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Concurrent Implementation of the Optimal Incremental Approximation Method for the Adaptive and Meshless Solution of Differential Equations
Department of Mechanical Engineering and Materials Science, Rice University.
Software Engineer, Vignette Corporation.
2003 (English)In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 4, no 4, p. 271-289Article in journal (Refereed) Published
Abstract [en]

The optimal incremental function approximation method is implemented for the adaptive and meshless solution of differential equations. The basis functions and associated coefficients of a series expansion representing the solution are selected optimally at each step of the algorithm according to appropriate error minimization criteria. Thus, the solution is built incrementally. In this manner, the computational technique is adaptive in nature, although a grid is neither built nor adapted in the traditional sense using a posteriori error estimates. Since the basis functions are associated with the nodes only, the method can be viewed as a meshless method. Variational principles are utilized for the definition of the objective function to be extremized in the associated optimization problems. Complicated data structures, expensive remeshing algorithms, and systems solvers are avoided. Computational efficiency is increased by using low-order local basis functions and the parallel direct search (PDS) optimization algorithm. Numerical results are reported for both a linear and a nonlinear problem associated with fluid dynamics. Challenges and opportunities regarding the use of this method are discussed

Place, publisher, year, edition, pages
2003. Vol. 4, no 4, p. 271-289
Identifiers
URN: urn:nbn:se:ltu:diva-6284DOI: 10.1023/B:OPTE.0000005388.31401.82Local ID: 47f2fd6e-7406-4839-8169-01267e5456c2OAI: oai:DiVA.org:ltu-6284DiVA, id: diva2:979161
Note
Upprättat; 2011; 20110826 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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Kokkolaras, Michael

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