Abstract: A simulation method for simulating a three-dimensional structure, comprises the steps of: discretizing the three-dimensional structure into two-dimensional (“2-D”) layers; constructing a two-dimensional basis for each of the 2-D layers; and constructing a one-dimensional finite difference basis between the 2-D layers.

Abstract: The present invention provides methods and apparatuses for an electromagnetic simulator. The method for circuit simulation comprises the steps of discretizing the circuit element into charge elements and current elements, generating internal data structures to include the charge elements and current elements wherein the internal data structures include Mixed-Potential Integral Equation Green's functions and Partial Element Equivalent Circuit (PEEC) incident matrixes, and calculating relationship between the charge elements and current elements using multilayer Green's function to provide electromagnetic interactions in the internal data structures.