Error trends in higher-order discretizations of the EFIE and MFIE

We concern ourselves with the EFIE and MFIE applied to 2D or cylindrical perfectly conducting scatterers. The MoM procedure is used with subsectional Legendre polynomial basis functions, without the imposition of cell-to-cell continuity. The equations are enforced by point testing, or equivalently Dirac delta testing functions, located at the nodes of open Newton-Coates quadrature rules. The discretization process may yield a square system matrix, or an overdetermined system matrix, depending on the number of testing points that we employ. If used with an overdetermined matrix, the approach is also known as the boundary residual method. We investigate error trends for the square matrix case and the case where the matrix is overdetermined by a factor of 2. A benefit to the overdetermined matrix is that the residual error in the matrix equation can be obtained as part of the matrix solution process, and used to estimate the residual error in the continuous equation. For geometries with corners or edges, the polynomial basis is modified to incorporate the expected behavior of the current density at those locations.