Numerical Evaluation via Singularity Cancellation Schemes of Near-Singular Integrals Involving the Gradient of Helmholtz-Type Potentials

@article{Vipiana2013NumericalEV,
  title={Numerical Evaluation via Singularity Cancellation Schemes of Near-Singular Integrals Involving the Gradient of Helmholtz-Type Potentials},
  author={Francesca Vipiana and D. R. Wilton},
  journal={IEEE Transactions on Antennas and Propagation},
  year={2013},
  volume={61},
  pages={1255-1265}
}
In this paper, we present a purely numerical procedure to evaluate strongly near-singular integrals involving the gradient of Helmholtz-type potentials for observation points at finite, arbitrarily small distances from the source domain. In the proposed approach the source domain is subdivided into a disc plus truncated subtriangles, and proper variable transformations are applied in each integration domain to exactly cancel the kernel singularity. A novel feature of the proposed angular… CONTINUE READING

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