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A three-dimensional (3-D) multidomain pseudospectral time-domain (PSTD) method with a strongly well-posed perfectly matched layer (PML) is developed as an accurate and flexible tool for the simulation of electromagnetic wave propagation and scattering in inhomogeneous and conductive media. This approach allows for an accurate treatment of curved geometries by multidomain decomposition and curvilinear coordinate transformation. Numerical experiments show the results agree excellently with analytical solutions and results of other well-known algorithms, and demonstrate a remarkable improvement in accuracy and efficiency over the FDTD method. The 3-D multidomain PSTD algorithm is then applied to calculate radar cross sections (RCS).