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International Conference on Mathematical Modeling and Scientific Computing
April 2-6, 2001
Middle East Technical University and Selcuk University
Ankara and Konya, Turkey

Organizers
F. Bornemann (Munich University of Tecnology, Germany), H. Bulgak (Selcuk University, Konya, Turkey), V. Ganzha (Munich University of Technology, Germany), B. Karasozen (METU, Ankara, Turkey), A. Sinan (Selcuk University, Konya, Turkey), C. Zenger (Munich University of Technology, Germany)

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Factorized High Dimensional Model Represenation (FHDMR) in the Boundary Value Problems of Partial Differential Operators
by
Metin Demiralp
Informatics Institute, Istanbul Technical University , Turkey

In this meeting an oral presentation is given to introduce the FHDMR (Factorized High Dimensional Model Representation) for approximating the functions with many variables. The aim of that contribution however is to approximate just a function. Some orthogonality conditions which are used to construct HDMR expansion of the function and a factorization scheme based on a perturbative expansion are main components of the approach. Here we develop an HDMR expansion for the solution of the partial differential equations with some compatible boundary conditions first. The approach tries to expand everything, differential equation, boundary conditions, and the unknown function to be solved, into HDMR expansions. Then the resulted HDMR expansion is factorized via FHDMR. To this end some nominal factors, fluctuation functions, and product approximants are defined and determined. Some illustrative applications finalizes the presentation. The approach to be presented here seems to be a powerful candidate for applications to many dimensional problems like Poisson equation in N-dimension. Many operator inversion problem of physics, quantum field theory and similar area may be treated by FHDMR as well.

Date received: February 21, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagk-75.