三次元静電界問題における境界要素法の信頼性

抄録

In our previous papers, we investigated into fundamental natures of the discretization errors inherent to the boundary element method (BEM) in 3-D. We showed that the discretization error is smaller than usually expected even in the case where the lowest order of approximation is used for discretizing the unknown function to be solved. Our previous numerical experiments were conducted by arranging elements with an equal mesh size over the boundary surfaces. In practical applications to design problems of electron optical instruments, we have to treat boundary configurations with details of shape with different curvatures. In this paper, we describe another series of numerical experiments conducted to find out the effect of varying the mesh size upon the local accuracy of solution. From these results we can formulate a strategy to estimate the discretization error of a numerical solution in most of practical applications where no exact solution is available. Following this we found that in several practical applications the accuracy of the numerical solution of potential problems in general 3-D can be reduced sufficiently by adjusting the local mesh size.