SummationByPartsOperators.jl

The Julia library SummationByPartsOperators.jl provides a unified interface of different discretization approaches including finite difference, Fourier pseudospectral, continuous Galerkin, and discontinuous Galerkin methods. This unified interface is based on the notion of summation-by-parts (SBP) operators. Originally developed for finite difference methods, SBP operators are discrete derivative operators designed specifically to get provably stable (semi-) discretizations, mimicking energy/entropy estimates from the continuous level discretely and paying special attention to boundary conditions. SummationByPartsOperators.jl is mainly written to be useful for both students learning the basic concepts and researchers developing new numerical algorithms based on SBP operators. Thus, this package uses Julia’s multiple dispatch and strong type system to provide a unified framework of all of these seemingly different discretizations while being reasonably optimized at the same time, achieving good performance without sacrificing flexibility