A highly accurate method is presented for the construction of the charge density for the solution of the Poissonequation in particle simulations. The method is based on an operator adjusted source term which can be shown to produceexact results up to numerical precision in the case of a large support of the charge distribution, therefore compensating thediscretization error of finite difference schemes. This is achieved by balancing an exact representation of the known Green’sfunction of regularized electrostatic problem with a discretized representation of the Laplace operator. It is shown that theexact calculation of the potential is possible independent of the order of the finite difference scheme but the computationalefficiency for higher order methods is found to be superior due to a faster convergence to the exact result as a function of thecharge support
