A linear second order partial differential equation, which has historically been used for computing the approximate distance to the nearest solid domain boundary, is decomposed into a first order system of linear equations. The importance of the details of the decomposition on the stability, accuracy, and convergence speed of the discretised system are investigated. Inferences are drawn about the requirements of the decomposed system which ensure that it results in the discretised system being stable and convergent under explicit time stepping. A multiobjective optimisation is undertaken to find the Pareto front which balances the accuracy with which the discretised system represents the underlying equations against the condition number of the system, which serves as a surrogate for convergence speed. From this, optimised first order decompositions are generated, the best of which is found to reduce the numerical error to \(10\%\) of that found in the baseline case, and the number of time steps required to converge to \(30\%\) of the baseline.