On the construction of a high order difference scheme for complex domains in a Cartesian grid Original Research Article

We consider fourth order accurate compact schemes for the numerical solutions of the two dimensional Maxwell equations. We base this scheme on Ty(2,4) scheme [6]. We solve the equations on a Cartesian mesh but consider boundaries which do not necessarily conform with the Cartesian grid. On the boundaries we use second or third order accurate approximations. We also discuss the numerical approximation to the PML layer.