As　modern　high　speed　Package　Circuit　Boards　(PCBs)　and　Integrated　Circuit　(IC)　packages　become　more　and　more　complicated,　the　electromagnetic　simulation　inside　the　PCBs　and　IC　packages　becomes　more　and　more　difficult.　The　most　challenge　work　is　that　complicated　multiple　layer　shapes　inside　PCBs　and　IC　packages　need　very　huge　amount　of　high　quality　meshes　for　electromagnetic　simulation,　which　lead　to　huge　memory　requirement　for　solving　the　linear　matrix.　For　most　personal　computers,　that　requirement　usually　lead　to　out　of　memory　in　matrix　solution.　To　overcome　this　problem　without　losing　the　simulation　precision,　this　article　presents　an　algorithm　to　simplify　complex　2-D　polygons　based　on　Delaunay　triangulation.　By　checking　the　smallest　angles　of　triangles　which　contain　an　edge　of　the　polygons,　the　algorithm　simplifies　polygons　adaptively　and　updates　the　simplified　polygons＇　Delaunay　triangulation.　Different　from　other　simplifications　which　try　to　decrease　the　count　of　vertices,　this　algorithm　tries　to　delete　redundant　short　edges,　leading　to　greatly　reduced　mesh　points　during　the　process　of　generating　the　constrained　and　quality　Delaunay　triangulation.　The　algorithm　presented　here　has　been　applied　for　mesh　generation　for　finite-element　analysis　of　complicated　PCBs　and　IC　packages.　Test　results　show　that　the　proposed　algorithm　can　reduce　more　than　75%　in　total　nodes　in　comparison　with　the　approach　without　simplification,　resulting　in　significant　reduction　of　computer　resources　in　numerical　computation.　©　2011　IEEE.