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The convergence for nodal expansion method

Applied Mathematics, 1993
This paper is concerned with conditions for convergence of approximations using the nodal expansion method, a relatively new method for approximate solution of partial differential equations. The essence of the method, which is discussed in the context of a model linear elliptic equation (the Helmholtz equation), is that the domain is partitioned into ...
Huang, Aixiang, Zhang, Bo
exaly   +3 more sources

New basis functions for reactor core calculations using the nodal expansion method

Annals of Nuclear Energy, 2022
Abstract In 1977 Finnemann, Bennewitz and Wagner introduced the Nodal Expansion Method (NEM), by combining neutron diffusion theory, polynomial expansions, interface currents continuity, and weighted residual techniques. Extensive testing clearly indicated that it was consistent, computationally efficient, and accurate for meshes up to the typical ...
Sérgio B. Paixão, Fernando C. Silva
exaly   +2 more sources

A development of the HEXNEM nodal expansion method

Annals of Nuclear Energy, 2013
Abstract In this paper a development of the HEXNEM nodal expansion methods is presented, together with a program implementation and results from comparisons with benchmark problem solutions. The new development consists in the introduction of tangentially weighted exponential basis functions and continuity and boundary conditions for the tangential ...
Ivaylo Christoskov, Petko T. Petkov
openaire   +1 more source

An Alternate Formulation of the Nodal Expansion Method

Nuclear Science and Engineering, 2001
An alternate formulation of the two-group transverse-integration-based nodal expansion method is presented. In this formulation, the two-group problem is formulated by using the relationship between the group fluxes derived from an analytical procedure. As a result, a simplified procedure for the thermal group is suggested. The numerical results of the
Keqiang Ruan, Xiaogang Xue, Xuedong Fu
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Exponential Function Expansion Nodal Diffusion Method

18th International Conference on Nuclear Engineering: Volume 2, 2010
An exponential function expansion nodal diffusion method is proposed to take care of diffusion calculation in unstructured geometry. Transverse integral technique is widely used in nodal method in regular geometry, such as rectangular and hexagonal, while improper in arbitrary triangular geometry because of the mathematical singularity.
Yunzhao Li   +3 more
openaire   +1 more source

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