We have developed an algorithm coupling mesoscopic simulations on different levels in a hierarchy of Cartesian meshes. Based on the multiscale nature of the chemical reactions, some molecules in the system will live on a fine-grained mesh, while others live on a coarse-grained mesh. By allowing molecules to transfer from the fine levels to the coarse levels when appropriate, we show that we can save up to three orders of magnitude of computational time compared to microscopic simulations or highly resolved mesoscopic simulations, without losing significant accuracy. We demonstrate this in several numerical examples with systems that cannot be accurately simulated with a coarse-grained mesoscopic model.

中文翻译：

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反应扩散主方程的分层算法。

我们已经开发了一种在笛卡尔网格层次结构中的不同级别上耦合介观模拟的算法。基于化学反应的多尺度性质，系统中的某些分子将生活在细粒度的网格上，而其他分子则生活在粗粒度的网格上。通过在适当的时候允许分子从精细水平转移到粗糙水平，我们证明与微观模拟或高度解析的介观模拟相比，我们可以节省多达三个数量级的计算时间，而不会损失明显的准确性。我们用无法用粗粒度介观模型精确模拟的系统在几个数值示例中证明了这一点。