无网格法计算中一种新的积分点搜索算法

 无网格法计算中常采用背景网格积分法进行数值积分，需判断积分点与分析域的关系，当工程问题域边界较复杂时，虽可采用常用的射线法判断积分点与分析域的关系，但当分析域边界线段处于同一直线时，算法的复杂性大大增加，使其效率不高。为此，提出采用矩阵法判断积分点与分析域的关系，在此基础上，为加快搜索速度，提出并建立一种新的数据结构——稀疏矩阵，该矩阵中的元素记录各节点的信息，包括节点与其相邻节点的距离、节点编号和节点影响域尺寸等，通过稀疏矩阵可快速计算矩阵的行列式，从而给出一种积分点搜索速度更快的算法。算例表明，该算法大大加快积分点的搜索速度，提高无网格法的计算效率。

A NEW QUADRATURE POINT DETECTION ALGORITHM IN MESHLESS CALCULATION

Background cell integration method is widely used to implement numerical integration in meshless computation，in this procedure，the relationship between quadrature points and the problem domain must be assured. Radial method is commonly used when the boundary is complicated. However，the complexity of the algorithm is increased while several line sections are parallel，which results in low efficiency. In order to fasten the quadrature point detection，the matrix method is proposed to implement the detection through calculating the determinant of matrix，and furthermore，a new data structure—sparse matrix is presented；each element in this sparse matrix stores the following information associated with the nodes such as the distance between the node and its neighbor，the number of the node and radius of the node influence domain and the computational cost of determination of matrix can be decreased dramatically by sparse matrix. As a result，an advanced algorithm，which can fasten the quadrature point detection more quickly，is generated. Numerical results show that this algorithm can fasten the quadrature point detection sharply and therefore improve the efficiency of meshless numerical computation.