[en] The driver linac of the proposed Rare Isotope Accelerator (RIA) requires a great variety of high intensity, high charge state ion beams. In order to design and to optimize the low energy beamline optics of the RIA front end,we have developed a new parallel three-dimensional model to simulate the low energy, multi-species ion beam formation and transport from the ECR ion source extraction region to the focal plane of the analyzing magnet. A multisection overlapped computational domain has been used to break the original transport system into a number of each subsystem, macro-particle tracking is used to obtain the charge density distribution in this subdomain. The three-dimensional Poisson equation is solved within the subdomain and particle tracking is repeated until the solution converges. Two new Poisson solvers based on a combination of the spectral method and the multigrid method have been developed to solve the Poisson equation in cylindrical coordinates for the beam extraction region and in the Frenet-Serret coordinates for the bending magnet region. Some test examples and initial applications will also be presented