In this talk we will present an efficient direct-forcing immersed boundary method (IBM) for moving boundary simulations. In the recently suggested SIMPLE approach for IBM [1], an intermediate velocity field is first calculated, followed by a generalized saddle-point system in which the pressure and force corrections are coupled. In [1], this saddle-point system was addressed by utilizing a standard block-reduction, solving first for the force correction field from which the pressure correction field is next calculated. However, this method was prohibitively expensive for moving bodies, as the dual Schur-complement used there is a product of an inverse Laplacian with coupling blocks that change at each time step. Hence, it is impractical for realistic 3D problems to form the Schur-complement, that must be rebuilt in each time step. In this work, we suggest performing the block reduction the other way around, solving first the primal Schur-complement for the pressure correction field, from which the forces correction field can be calculated. Together with an approximation of the regularization block by a scalar matrix, the primal Schur-complement is formed by a matrix product, without inversion of any block. However, the obtained matrix is large and ill-conditioned, and hence to make the method scalable, we solve it iteratively using an efficient preconditioner. To this end, we take the Laplacian as a preconditioner for the primal Schur-complement of the pressure-force corrections system. We prove rigorously that the Laplacian is spectrally equivalent to the primal Schur-complement. That is, the preconditioned system can be solved by a constant number of Krylov iterations, regardless of the grid size, Reynolds number, and time step. The method's performance is validated through simulations of flow around a periodically oscillating sphere in a three-dimensional box. The memory requirements are notably low, allowing precise moving boundary simulations to run on standard workstations.