This paper present a multidomain pseudospectral method for accurately solving Maxwell's equations in the time domain. The Traditional spectral methods suffer from having a fixed scheme is developed for computing scattering by two-dimensional distribution of grid points, thereby making it difficult to smooth perfectly conducting objects like circular or elliptic cylinders apply such methods for solving problems with strong interin free space and utilizes a Fourier collocation method in the azinal layers or problems in complex geometries. Using a muthal direction and a multidomain Chebyshev collocation method multidomain approach, i.e., splitting the computational doin the radial direction. Proper absorbing boundary conditions are discussed and a new perfectly matched layer (PML) method in polar main into several geometrically simple body conforming coordinates is constructed and shown to be superior to other PML domains, has proven to be a powerful way of overcoming methods. For the elliptic cylinders we propose to use a matched these restrictions on the applicability of spectral methods layer in connection with the multidomain approach and a cubic (see, e.g., [5]). Moreover, such an approach allows for an grid mapping. Numerical results of monochromatic electromagnetic efficient implementation on contemporary parallel comscattering by circular and elliptic perfectly electrically conducting cylinders are presented. Comparisons between results obtained us-puters [6] and relieves much of the computational burden ing the multidomain pseudospectral method and the finite-differof spectral methods even on serial computers, since one ence time domain method clearly illustrate the superiority of speccan increase the number of subdomains rather than the tral methods in obtaining accurate values for the scattered fields number of points in each subdomain resulting in a signifiand the bistatic radar cross section.