高阶非局部算子方法
Higher order nonlocal operator method
AI总结：
本文提出一种高阶非局部算子方法，通过使用未知场的高阶泰勒级数展开扩展了非局部算子方法，提高了收敛阶数，并展示了该方法在求解偏微分方程中的应用能力。
摘要：
我们通过使用未知场的高阶泰勒级数展开，将非局部算子方法扩展到高阶方案。这种高阶方案改进了作者在[A nonlocal operator method for solving partial differential equations]中提出的一种只能实现一阶收敛的非局部算子方法。高阶非局部算子方法能够同时获得所有指定最大阶数的偏导数，而无需使用形函数。基于非局部算子的功能将残差和刚度矩阵的构造转化为非局部算子矩阵上的若干矩阵乘法。几个通过强形式或弱形式求解的数值例子展示了该方法的能力。
英文摘要：
We extend the nonlocal operator method to higher order scheme by using a higher order Taylor series expansion of the unknown field. Such a higher order scheme improves the original nonlocal operator method proposed by the authors in [A nonlocal operator method for solving partial differential equations], which can only achieve one-order convergence. The higher order nonlocal operator method obtains all partial derivatives with specified maximal order simultaneously without resorting to shape functions. The functional based on the nonlocal operators converts the construction of residual and stiffness matrix into a series of matrix multiplication on the nonlocal operator matrix. Several numerical examples solved by strong form or weak form are presented to show the capabilities of this method.
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。
