论文标题
用于非线性偏微分方程的自适应小波方法，并应用于动态损伤建模
An adaptive wavelet method for nonlinear partial differential equations with applications to dynamic damage modeling
论文作者
论文摘要
多尺度和多物理问题需要新颖的数值方法，以便正确和预测地解决它们。为此，我们开发了一种基于小波的技术来解决非线性偏微分方程（PDE）的耦合系统，同时在各种空间和时间尺度上解决特征。该算法利用了小波基函数的多分辨率性质，以解决稀疏多分辨率空间离散化的有限域上的初始限值问题。通过利用小波理论并在时间上升循环内嵌入预测器 - 校正程序，我们会动态调整计算网格并保持PDES进化时溶液的准确性。因此，我们的方法提供了具有重大数据压缩的高忠诚模拟。我们介绍了算法的验证，并通过使用新型Eulerian-Lagrangian Continuum框架在非线性固体中建模高应变速率损伤成核和传播来证明其能力。
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential equations (PDEs) while resolving features on a wide range of spatial and temporal scales. The algorithm exploits the multiresolution nature of wavelet basis functions to solve initial-boundary value problems on finite domains with a sparse multiresolution spatial discretization. By leveraging wavelet theory and embedding a predictor-corrector procedure within the time advancement loop, we dynamically adapt the computational grid and maintain accuracy of the solutions of the PDEs as they evolve. Consequently, our method provides high fidelity simulations with significant data compression. We present verification of the algorithm and demonstrate its capabilities by modeling high-strain rate damage nucleation and propagation in nonlinear solids using a novel Eulerian-Lagrangian continuum framework.
