1,721,013 research outputs found
On the numerical evaluation of near-hypersingular integrals involving the gradient of Helmholtz-type potentials
No full textNumerical evaluation of near strongly singular integrals via singularity cancellation techniques
No full textNumerical evaluation via singularity cancellation schemes of near-singular integrals involving the gradient of Helmholtz-type potentials
No full textIn this work 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 transform is that required discrete values of the inverse transform, which is transcendental, are determined via a rootfinding procedure; the same idea can also be applied to other transforms that arise in singularity cancellation methods. The resulting integral may then evaluated via a low order Gauss- Legendre quadrature schem
On the numerical evaluation of singular and near-ningular MoM integrals involving junction basis functions
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Hybrid Integration Scheme for the Evaluation of Strongly Singular and Near-Singular Integrals in Surface Integral Equations
Full text linkThe accurate and efficient evaluation of surface source integrals is a key step in obtaining reliable solutions to electromagnetic problems using integral equation formulations. In this paper, we propose to combine two of the most extensively used schemes to efficiently evaluate strongly singular and near-singular source integrals, such as those arising in the K operator. In the proposed approach, singularity subtraction is first applied to remove the most dominant singular part; singularity cancellation, using the radial-angular variable transformation, is then employed to treat the remaining integrand. The method is compared to other common numerical schemes to demonstrate its effectiveness
Hybrid integration scheme for the evaluation of strongly singular integral over curvilinear triangle surface
No full textOn the fully numerical evaluation of 4-D Singular and near singular integrals in the Method of Moments
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