The reproducing singularity particle shape functions for problems containing singularities

摘要

In this paper, we construct particle shape functions that reproduce singular functions as well as polynomialfunctions.We also construct piecewise polynomial convolutionpartition of unity functions by taking the convolution ofthe scaled conical window function with the characteristicfunctions of quadrangular patches (we provide the computercode for this construction).We demonstrate that the reproducingsingular particle shape functions yield highly accuratenumerical solutions for the singularity problems with cracksingularity or a jump boundary data singularity.