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This letter describes a locally implicit latency insertion method (LILIM) for the fast simulation of an arbitrary shaped power distribution network (PDN) modeled by triangular meshes. First, an efficient modeling method based on triangular mesh is reviewed and we refer to the limitation of the LIM for the meshed PDN analysis. Next, in order to overcome the problem, we formulate the LILIM by combining the efficient modeling and the locally implicit schemes. Finally, the numerical results show that the LILIM is applicable and efficient for the simulation of the PDN analysis.