A method of performing an electro-thermo simulation includes defining a non-linear heat diffusion problem for at least a portion of a semiconductor device to be modeled, performing a finite volume discretization of the non-linear heat diffusion problem, reformulating a non-linear term of the discretized non-linear heat diffusion problem to decrease dimensions thereof, performing a hyper reduction of the reformulated non-linear term, and recovering the non-linear heat diffusion problem for the portion of the semiconductor device, and manufacturing the modeled semiconductor device.