Constrained Locally Corrected Nyström Method

A generalization of the locally corrected Nyström (LCN) discretization method is outlined wherein sparse transformations of the LCN system matrix are obtained via singular-value decompositions of local constraint matrices. The local constraint matrices are used to impose normal continuity of the currents across boundaries shared by mesh elements. Due to the method's simplicity and flexibility, it is straightforward to develop high-order constrained LCN (CLCN) systems for different formulations and mesh element types. Numerical examples demonstrate the memory savings provided by the CLCN method and its improved accuracy when applied to geometries with sharp edges. It is also shown that the CLCN method maintains the high-order convergence of the LCN method, and it eliminates the need to include line charges in Nyström-based discretizations of formulations that involve the continuity equation.