Integral Equation Based On Domain Decomposition Algorithm For Engineering Applications

With the development of science and technology,modern scientific research has formed a basic model of scientific experiments,theoretical analysis,and scientific high-performance computing.With the advent of computers,scientific computing has gradually become one of the important technological advances of the 20 th century.Especially with the advent of more and more high-performance scientific computers,scientific computing has promoted numerous major scientific discoveries.Nowadays,scientific computing ability is an important symbol reflecting the core competitiveness of national science and technology and one of the key elements of national science and technology innovation development.Electromagnetic modeling and calculation for complex targets has always been a research hotspot.However,many numerical algorithms for multi-scale electromagnetic targets combined with fine structures and smooth structures have been difficult to obtain satisfactory results.The proposed method of domain decomposition of integral equations solves this problem to a large extent.Therefore,this paper will do further research on the basis of the decomposition method of the integral equation to improve the performance of the algorithm.The integral equation domain decomposition method is better oriented to engineering applications.First,we briefly introduce some basic electromagnetic theories that will be used in this topic.The internal and external equivalent source principle is introduced by the boundary value problem of the ideal conductor.Then the electromagnetic field boundary condition and integral equation operator are introduced.Then,the moment method which is of great significance in the field of computational electromagnetics is introduced,and the solution process is explained.The selection of functions and weight functions introduces direct and iterative algorithms for solving matrix equations.Then the process of establishing the electromagnetic field integral equation is studied,and the research target is further decomposed into two sub-regions with interface and the electromagnetic field integral equation under the domain decomposition framework is re-established for the sub-target.The polar method,the process of moment vector multiplication in the process of accelerating matrix solution,and then the fast far field approximation method based on multi-layer fast multipole in the domain decompositionframework of integral equation is studied in detail.Firstly,the scalar Green's function is studied infinitely.The vector addition theorem in free space,and then deduced in detail the multi-layer fast multipole expression of the fast far-field approximation,which makes it possible to simplify the calculation of the transfer amount,and then quantify the far-field conditions,making it suitable for fast far-field The approximate group is clearly defined to ensure the accuracy of the calculation.Based on this,the fast far-field approximation multi-layer fast multipole method is applied to the domain decomposition framework to further improve the computational power of the domain decomposition method.Finally,the application of traditional Galerkin method in solving integral equations is introduced.Then,based on this,the discontinuous Galerkin method based on integral equation is further studied.