标题： 二阶形式的$P_N$方程与 Marshak 边界条件 显示英文标题

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

摘要： 我们考虑将经典的$P_N$方法与 Marshak 边界条件相结合，用于近似单能稳态线性输运方程，将其重新表述为二阶偏微分方程组。 我们的推导允许自动生成模型层次结构，然后可以传递给标准的偏微分方程工具。 该方法允许非均匀系数、不规则网格、各向异性边界源和各向异性散射。 在多个数值测试案例中展示了其广泛的应用性。 我们在线提供了实现代码，这有助于快速原型设计。 显示英文摘要

摘要： We consider a reformulation of the classical $P_N$ method with Marshak boundary conditions for the approximation of the monoenergetic stationary linear transport equation as a system of second-order PDEs. Our derivation allows the automatic generation of a model hierarchy which can then be handed to standard PDE tools. This method allows for heterogeneous coefficients, irregular grids, anisotropic boundary sources and anisotropic scattering. The wide applicability is demonstrated in several numerical test cases. We make our implementation available online, which allows for fast prototyping.