This paper presents the mathematical formulation, numerical solution, calibration and testing of a physics-based model of wildfire propagation aimed at faster-than-real-time simulations. Despite a number of simplifying assumptions, the model is comprehensive enough to capture the major phenomena that govern the behaviour of a real fire - namely the pyrolysation of wood; the combustion of a mono-phase medium composed of premixed gas of fuel and air; and the heat transferred by conduction, convection, radiation, mass diffusion and transport due to atmospheric wind. The model consists of a system of coupled partial differential equations, one ensuring the balance of enthalpy, and a set of equations representing the mass formation of each chemical species involved in the combustion. Dimensionality reduction is sought by modelling these three-dimensional phenomena in a two-dimensional space, which has been achieved by means of heat-sources and heat-sinks to account for the third dimension in the energy balance equation. Once calibrated with a widely used non-physics-based commercial wildfire simulator, the proposed Fire Propagation Model for Fast simulations (FireProM-F) is tested, returning similar predictions in terms of the size and shape of the burnt area although similarity deteriorates for windy conditions. FireProM-F has the added benefit of being both physics-based and computationally inexpensive so that its interaction with fire suppressants may also be modelled in the future and simulated in real time.