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Purpose: The purpose of this paper is to present an adaptive binary-tree element subdivision method (BTSM) for the evaluation of nearly singular integrals in three-dimensional boundary element method, which can facilitate automatic and high-quality patch generation. Design/methodology/approach: In this method, the nearly singular element is split into two sub-elements. Each sub-element is then examined to determine if it is to be subdivided based on a specific subdivision criterion. The specific subdivision ensures that those sub-elements far from the source point are sparse. And then those sub-elements in close proximity to the source point are replaced by regular triangular elements. Findings: With the proposed method, the sub-elements obtained are automatically refined as they approach the projection point, and they are "good" in shape and size for standard Gaussian quadrature. Thus, the proposed method can be used to evaluate nearly singular integrals accurately for cases of different element shapes and various locations of the source point. Originality/value: Numerical examples for surface elements with various relative locations of the source point are presented. The results demonstrate that the proposed method has much better accuracy and robustness than some other methods. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to present an algorithm for determining the inner and outer loops of arbitrary parametric surfaces. Design/methodology/approach: The algorithm considers two sub-algorithms: one for non-closed surfaces and another one for closed surfaces. The first sub-algorithm named by area positive and negative method (APNM), combines a curve discretization algorithm with the polygon direction judgment algorithm to judge the inner and outer loops of non-closed surfaces. The second sub-algorithm, called by cross-period number method (CPNM), combines a curve discretization algorithm with the periodicity of closed surfaces to judge the type of boundary loops. Findings: The APNM can use less CPU time to determining the inner and outer loops of the non-closed parametric surfaces. The CPNM can also determine the inner and outer loops of closed parametric surfaces effectively. The judgment results of loops can ensure that the direction of meshes generated on these surfaces is right. And finally ensure the correctness of the numerical simulation results. Originality/value: Several numerical examples presented have verified the robustness and efficiency of the proposed algorithm. Compared with the conventional algorithm, the more complex the model, the more time the APNM saves in the process of determining the inner and outer loops for non-closed surfaces. The CPNM is also a new method to determining the inner and outer loops for closed parametric surfaces. The single run-time of CPNM is very small and can reach the level of microseconds. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to present a fast algorithm for the adaptive discretization of three-dimensional parametric curves. Design/methodology/approach: The proposed algorithm computes the parametric increments of all segments to obtain the parametric coordinates of all discrete nodes. This process is recursively applied until the optimal discretization of curves is obtained. The parametric increment of a segment is inversely proportional to the number of sub-segments, which can be subdivided, and the sum of parametric increments of all segments is constant. Thus, a new expression for parametric increment of a segment can be obtained. In addition, the number of sub-segments, which a segment can be subdivided is calculated approximately, thus avoiding Gaussian integration. Findings: The proposed method can use less CPU time to perform the optimal discretization of three-dimensional curves. The results of curves discretization can also meet requirements for mesh generation used in the preprocessing of numerical simulation. Originality/value: Several numerical examples presented have verified the robustness and efficiency of the proposed algorithm. Compared with the conventional algorithm, the more complex the model, the more time the algorithm saves in the process of curve discretization. [ABSTRACT FROM AUTHOR]