Fast Positive And Negative Concentrate Equivalent Charges Method’s Implementation In Galerkin Boundary Element Algorithm

With the development of Ultra-high voltage transmission technology, the electric power industry puts forward higher requirements on electromagnetic fields numerical calculations. As an effective tool for solving massive degree of problems, the boundary element method has advantages of high accuracy, fewer nodes, processing boundary problems and so on, and have gotten more and more attentions in engineering field in recent years. The research about optimization of boundary element method is one of hotspots and frontier issues in numerical computing field.A fast positive and negative concentrate equivalent charges algorithm be proposed in this thesis, and be applied in the optimization of two-dimensional boundary element analysis. The main works in this thesis include:Based on the principle of two-dimension boundary element method, and draw lessons from the thought and principle of the concentration of far zone elements which in fast multipole algorithm, the thesis proposed a fast positive and negative concentrated equivalent charges algorithm. Studied and deduced formulas of fast positive and negative concentrated equivalent charges algorithm. Gave out the calculation steps of Restart-GMRES algorithm, The advantages of rapid positive and negative concentrate equivalent charges algorithm be declared through a numerical example.A lot of researches have been done to study quadtree structure which have been used in fast positive and negative concentrate equivalent charges algorithm. With the demands of judging far zone and near zone, the thesis gave out hierarchical coding method in pointer tree and neighbor region search algorithm which based on hierarchical coding of quadtree, combined tree structure’s coding way, derived the neighbor region search algorithm formula in quadtree knot points. An example be given to verified the validity of the neighborhood search algorithm.Studied the accuracy problem about fast positive and negative concentrate equivalent charges algorithm. Compared calculation time and storage space of fast positive and negative concentrate equivalent charges algorithm with iteration method boundary element algorithm and traditional Gaussian elimination method of boundary element algorithm in different factors. Studied the calculation time and storage space of restart-GMRES method in different restart parameter. Verified the effectiveness of fast positive and negative concentrate equivalent charges boundary element algorithm in two-dimension model.