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| 无网格稳定配点法及其在弹性力学中的应用 |
| Meshfree Stabilized Collocation Method in Elasticity |
| 投稿时间：2021-01-15 修订日期：2021-02-10 |
| DOI： |
| 中文关键词: 无网格稳定配点法 重构核近似 精度 稳定性 效率 |
| 英文关键词:Meshfree stabilized collocation method reproducing kernel function accuracy stability efficiency |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 中文摘要: |
| 伽辽金型无网格法具有精度高、稳定性好的优点，但是实现高阶准确积分过程复杂，且导致其计算效率低。配点型无网格法的计算效率高，但是其在求解复杂问题时往往会出现精度和稳定性较差的结果。本文介绍一种新的无网格法-无网格稳定配点法，这种方法采用重构核近似作为近似函数，在规则子域内非常容易实现高阶准确积分，既保留了配点型无网格法效率高的特点，又具备伽辽金型无网格法精度高和稳定性好的特点，而且还兼具有限体积法满足局域离散方程守恒的特点。本文中给出的几个弹性力学算例验证了该算法的优越性，未来可将其进一步应用于流体和流固耦合问题分析。 |
| 英文摘要: |
| Galerkin-type meshfree methods have the advantages of high accuracy and good stability, but the process of achieving high-order accurate integration is complicated, which results in the low efficiency of such methods. The collocation-type meshfree methods have high computational efficiency, but they often suffer the poor accuracy and stability when solving the complex problems. Therefore, this paper introduces a new meshfree method-meshfree stabilized collocation method. In this method, the reproducing kernel function is utilized as the approximation function. Regular subdomains are established to achieve the high-order accurate integration. This method not only possesses the high efficiency as the direct collocation method, but also has the high accuracy and good stability as the Galerkin-type meshfree methods. Besides, it is also characterized by satisfying the conservation of local discrete equations as the finite volume method. Several elasticity examples are presented to verify the superiority of the proposed method, and it can be further applied to the fluid and fluid-structure interaction problems in the future. |
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