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Abstract 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.
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Received: 19 October 2008
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