In this paper, we present a new implicit Monte-Carlo scheme for photonics. The new solver combines the benefits of both the IMC solver of Fleck & Cummings and the SMC solver of Ahrens & Larsen. It is implicit hence allows taking affordable time steps (as IMC) and has no teleportation error (as SMC). The paper also provides some original analysis of existing schemes (IMC, tilted IMC, SMC), especially with respect to the teleportation error in the equilibrium diffusion regime. In particular, we demonstrate that any small spatial inaccuracies during the sampling of source particles for IMC lead to a competing behaviour between the spatial and time discretisation parameters. The new scheme we suggest is implicit, conservative, has no teleportation error (and as a consequence does not need tilting), does not rely on source sampling for the emission of source particles, captures the equilibrium diffusion limit (provided a small enough time step), can be used with arbitrary equations of state and does not suffer the above competing behaviour. All those properties are either demonstrated or numerically highlighted in the paper.

在本文中，我们提出了一种新的隐式蒙特卡洛光子学方案。新的求解器结合了Fleck＆Cummings的IMC求解器和Ahrens＆Larsen的SMC求解器的优点。它是隐式的，因此允许采取可承受的时间步长（如IMC），并且没有传送错误（如SMC）。本文还提供了对现有方案（IMC，倾斜的IMC，SMC）的一些原始分析，尤其是关于平衡扩散状态下的隐形传态误差。特别是，我们证明了在IMC的源粒子采样过程中任何小的空间误差都会导致空间离散化和时间离散化参数之间的竞争行为。我们建议的新方案是隐式的，保守的，没有传送错误（因此不需要倾斜），它不依赖于源采样来发射源粒子，捕获了平衡扩散极限（提供了足够小的时间步长），可以与任意状态方程一起使用，并且不会遭受上述竞争行为。本文中所有这些特性都得到了证明或用数字突出显示。