Node placement method with bubble simulation can generate high-qualify node sets in complex domains.However,its efficiency needs to be increased.Several modifications were done to reduce the cost of simulation.Firstly,let viscosity coefficient c gradually increases instead of being taken as a constant.It speeds up convergency.Moreover,at the end of each round simulation,in which bubbles additions or deletions are operated,c is assigned to a small value in order to ensure quality of bubble distribution.Secondly,as solving ordinary differential equations that control movement of bubbles,a low order numerical algorithm is chosen.Finally,sort process of overlapping rate of bubbles is removed.It is replaced by setting only threshold for bubbles additions and deletions.Numerial examples show that computing cost decreases by approximately 40% and average quality of Delaunay triangulation corresponding to node set is over 0.9.It shows that the algorithms are efficient and generate node sets with high-quality.

For mesh generation of a two-parameter surface, anisotropic and non-uniform node placement method with bubble simulation is applied to optimize node distribution in parameter area. Then the parameter area is meshed with constrained Delaunay triangulation. Finally, according to the mapping method, two-parametric surface mesh is obtained. A second order Riemann metric tensor determines distribution of nodes in the parameter area. It could be co-generated with a three-dimensional surface metric tensor and gradient of surface functions. Numerical examples show that the node placement method with bubble simulation can generate node set meeting requirements of Riemann metric in parameter area. Nodes are meshed and mapped back into the surface. A high quality surface mesh is obtained.