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The analysis of a plane wave incident on a large microstrip patch is studied using the method of moments (MoM) with the layered medium Green's functions and the rooftop basis functions. A fast numerical approach, the multilevel UV method, is employed to speed up the method of moment solution. A conjugate gradient method solver with preconditioning is applied as an iterative matrix solver to accelerate the matrix-vector multiplication. The multilevel UV method has O(N log N) complexity for CPU per iteration and memory.