Meshless Method For Time Domain Decomposition And Its Application In Electromagnetic Field Equations

Unymmetric collocation method is a real meshless method and a powerful tool for solving partial differential equations.The advantage of this method is that it does not need to generate a grid,but directly approximates the numerical solution of the differen-tial equation with the linear combination of solving the points in the domain.This paper mainly uses the meshless method of time domain decomposition to solve the electromag-netic field equation which is similar to the heat conduction equation.Therefore,the key research direction is to use the meshless method of time domain decomposition to solve the general heat conduction equation,analyze the convergence of the algorithm and simulate the numerical solution of the electromagnetic field equation.Firstly,the background significance and theoretical knowledge of the research work are introduced,and then numerical experiments are used to test which radial basis function and which iterative method(GMRES Iterative method and Conjugate Gradient)are used to solve the elliptic equation.Numerical experiments show that the multi-quadric function,Inverse multi-quadric,Thin splines,etc.have the best effects under GMRES iteration,and the numerical tests of this part also lay a foundation for the following contents.Secondly,the general heat conduction equation is solved by the meshless method of time domain decomposition.The core idea of the algorithm is to divide the time region into several cells,and then solve them in parallel.In the space,asymmetric arrangement and meshless method are adopted,and jump points are set to ensure the accuracy of the solution.The numerical solution of the original problem can be obtained through finite iterations.The region is divided into regular and irregular solutions respectively,and the experimental results under parallel conditions are analyzed and compared.Numerical ex-amples show the effectiveness and feasibility of the algorithm.Secondly,the convergence of the algorithm is simply analyzed and verified from time and space respectively,and the result is O(?~p+h~?)(p depends on the choice of algorithm format,For example,the olag for-mula is of order 1,?is related to the spatial dimension).The chart also provides relevant data support.Finally,the algorithm is applied to the electromagnetic field equation to simulate the eddy current problem,and the eddy current distribution at different time is given.