Generalization of new finite element method using "imaginary" nodal points.

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概要

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• A method for improving the accuracy of finite element solutions to diffusion equations has been developed. The author previously suggested a method for improving the accuracy of finite element solutions to neutron diffusion equations, a kind of Helmholtz equations, within a short computing time. The method has been generalized so that it can be applied to problems described by the Laplace equation, too, such as temperature distributions and electric fields. In this generalized method, 3 'imaginary' nodal points are added at the midsides of each data-given triangular element and the element is subdivided into 4 triangular subelements of the same dimension to improve accuracy. Then, approximate expressions, which express solutions at the 'imaginary' nodal points using those at 'real' nodal points, are derived by Jacobi's iteration method. These approximate expressions are used to reduce the number of unknowns in the final linear equations. The computing time required for the method described here is much shorter than that required for the straight-forward method of increasing the number of elements 4 times under the same accuracy.

• 一般社団法人 日本原子力学会の論文

著者

• AZEKURA Kazuo

  Energy Research Laboratory, Hitachi Ltd.

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