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We consider a reformulation of the classical $P_N$ method with Marshakboundary conditions for the approximation of the monoenergetic stationarylinear transport equation as a system of second-order PDEs. Our derivationallows the automatic generation of a model hierarchy which can then be handedto standard PDE tools. This method allows for heterogeneous coefficients,irregular grids, anisotropic boundary sources and anisotropic scattering. Thewide applicability is demonstrated in several numerical test cases. We make ourimplementation available online, which allows for fast prototyping.

The second-order formulation of the $P_N$ equations with Marshak boundary conditions