A characteristic domain decomposition and space-time local refinement method for first-order linear hyperbolic equations with interfaces

We develop a characteristic-based domain decomposition and space-time local refinement method for first-order linear hyperbolic equations. The method naturally incorporates various physical and numerical interfaces into its formulation and generates accurate numerical solutions even if large time-steps are used. The method fully utilizes the transient and strongly local behavior of the solutions of hyperbolic equations and provides solutions with significantly improved accuracy and efficiency. Several numerical experiments are presented to illustrate the performance of the method and for comparison with other domain decomposition and local refinement schemes.