1. A method for determining ampacity risks in a circuit, comprising: receiving geometry data of the circuit; initializing boundary conditions; initializing circuit geometry assumptions; modeling the circuit geometry data as a three-dimensional solid; computing non-Fourier heat conduction through the three-dimensional solid model using conjugate gradient numerical analysis with an incomplete Cholesky preconditioner; and generating an output indicative of a location in the three-dimensional solid model where potential thermal damage may occur in response to a predetermined excitation.