Simulation of electrical circuits in real-time requires very short latency implementations that can be achieved only on special-purpose hardware accelerators. The heart of such algorithms is a matrix-vector multiplication between the inverse of the admittance matrix of the circuit and of its current state vector, yielding the next state vector. The main difficulty is to obtain the inverse of the admittance matrix in real-time, as this matrix depends on the state-open or closed-of the switches of the circuit. We consider here the problem of obtaining a new inverse matrix, using the Sherman-Morrison update algorithm, and we explain how various VHDL implementations of this algorithm can be obtained from a high-level, polyhedral equational, description of the circuit.