Numerical evaluation of singular and near-singular potential Integrals

By M. A. Khayat, D. R. Wilton. IEEE Transactions on Antennas and Propagation, 2005

278 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/f2cff27ed940f1d2715cb0a274bb55e531ba3308

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In Atomic and Molecular Physics, and Optics

In Electrical and Electronic Engineering

Citations in the corpus

Evaluation of Weakly Singular Integrals Via Generalized Cartesian Product Rules Based on the Double Exponential Formula (2010, background): “Moreover, in some recent publications [11], [12], [17]–[19] it was clearly demonstrated that in many cases the near-singular potential integration (the inner 2-D integration) is more challenging than the singular one.”
Generalized Duffy transformation for integrating vertex singularities (2009, unknown): “ture [27–33].”
On the Direct Evaluation of Weakly Singular Integrals in Galerkin Mixed Potential Integral Equation Formulations (2008, methodology): “Although the singularity extraction method leads to quite accurate results, it also exhibits a number of major disadvantages, as it is thoroughly explained in [18].”
New strategies for some issues of numerical manifold method in simulation of crack propagation (2014, methodology): “Clearly, the proposed procedure can be directly applied to the three-dimensional BEMs, causing the implementation far simpler than the Duffy transformation and other transformations such as [32].”
Complete semi‐analytical treatment of weakly singular integrals on planar triangles via the direct evaluation method (2010, methodology): “In general, weakly singular integrals are treated by using mainly the singularity subtraction method [4–14] or the singularity cancellation method [15–25].”
Higher Order Frequency-Domain Computational Electromagnetics (2008, methodology): “On the other hand, the improved singularity cancellation technique in [144] accurately and efficiently handles both singular and near-singular potential integrals.”