PML　(Perfectly　Matched　Layer)　is　treated　as　a　substructure.　The　transverse　section　of　the　substructures　is　made　discrete　by　using　regular　edge　elements,　and　the　stiff　matrices　can　be　calculated　by　precision　integration　based　on　Riccati　equations　in　a　Hamiltonian　system.　Finally,　we　can　solve　the　waveguide　discontinuity　problems　by　the　combination　of　the　export　stiff　matrices　of　substructures.　The　rectangular　discontinuous　waveguides　are　calculated　and　the　influence　of　energy　loss　with　the　change　of　substructure　length　is　shown.　The　results　demonstrate　that　the　method　has　high　efficiency,　accuracy　and　suitability　for　the　analyses　of　waveguide　discontinuities.　©　2011　IEEE.