Initialization of linear multistep methods in multidimensional wave digital models

The wave digital concept for numerical integration of PDEs can easily be extended to linear multistep methods other than the trapezoidal rule, while retaining all the desirable robustness properties of the resulting algorithms. Interchanging integration methods urges the need for automatable wave initialization schemes, which are independent of the PDEs. We propose an algorithm fulfilling these requirements. It uses a 1-step method to initialize a multistep method via state estimation. We discuss a complete scheme for initial and boundary conditions and choose the advection equation as a simple example to demonstrate the effectiveness of the proposed algorithm.