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In this thesis, the Transmission Line Matrix - Multipole Expansion method (TLMME) is presented. TLMME allows an efficient and potentially exact modeling of radiating electromagnetic structures by combining the time-domain transmission line matrix (TLM) method with the multipole expansion method (ME) of radiated fields. The total radiated field is decomposed into orthonormal radiation modes which are connected to the TLM simulation domain on a common spherical boundary. In a global network model the simulation domain is modeled by the TLM mesh of transmission lines, every impedance of the radiation mode is modeled by a ladder network one port, and the connection of these partial networks is accomplished by a connection subnetwork consisting of ideal transformers. This allows to include potentially exact radiating boundary conditions into the TLM model by lumped element equivalent circuits representing the impedance of the radiation modes.