MultiWave: A computational laboratory for adaptive numerical methods approximating hyperbolic balance laws

Abstract

The MultiWave C++-framework for adaptive numerical methods approximating hyperbolic balance laws is presented. MultiWave has been designed as a computational laboratory where new mathematical concepts can be quickly implemented and tested. Starting from the mathematical background and proceeding to the low-level implementation details, the realisation of a discontinuous Galerkin method with multiresolution-based grid adaptation is demonstrated. The design choices, in particular regarding the modularity that allows one to extend the code reusing existing infrastructure, is discussed. Scaling studies on a distributed-memory machine show that the framework retains its efficiency up to large rank counts, and that multiresolution-based adaptivity reduces the cost per time step by orders of magnitude compared to the uniform-grid computation at the order of accuracy of the full reference discretisation.