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| 一种采用Monte-Carlo积分的局部最大熵估计方案 |
| A Local Maximum Entropy Approximation Scheme using Monte-Carlo integration |
| 投稿时间：2025-02-20 修订日期：2025-04-26 |
| DOI： |
| 中文关键词: 局部最大熵估计方案 Monte-Carlo积分 无网格法 |
| 英文关键词:Local Maximum Entropy approximation scheme Monte-Carlo integration meshfree method |
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| 摘要点击次数: 13 |
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| 中文摘要: |
| 局部最大熵估计方案是一种基于最大熵原理的无网格法。文献[1]中用到β=γh^2调参使得λ收敛，我们将参数β由标量拓展为节点i上的倒格矢矩阵β_i，同样使得λ收敛。基于文献[2]，我们引入了材料的非均匀性，强调了局部最大熵估计是跨尺度模拟的重要方法。在宏观尺度的应用中，有别于常用的高斯积分法，我们使用Monte-Carlo积分避免等参变换的雅可比矩阵求逆，达到了“无网格”的目的，其应用在线弹性力学的算例中得到了合理的近似解。 |
| 英文摘要: |
| Local Maximum Entropy approximation scheme is a meshfree method derived from the principle of maximum entropy. The parameter β=γh^2 is tuned in literature[1] to ensure the convergence of the solution λ. We extended the scalar β to the reciprocal lattice vectors β_i attached to the node i, which also makes the λ convergent. Based on the literature[2], we further introduced the material’s inhomogeneous property and therefore raised the Local Maximum Entropy method as an important tool to bridge the gap between different length scales. When applied in the macro scale, we used Monte-Carlo integration apart from the Gauss quadrature to avoid the inverse of Jacobian in the iso-parametric transformation and leads to the “meshfree” in a simple way. In the numerical examples, the Monte-Carlo integration did approximate the analytical solutions. |
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