Duffy transformation with a simple polynomial smoothing strategy for weakly singular integrals

Abstract

Duffy transformation is a well-known singularity cancellation method for handling weakly singular integrals in integral equation solutions. However, Duffy transformation is found to be inaccurate and inefficient for irregularly shaped triangles in several academic papers. In order to alleviate the deformed shape problem of Duffy transformation, a simple polynomial smoothing strategy for Duffy transformation is presented for calculating weakly singular integrals over irregular triangular domains, which also results in faster convergence than that of Duffy transformation. Some numerical results are given to demonstrate the accuracy and the flexibility of the proposed proposed scheme.