High Order Locally Corrected Nystrom Method with Normal Continuity

A constrained locally corrected Nystrom (CLCN) method has recently been developed. The CLCN method enables the imposition of normal continuity on underlying vector quantities across mesh element boundaries. This is accomplished by deriving appropriate transformation vectors through simple algebraic analyses of local, homogeneous constraint conditions. Compared to the LCN method, the CLCN method improves the condition numbers of the system matrix, it reduces computational costs through a reduction in the number of degrees of freedom (DOFs), and it improves accuracy for sharp geometries. In the case of the magnetic field integral equation (MFIE), it is shown that the CLCN method yields stable condition numbers as the order increases.