Local time-stepping for discrete exterior calculus on spacetime mesh with refinements

Abstract

A geometrical method for solving wave equations on a spacetime mesh is studied. The construction can be used for local mesh refinement both in space and time or efficient and simple simulation of moving domains. The construction uses a pair of mesh and dual mesh that is orthogonal with respect to the Minkowski metric. Orthogonality is the key factor in defining a diagonal discrete Hodge operator, which can then be efficiently used for explicit time-stepping. The approach considered is well suited for wave problems defined on Minkowski spacetimes where geometric accuracy, topological correctness, and the preservation of physical laws are crucial for obtaining reliable and accurate results.