Geometrically Symmetric Quadrature Rules for Singular Integrals in the Method-of-Moments Implementation of the Electric-Field Integral Equation.
Abstract not provided.
Freno, Brian Andrew↗
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Symmetric triangle quadrature rules for arbitrary functions
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97 MATHEMATICS AND COMPUTING↗
Characterization and integration of the singular test integrals in the method-of-moments implementation of the electric-field integral equation
In this paper, we characterize the logarithmic singularities arising in the method of moments from the Green’s function in integrals over the test domain, and we use two approaches for designing geometrically symmetric quadrature rules to integrate these singular integrands. These rules exhibit better convergence properties than quadrature rules for polynomials and, in general, lead to better accuracy with a lower number of quadrature points. In this work, we demonstrate their effectiveness for several examples encountered in both the scalar and vector potentials of the electric-field integral equation (singular, near-singular, and far interactions) as compared to the commonly employed polynomial scheme and the double Ma–Rokhlin–Wandzura (DMRW) rules, whose sample points are located asymmetrically within triangles.
42 ENGINEERING↗
An Overview of Gemma FY20 Verification Activities
Gemma verification activities for FY20 can be divided into three categories: the development of specialized quadrature rules, initial progress towards the development of manufactured solutions for code verification, and automated code-verification testing. In the method-of-moments implementation of the electric-field integral equation, the presence of a Green’s function in the four-dimensional integrals yields singularities in the integrand when two elements are nearby. To address these challenges, we have developed quadrature rules to integrate the functions through which the singularities can be characterized. Code verification is necessary to develop confidence in the implementation of the numerical methods in Gemma. Therefore, we have begun investigating the use of manufactured solutions to more thoroughly verify Gemma. Manufactured solutions provide greater flexibility for testing aspects of the code; however, the aforementioned singularities provide challenges, and existing work is limited in rigor and quantity. Finally, we have implemented automated code-verification testing using the VVTest framework to automate the mesh refinement and execution of a Gemma simulation to generate mesh convergence data. This infrastructure computes the observed order of accuracy from these data and compares it with the theoretical order of accuracy to either develop confidence in the implementation of the numerical methods or detect coding errors.
97 MATHEMATICS AND COMPUTING↗