Research And Application Of The Parallelization Of Integral Equation Domain Decomposition

With the continuous development of science and technology,the application of electromagnetic waves is becoming more and more extensive.The analysis of the electromagnetic scattering of electrically large targets has always been a hot spot in the research of computational electromagnetics.Especially in the military field,the electromagnetic scattering analysis of electrically large and complex targets such as aircraft and aircraft carriers is the focus of future research on information warfare.The integral equation method is a powerful method to analyze the electromagnetic scattering problem,but the traditional integral equation method has the problems of slow iteration speed and iterative non-convergence.Multilevel fast multipole algorithm(MLFMA)is a fast algorithm,which can reduce the time complexity of matrix vector products to O(NlogN).The domain decomposition method can effectively solve multi-scale problems.But only through these two methods,it is still very difficult to analyze the electromagnetic scattering problem of electrically large targets.To solve this problem,this work has done the research on the parallelization of the domain decomposition method based on the parallel multilevel fast multipole algorithm.First of all,this work derives the surface integral equation based on the equivalence principle.To solve the integral equation,the method of moment has been used,and several important steps are introduced: mesh discretization,basis function selection,testing method and matrix solving method.The GMRES iterative method based on Krylov subspace is introduced,and the detailed implement of the multilevel fast multipole algorithm is elaborated.This work also briefly introduces OpenMP based on shared memory parallel environment and MPI based on distributed memory parallel environment.Then,the integral equation based on discontinuous Galerkin method is derived in detail.Firstly,the mono-polar RWG basis functions commonly used for non-conformal mesh are introduced.Then,based on the dual pairing testing principle,two kinds of interior penalty terms are established.With the application of mono-polar RWG basis function,the matrix form of integral equation based on discontinuous Galerkin method is obtained.To verify the accuracy of this method,several numerical results are presented.Finally,to analyze the electromagnetic scattering from electrically large targets,this work introduces the basic scheme of domain decomposition method.And a parallel strategy of domain decomposition method based on hybrid of MPI and OpenMP parallel MLFMA is also introduced.The coarser level uses box parallelism strategy,while the finer level uses angular spectrum parallelism strategy.Both the inner iteration and the outer iteration of the domain decomposition method accelerate by MLFMA.However,the data structure of the two iterations process is not the same,it cannot be parallelized easily.To solve this problem,this work proposes a parallel domain decomposition method.To present the capability of this parallel method,several numerical results are proposed including an aircraft with total 27 million unknowns.