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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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Multifrontal Method for 2D Neutron Diffusion Calculations
by
Murat Kaplan
Informatics Institute, Istanbul Technical University
Coauthors: Hasan Saygin(Informatics Institute and Nuclear Energy Institute,Istanbul Technical University, Turkey)

A sparse linear system is solved in many large scale scientific and engineering computations. It can be done in two ways; iterativ methods and direct methods. However, the use direct methods is suitable for the solution of the resulting linear systems in one dimensional problems, the use of indirect (iterative) methods are prefered in two and three dimensional problems beacuse of huge computer memory allocation and time requirements. In Conventional sparse matrix factorization algorithims, indirect addressing is usually used. This leads an irregular memory access pattern that limit their performance. But, a good ordering of rows and columns of a sparse matrix can significantly reduce the storage and execution time required with such a direct method algorithms like multifrontal method.

The multifrontal method is based on an assembly tree factorization generated from the original matrix and an ordering such as minimum degree. The computational kernel, executed at each node of the tree, is one ore more steps of LU factorization within a rectangular, dense frontal matrix defined by the nonzero pattern of a pivot row and column. These steps of LU factorization compute a contribution block (a Schut complement) that is later assembled (added) into the frontal matrix of its parent in the assembly tree. In this study, multifrontal method is used in computing linear algebraic equations obtained by discretization of two dimensional neutron diffusion equation. For numeric computations, a code which name is FDM (Finite Difference Method) is based on finite difference discretisation has been developed. FDM applied two dimensional reactor models to obtain linear algebraic systems with a positive definite coefficient matrices. To solve these matrices, a multifrontal code, UMFPACK 2.2 is used

Date received: February 13, 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-47.