A new, very fast, approach for calculations of the electromagnetic excitation field for MRI is presented. The calculation domain is divided in different homogeneous regions, where for each region a general solution is obtained by a summation of suitable basis functions. A unique solution for the electromagnetic field is found by enforcing the appropriate boundary conditions between the different regions. The method combines the speed of an analytical method with the versatility of full wave simulation methods and is validated in the pelvic region against FDTD simulations at 3 and 7 T and measurements at 3 T. The high speed and accurate reproduction of measurements and FDTD calculations are believed to offer large possibilities for multi-transmit applications, where it can be used for on-line control of the global and local electric field and specific absorption rate (SAR) in the patient. As an example the method was evaluated for RF shimming with the use of 7 T simulation results, where it was demonstrated that the magnetic excitation field could be homogenized, while both the local and average SAR were reduced by 38% or more. © 2009 Institute of Physics and Engineering in Medicine.