A new volume integral method for 2-D inhomogeneous composite structures using one unknown per node

A volume integral equation is used to calculate the scattering from inhomogeneous two-dimensional dielectric, magnetic, and perfectly conducting bodies at TM_z or TE_z polarization. The scatterer is modeled by a triangular mesh. Linear pyramid basis functions are used to expand the unknown total z-directed field at the triangle nodes. Placement of perfectly conducting strips along the edges of the cells can be done without increasing the number of unknowns. Example cases show good agreement with series solutions, moment methods, and finite-element solutions. This method requires only one unknown per node, reducing the number of unknowns compared to traditional methods.