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The accurate and efficient electromagnetic simulation of antenna elements poses a substantial challenge due to the wide variation present in antenna topologies and operating specifications as well as the environments they are installed in for end use. This paper provides an overview of several of the most robust numerical techniques currently employed by commercial simulation packages, including transient, finite element and integral equation based methods. The details of each algorithm are discussed, and their relative strengths and weaknesses are compared. Several antenna examples are presented to demonstrate where each solver technology is most applicable.