Meshless singular boundary methods for biharmonic problems

In this paper, the meshless singular boundary method (SBM) is first presented for the numerical solution of biharmonic problems. The SBM uses the source intensity factor to isolate the singularity of fundamental solutions and an inverse interpolation technique (IIT) to compute the source intensity factor, and thus avoids the fictitious boundary required in the method of fundamental solutions. However, the IIT may worsen the performance of the SBM. Then, a further development of the improved SBM (ISBM) is also presented for boundary-only analysis of biharmonic problems. In the ISBM, a new regularization technique is developed to compute the source intensity factor, which leads to higher computational precision and better numerical stability. Some numerical examples illustrate the efficiency and accuracy of both the SBM and the ISBM.