The LS method as initially proposed in  uses a LS function which is defined on the entire simulation domain. Consequently, the memory requirements for the discretization of the LS function scale with the domain size. The scaling law of the computation time for the time update scheme is similar. However, the optimal complexity for storing and evolving a surface over time should linearly depend on the surface area (measured in grid spacings). Different approaches have been developed in the past to make the LS method more efficient.