A　hybrid　surface　integral　equation　partial　differential　equation　(SIE-PDE)　formulation　without　the　boundary　condition　requirement　is　proposed　to　solve　the　transverse　magnetic　(TM)　electromagnetic　problems.　In　the　proposed　formulation,　the　computational　domain　is　decomposed　into　two　overlapping　domains:　the　SIE　and　PDE　domains.　In　the　SIE　domain,　complex　structures　with　piecewise　homogeneous　media,　e.g.,　highly　conductive　media,　are　included.　An　equivalent　model　for　those　structures　is　constructed　by　replacing　them　with　the　background　medium　and　introducing　a　surface　equivalent　electric　current　density　on　an　enclosed　boundary　to　represent　their　electromagnetic　effects.　The　remaining　computational　domain　and　homogeneous　background　medium　replaced　domain　consist　of　the　PDE　domain,　in　which　inhomogeneous　or　nonisotropic　media　are　included.　Through　combining　the　surface　equivalent　electric　current　density　and　the　inhomogeneous　Helmholtz　equation,　a　hybrid　SIE-PDE　formulation　is　derived.　It　requires　no　boundary　conditions　and　is　mathematically　equivalent　to　the　original　physical　model.　Through　careful　construction　of　basis　functions　to　expand　electric　fields　and　the　equivalent　current　density,　the　discretized　formulation　is　made　compatible　with　the　SIE　and　PDE　domain　interface.　The　accuracy　and　efficiency　are　validated　through　two　numerical　examples.　Results　show　that　the　proposed　SIE-PDE　formulation　can　obtain　accurate　results,　and　significant　performance　improvements　in　terms　of　CPU　time　and　memory　consumption　compared　with　the　FEM　are　achieved.　©　1963-2012　IEEE.