent candidate for higher dimensional systems and the transient problem. Variations of the conventional PUFEM are used to Improve the quality of approximation, by using novel pasting functions to blend the various local approximations. These functions, besides satisfying the conditions for a partition of unity are easy to integrate numerically and provide solution continuity of any desired order. Results are compared with existing global and local techniques.

Original languageEnglish (US)
Title of host publicationCollection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference, 2006
Pages602-616
Number of pages15
StatePublished - Dec 1 2006
EventAIAA/AAS Astrodynamics Specialist Conference, 2006 - Keystone, CO, United States
Duration: Aug 21 2006Aug 24 2006

Publication series

NameCollection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference, 2006
Volume1

Other

OtherAIAA/AAS Astrodynamics Specialist Conference, 2006
CountryUnited States
CityKeystone, CO
Period8/21/068/24/06

All Science Journal Classification (ASJC) codes

  • Engineering(all)

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    Kumar, M., Singla, P., Chakravorty, S., & Junkins, J. L. (2006). The partition of unity finite element approach to the stationary fokker-planck equation. In Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference, 2006 (pp. 602-616). (Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference, 2006; Vol. 1).