Discrete Transparent Boundary Conditions for Wide Angle Parabolic Equations for Non–vanishing Starting Fields

Transparent boundary conditions (TBCs) are an important tool for the truncation of the computational domain in order to compute solutions on an unbounded domain. In this work we want to show how the standard assumption of ‘compactly supported data’ could be relaxed and derive TBCs for the wide angle parabolic equation directly for the numerical scheme on the discrete level. With this inhomogeneous TBCs it is not necessary that the starting field lies completely inside the computational region. However, an increased computational effort must be accepted.