Purpose - Optimization processes and movement modeling usually require a high number of simulations. The authors propose to reduce global central processing unit (CPU) time by decreasing each evaluation time. Design/Methodology/Approach - Remeshing the geometry at each iteration is avoided in the proposed method. The idea consists in using a fixed mesh on which functions are projected in order to represent geometry and supply. Finding - Results are very promising. Central processing unit (CPU) time is reduced for three dimensional problems by almost a factor two, keeping a low relative deviation from usual methods. CPU time saving is doable by avoiding meshing step, and with a better initialization of iterative resolution. Optimization, movement modeling and transient-state simulation are very efficient and give the same results as the usual FE method. Research limitations implications - The method is restricted to simple geometry due to the difficulty of finding spatial mathematical function describing the geometry. Moreover, a compromise between imprecison-caused by the boundary evaluation-and time saving must be found. Originality/Value - The method can be applied to optimize the design of rotating machines. Moreover, movement modeling is performed by shifting functions corresponding to moving parts.