Multi-physics simulations are a crucial tool to design and optimize the geometry of edge-emitting semiconductor optical amplifiers (SOA) for a wide range of applications. However, simulating the optical, electrical and thermal characteristics is in general computationally challenging due to the different dimensionalities and relevant length scales of the individual problems. By utilizing the geometry of edge-emitting SOAs, the optical model can be reduced to 1D 1D simulation of the forward propagating optical wave. Consequently, the electrical and thermal models can be greatly reduced in complexity. Thereby a beam propagation method with a symmetrized split-step algorithm for the optical field, a finite differences scheme for the elec-trical model and a Green?s function method for the thermal model are applied. The highly optimized multi-physics simulation is implemented in Python and allows the simulation of millimeter-sized SOAs within seconds on a standard computer.