Research And Application Based On The Wavelet Meshless Method And Improved Meshless Method

As a new type of numerical method in recent years, meshless method is independentof the element which traditional element-type method depends on. It is solved byconstructing a series of nodes and so it avoids the onerous mesh generation, so that theyare paid much attention of scientists and engineers in various computational areasbecause of their greatly theoretical and applicable value. Meshless method constructs theapproximate function by solving the domain of scattered nodes. It doesn't need the initialreconstruction and dividing of the grid. It has the characteristic such as the high precisionin calculation and the simple pretreatment and it has a good application prospect. Thispaper mainly includes:Firstly, this paper describes the development of the production about theElement-Free Galerkin Method, then give the definition and construction principles ofthe basic elements of the method, and derives the calculation of the Element-freeGalerkin method. With we study shape function, weight function and the influencedomain radius factor for numerical examples, through the comparie calculation resultsand analysis, study how to improve the accuracy of the conclusion.Secondly, under the define of the inner product space, we used the orthogonal basisfunction as the base function of meshless method. We deduct the shape function and itsderivatives and improve the orthogonal basis function. Because of orthogonal basis don'tneed the inverse matrix, it is very complex when solving the derivation of the constructedshape function, and it need much deduction, and can also simplify the calculation of thederivatives of the shape function. We put forward the local orthogonal meshless method.This method made solving the derivation very simple and has higher efficient. This paperapplied local orthogonal basis meshless method to the electromagnetic field, andconstructed the discrete model and proved the validity and feasibility of the methodthrough numerical column.Finally, apply the wavelet function to Galerkin meshless method based on the goodproperty of wavelet base function, such as compactly supported and orthogonality, and it can forms the corresponding function by extending and moving the wavelet function.Combining with wavelet function and advantages of meshless method it can forms themeshless method. It can overcome other field function the redundancy in the calculationand reduce the computation cost or improve the calculation accuracy characteristics. Inthis paper, we applied the meshless method to the area of electromagnetic. We show thatthe wavelet meshless method is feasible in the area of electromagnetic and it has a gooddevelopment prospect.