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Typically, the problem size that can be solved by the Method of Moments (MoM) is limited by the amount of RAM installed in the computer. To reduce the number of unknowns for MoM, higher-order polynomial functions have been introduced as the basis functions. To extend the capability of the MoM code, this paper presents a new development: the use of a new parallel out-of-core solver called PLAPACK. The PLAPACK library package offers benefits that are not available in the more commonly used ScaLAPACK libraries. Numerical results on a typical computer platform for two different challenging electromagnetic problems show that the PLAPACK out-of-core solver introduced here is a very efficient way to deal with large matrix equations. The implementation of these advancements creates a powerful tool for the efficient computational electromagnetic solution of large and complex real-world problems.