In this paper, a domain decomposition approach for design purposes is proposed. The analysis domain is divided into subdomains according to the arbitrarily shaped parts that should be modified in the synthesis process. A full-wave matrix-valued transfer function describes each decomposition subdomain, namely, an admittance-type matrix. Field continuity between subdomains is directly enforced by an admittance matrix connection. This methodology makes it possible to analyze only those parts of the analysis domain that are supposed to evolve in order to satisfy the design specifications. Furthermore, several modifications in the shape of the components are allowed as a consequence of the easy matrix connection process, where the consideration of different admittance-type matrices or absence of them gives rise to distinct geometric structures. A model order reduction technique is also considered for fast frequency sweeping. Finally, several numerical examples illustrate the capabilities of the proposed procedure, as well as its accuracy.