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We present the N-body simulation techniques in EXP. EXP usesempirically-chosen basis functions to expand the potential field of an ensembleof particles. Unlike other basis function expansions, the derived basisfunctions are adapted to an input mass distribution, enabling accurateexpansion of highly non-spherical objects, such as galactic discs. We measurethe force accuracy in three models, one based on a spherical or asphericalhalo, one based on an exponential disc, and one based on a bar-based discmodel. We find that EXP is as accurate as a direct-summation or tree-basedcalculation, and in some ways is better, while being considerably lesscomputationally intensive. We discuss optimising the computation of the basisfunction representation. We also detail numerical improvements for performingorbit integrations, including timesteps.

EXP: N-body integration using basis function expansions