A method and system to efficiently create electromagnetic coupled basis functions for an electronic circuit that is defined by geometry data and topology data. The geometry data for the circuit are read, and a three-dimensional mesh of polygons for the circuit is created. External port geometry and internal port geometry (internal ports occur where vias are attached to conductive layers) are determined from the geometry data. Circuit electromagnetic basis functions are then created as are loop-tree formations that are coupled to the basis functions. The loops include local loops, via loops, and hole loops. The three-dimensional mesh is efficiently created by extruding a two-dimensional mesh for each layer and via in the circuit.