Systems and methods are provided for modeling electromagnetic properties of an assembly. The system includes a modeling component configured to divide the assembly into a plurality of subdomains, with each subdomain representing a three-dimensional volume of the assembly, and determine a set of standard elemental basis functions for each subdomain, such that a linear combination of elemental basis functions represents the electromagnetic properties of a portion of the geometry of the subdomain. A synthetic function generator is configured to generate a set of synthetic “entire-domain” basis functions for each subdomain from its set of elemental basis functions. A response characterization component is configured to determine the electromagnetic properties of the assembly from the sets of synthetic basis functions for each subdomain and an excitation matrix representing simulated incident electrical and magnetic stimulation to the assembly.