A MODIFIED INTERPOLATION APPROACH FOR TOPOLOGY OPTIMIZATION

In view of the fact that the follow-up search for an optimal topology is affected by deleting a large number of high-relative-density elements. When the typical density interpolation approach, namely, solid isotropic microstructures with penalization （SIMP）, is employed in the continuum structural topology optimization, a new density interpolation approach based on the logistic function is proposed in this paper. This method can weaken low-relative-density elements while enhancing high-relative-density elements by polarization, and then rationally realize polarization of the intermediate density elements. It can reduce the number of gray-scale elements as much as possible to get the optimal topology with distinct boundaries in conjunction with the sensitivity filtering method based on particle swarm optimization （PSO）. Several typical numerical examples are given to demonstrate this method.

The SIA method for spatial analysis of precipitation in the upper-middle reaches of the Yangtze River

Using geographic information system (GIS) techniques and the newest seasonal and annual average precipitation data of 679 meteorological stations from 1971 to 2000, the multiple regressions equations of the precipitation and topographical variables are established to extract the effect of topography on the annual and seasonal precipitation in the upper-middle reaches of the Yangtze River. Then, this paper uses a successive interpolation approach (SIA), which combines GIS techniques with the multiple regressions, to improve the accuracy of the spatial interpolation of annual and seasonal rainfall. The results are very satisfactory in the case of seasonal rainfall, with the relative error of 6.86%, the absolute error of 13.07 mm, the average coefficient of variation of 0.070, and the correlation coefficient of 0.9675; in the case of annual precipitation, with the relative error of 7.34%, the absolute error of 72.1 mm, the average coefficient of variation of 0.092, and the correlation coefficient of 0.9605. The analyses of annual mean precipitation show that the SIA calculation of 3-5 steps considerably improves the interpolation accuracy, decreasing the absolute error from 211.0 mm to 62.4 mm, the relative error from 20.74% to 5.97%, the coefficient of variation from 0.2312 to 0.0761, and increasing the correlation coefficient from 0.5467 to 0.9619. The SIA iterative results after 50 steps identically converge to the observed precipitation.

RBFs-MSA Hybrid Method for Mesh Deformation

Simulating unsteady flow phenomena involving moving boundaries is a challenging task,one key requirement of which is a reliable and fast algorithm to deform the computational mesh.Radial basis functions（RBFs） interpolation is a very simple and robust method to deform the mesh.However,the number of operations and the requirement of memory storage will be increased rapidly as the number of grid nodes increases,which limits the application of RBFs to three-dimensional（3D） moving mesh.Moving submesh approach（MSA） is an efficient method,but its robustness depends on the method used to deform the background mesh.A hybrid method which combines the benefits of MSA and RBFs interpolation,which is called RBFs-MSA,has been presented.This hybrid method is proved to be robust and efficient via several numerical examples.From the aspect of the quality of deforming meshes,this hybrid method is comparable with the RBFs interpolation;from the aspect of computing efficiency,one test case shows that RBFs-MSA is about two orders of magnitude faster than RBFs interpolation.For these benefits of RBFs-MSA,the new method is suitable for unsteady flow simulation which refers to boundaries movement.