A block pseudospectral method for Maxwell's equations - I. One-dimensional case

A block pseudospectral (BPS) method is proposed as a new way to couple pseudospectral discretizations across interfaces in computations for a linear hyperbolic system. The coupling is achieved via discretized derivative-matching conditions obtained from the system. Compared to the standard technique of imposing compatibility conditions based on characteristics of the system, the BPS method offers better stability and accuracy, especially in the case where equation coefficients are discontinuous. Computational examples for Maxwell's equations in nonhomogeneous media demonstrate that BPS retains high accuracy over times that are orders of magnitude larger than those for not only low-order methods (such as Yee's), but also high-order methods, such as characteristic-based spectral elements. (C) 1998 Academic Press.