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

We present the MultiWave C++-framework for adaptive numerical methods approximating hyperbolic balance laws. MultiWave has been designed as a computational laboratory where new mathematical concepts can be quickly implemented and tested. We demonstrate the realisation of an adaptive perturbation discontinuous Galerkin method starting with the mathematical background and proceed to the low-level implementation details. We elaborate on the design choices made in particular regarding the modularity that allows one to extend the code reusing existing infrastructure.