通过自伴耦合实现高效计算均匀化的无方程补丁格式
Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling
摘要：
无方程宏观尺度建模是一种系统和严格的计算方法，用于在所需的宏观尺度系统水平上有效地预测微尺度系统的动态。在该方案中，给定的微尺度模型是在空间-时域上分布的小块中计算的，其中块耦合条件桥接未模拟的空间。为了精确的模拟，在设计贴片耦合条件时必须小心。在这里，我们构造新的耦合条件，保持平移不变性，旋转不变性，自伴对称性，从而保证与这些对称性相关的守恒律在宏观模拟中被保留。光谱和代数分析所提出的计划在一个和两个维度揭示机制，进一步提高模拟的准确性。证明了补丁方案的宏观尺度动力学与原微尺度模型的一致性。这种新的自伴补丁计划提供了一个有效的，灵活的，准确的计算均匀化在广泛的多尺度的情况下感兴趣的科学家和工程师。
英文摘要：
Equation-free macroscale modelling is a systematic and rigorous computational methodology for efficiently predicting the dynamics of a microscale system at a desired macroscale system level. In this scheme, the given microscale model is computed in small patches spread across the space-time domain, with patch coupling conditions bridging the unsimulated space. For accurate simulations, care must be taken in designing the patch coupling conditions. Here we construct novel coupling conditions which preserve translational invariance, rotational invariance, and self-adjoint symmetry, thus guaranteeing that conservation laws associated with these symmetries are preserved in the macroscale simulation. Spectral and algebraic analyses of the proposed scheme in both one and two dimensions reveal mechanisms for further improving the accuracy of the simulations. Consistency of the patch scheme's macroscale dynamics with the original microscale model is proved. This new self-adjoint patch scheme provides an efficient, flexible, and accurate computational homogenisation in a wide range of multiscale scenarios of interest to scientists and engineers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
