(2+1)-dimensional discrete exterior discretization of a general wave model in Minkowski spacetime

Abstract

We present a differential geometry-based model for linear wave equations in $(2+1)$-dimensional spacetime. This model encompasses acoustic, elastic, and electromagnetic waves and is also applicable in quantum mechanical simulations. For discretization, we introduce a spacetime extension of discrete exterior calculus, resulting in a leapfrog-style time evolution. The scheme further supports numerical simulations of moving and deforming domains. The numerical tests presented in this paper demonstrate the method’s stability limits and computational efficiency.