The conventional combined-field integral equation (CFIE) using a Galerkin scheme suffers from inaccuracy issues due to the incorrect testing of the identity operator in the magnetic-field integral equation (MFIE). In this contribution, a mixed discretization scheme is used for correct testing of MFIE in the context of CFIE. The projection of testing spaces of EFIE and MFIE onto each other is required while solving CFIE numerically with the mixed discretization scheme. For this purpose, computations of the Gram matrix inversions are required to perform the projection operations. Such an operation can easily become computationally expensive, especially when solving large-scale problems using accelerated algorithms, such as the multilevel fast multipole algorithm (MLFMA). In this work, matrix decomposition methods and iterative solvers are used to solve Gram systems while solving CFIE with the mixed discretization scheme in the framework of MLFMA. The accuracy and efficiency of the results are compared, in the context of large-scale problems.