Singular boundary method

[8][9] The basic idea is to introduce a concept of the origin intensity factor to isolate the singularity of the fundamental solutions so that the source points can be placed directly on the real boundary.

The first approach is to place a cluster of sample nodes inside the problem domain and to calculate the algebraic equations.

Like all the other boundary-type numerical methods, also it is observed that the SBM encounters a dramatic drop of solution accuracy at the region nearby boundary.

A nonlinear transformation, based on the sinh function, can be employed to remove or damp out the rapid variations of the nearly singular kernels.

Like the MFS and BEM, the SBM will produce dense coefficient matrices, whose operation count and the memory requirements for matrix equation buildup are of the order of O(N2) which is computationally too expensive to simulate large-scale problems.