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A novel method is developed to take into account realistic boundary conditions in intense nonlinear beam dynamics. The algorithm consists of three main ingredients: the boundary element method that provides a solution for the discretized reformulation of the Poisson equation as boundary integrals; a novel fast multipole method developed for accurate and efficient computation of Coulomb potentials and forces; and differential algebraic methods, which form the numerical structures that enable and hold together the different components. The fast multipole method, without any modifications, also accelerates the solution of intertwining linear systems of equations for further efficiency enhancements. The resulting algorithm scales linearly with the number of particles N, as m log m with the number of boundary elements m, and, therefore, establishes an accurate and efficient method for intense beam dynamics simulations in arbitrary enclosures. Its performance is illustrated with three different cases and structures of practical interest.