The Drossel-Schwabl forest fire model is one of the best studied models of nonconservative self-organized criticality. However, using an alternative algorithm, which allows us to study the model on large statistical and spatial scales, it has been shown to lack simple scaling. We thereby show that the considered model is not critical. This paper presents the algorithm and its parallel implementation in detail, together with large-scale numerical results for several observables. The algorithm can easily be adapted to related problems such as percolation.