Evaluation of the degenerate scale in Laplace equation by using Newton iteration method

摘要

This paper provides a numerical solution for the degenerate scale in antiplane elasticity or Laplace equation by using the null field boundary integral equation (BIE). When the used scale coincides with the degenerate scale, the relevant influence matrix is singular. The determinant of the influence matrix is expressed by a function of scale. Therefore, the problem for finding the degenerate scale can be reduced to a problem for finding the zeros of the function. Newton iteration method is used to find the zeros. Three numerical examples are provided in the paper.