| As an important research subject in the process of scientific computing visualization, Kriging interpolation has very important application value in many research fields, such as environmental science, geology, water conservancy, network and meteorology. In recent years, with the application of Kriging interpolation technology is more and more widely, the requirements of the higher efficiency of Kriging interpolation method are also raised. Therefore, how to improve the efficiency of Kriging interpolation has become a focus in the study of many scholars.In recent years, with the rapid development of GPU technology, its powerful ability of parallel computing has received the widespread attention from scientific all circles. The Kriging interpolation method based on GPU appeared. These studies provide a new idea for improving the Kriging interpolation efficiency, but they also have some problems. First of all, for the Kriging is an algorithm defined in the limited space domain, there is the problem of computational region selection unavoidably in application, which needs to select neighborhood points for the interpolation points as input. While the important factor neighborhood points is not considered in the existing Kriging interpolation method based on GPU, instead setting all the known points as input; Second, if set all the known points as input, the plan will be not feasible when the sample points data on a large scale. That is to say, this method does not apply to practical engineering application. Based on the above problems, this thesis proposes a fast Kriging interpolation method which based on 3-d Delaunay and CUDA. In addition, in order to apply this method to the practical geological engineering project, this thesis proposes a Kriging interpolation scheme based on space curved surface constrained triangle subdivision. In this thesis, the main work is as follows:1. This thesis proposes a fast three-dimentional Kriging interpolation method based on Delaunay. The method is divided into two parts. It accelerates the Kriging interpolation mainly by the search of neighbor points and parallel computing. One is a fast neighbor points search method based on 3-d Delaunay triangulation. Specific implementation is: before the processing of Kriging interpolation, construct 3-d Delaunay triangulation with known points. Then locate the tetrahedron which contains the interpolation point quickly by establishing spatial index for Delaunay triangulation. At last, set the vertices of the located tetrahedron and its surrounding tetrahedron as input to Kriging interpolation. The other one is that in view of the second problem of the existing Kriging interpolation method based on GPU, this thesis proposes a new parallel Kriging interpolation scheme based on CUDA. The scheme is not restricted by the known point data size and is more in line with the actual engineering application. Based on the test of real data, verify the algorithm effectively improves the efficiency of Kriging interpolation.2. This thesis proposes a Kriging interpolation method based on spatial curved surface constraints triangulation. In order to accelerate the Kriging interpolation algorithm, we construct Delaunay triangulation using known points for the fast search of neighborhood points. But in the actual geological engineering project, there is special constraint, such as horizon. However, the generating Delaunay triangulation dose not take into account these constraints, there will be tetrahedron that appear across the horizon. In this case the generated Delaunay triangulation model can not accurately express the actual geological model, the interpolation result is also not in conformity with the actual geological regularity, and it is also difficult to meet the needs of many practical geological applications. Therefore, this thesis proposes a Kriging interpolation method based on spatial curved surface constraints triangulation, and this method has important practical significance. |
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