• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.261-275
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• 2002

Besides asymptotic method, the method of orthogonal polynomials has been used to obtain the solution of the Fredholm integral equation. The principal (singular) part of the kerne1 which corresponds to the selected domain of parameter variation is isolated. The unknown and known functions are expanded in a Chebyshev polynomial and an infinite a1gebraic system is obtained.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.5
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• pp.413-420
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• 2012

In this study, the Kernel integration scheme for 2D linear elastic direct boundary element method has been discussed on the basis of subparametric element. Usually, the isoparametric based boundary element uses same polynomial order in the both basis function and mapping function. On the other hand, the order of mapping function is lower than the order of basis function to define displacement field when the subparametric concept is used. While the logarithmic numerical integration is generally used to calculate Kernel integration as well as Cauchy principal value approach, new formulation has been derived to improve the accuracy of numerical solution by algebraic modification. The subparametric based direct boundary element has been applied to 2D elliptical partial differential equation, especially for plane stress/strain problems, to demonstrate whether the proposed algebraic expression for integration of singular Kernel function is robust and accurate. The problems including cantilever beam and square plate with a cutout have been tested since those are typical examples of simple connected and multi connected region cases. It is noted that the number of DOFs has been drastically reduced to keep same degree of accuracy in comparison with the conventional isoparametric based BEM. It is expected that the subparametric based BEM associated with singular Kernel function integration scheme may be extended to not only subparametric high order boundary element but also subparametric high order dual boundary element.

• Nuclear Engineering and Technology
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• v.50 no.5
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• pp.673-682
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• 2018

One of the most widely used methods to estimate core damage during a nuclear power plant accident is containment radiation measurement. The evolution of severe accidents is extremely complex, leading to uncertainty in the containment dose rate (CDR). Therefore, it is difficult to accurately determine core damage. This study proposes to conduct uncertainty analysis of CDR for core damage assessment. First, based on source term estimation, the Monte Carlo (MC) and point-kernel integration methods were used to estimate the probability density function of the CDR under different extents of core damage in accident scenarios with late containment failure. Second, the results were verified by comparing the results of both methods. The point-kernel integration method results were more dispersed than the MC results, and the MC method was used for both quantitative and qualitative analyses. Quantitative analysis indicated a linear relationship, rather than the expected proportional relationship, between the CDR and core damage fraction. The CDR distribution obeyed a logarithmic normal distribution in accidents with a small break in containment, but not in accidents with a large break in containment. A possible application of our analysis is a real-time core damage estimation program based on the CDR.