Research On Key Techniques Of Parallel Method Of Moments And Its Domain Decomposition Method

With the development of national defense technology and the demand for modern electromagnetic engineering applications,the requirements for accurate electromagnetic simulation of electrically large targets with complex structures are growing rapidly.However,accurate electromagnetic field computation faces a common problem:increasing demand for computing resources and simulation time,which brings a huge challenge for computational electromagnetics.Specifically,the continuous increase of the electrical size makes the requirement of computing resources for accurate electromagnetic simulation grows exponentially.Fortunately,the rapid development of high-performance computing technology and domestic supercomputers have brought unprecedented opportunities for computational electromagnetics to achieve"accurate,fast and efficient"simulation of complex,elaborate and electrically large targets.There is no doubt that the simulation capability of the current electromagnetic algorithm with the help of powerful supercomputers can be improved by several orders of magnitude under the premise that the accuracy is not reduced.This greatly expands the simulation scale of the electromagnetic algorithm,and accelerates the simulation speed of the electromagnetic field.Thus,the simulation time for electromagnetic related weapons and civil equipment are greatly shortened.Moreover,fully leveraging the tremendous computing power of domestic supercomputers and truly realizing the"high performance"of electromagnetic computing on domestic supercomputing platforms,still requires the in-depth research on parallel optimization and numerical algorithms.It is well known that high-performance electromagnetic computation based on domestic supercomputers is a very effective way to simulate complex and electrically large problems.But it should not be our only reliance.Thus,we must focus on the development of numerical algorithms with high precision and strong generality in the field of computational electromagnetics,while keeping up with the strategic plans of the national high-performance computer system development.Based on the above background,the purpose of this thesis is to realize accurate electromagnetic field numerical simulation of electrically large and complex targets in electromagnetic engineering applications.Firstly,the optimization is carried out at parallel level to realize the high-performance electromagnetic simulation of parallel Mo M,which guarantees the high-performance electromagnetic simulation of parallel Mo M on domestic supercomputing platforms.Secondly,a parallel domain decomposition method(DDM)based on Mo M is proposed,which divides the original problem into several independent sub-problems that are easy to be solved,and provides an effective way for the Mo M to solve electrically large and complex problems.This thesis aims to expand the scale and speed up the solution of practical engineering problems.The main achievements and innovations are as follows:(1)In order to extend the scale of the problem that Mo M can solve and accelerate in simulation,the parallel Mo M is achieved using MPI distributed memory programming technology.In order to reduce the redundant calculation and make full use of the VPU of modern computers,the MPI+Open MP hybrid programming and fully vectored parallel filling strategy are proposed,which improves the performance of the impedance matrix filling by 2?13 times.For accelerating the solution of dense matrix equations generated by Mo M,a novel LU decomposition algorithm is proposed,which guarantees the transplantation and efficient operation of parallel Mo M in domestic supercomputer.Moreover,its performance on general processor platform is better than that of MKL commercial mathematics library.(2)The maximum number of CPU cores utilized in our simulation exceeds 6×10~5 CPU cores on domestically-made and many-core supercomputer platform named“Tianhe-2”.Furthermore,the parallel scale of the proposed Mo M are more than 10,000 CPU cores on domestic E-class supercomputing prototype,named“Tianhe-3”,which lays a foundation for the realization of parallel Mo M with billions of times of computing power and makes up for the shortage of domestic supercomputing platform electromagnetic simulation software.(3)A parallel DDM based on Integral Equation(IE-DDM)is studied.This method divides the original region into several closed sub-regions which are easy to be computed.Each sub-region can be meshed independently and the current is forced to be continuous with explicit boundary conditions on virtual interface.Moreover,the coupling between regions adopts field iteration instead of storing mutual impedance,which reduces memory consumption.MPI+Open MP hybrid programming is used to realize the parallel of IE-DDM,and the convergence of IE-DDM is studied.(4)In order to eliminate the additional unknown introduced by the addition of virtual surface and further expand the scale of solving the problem by Mo M,a novel DDM based on Full Basis Function division is proposed,named FBF-DDM,which divides the original model surface into several open sub-surfaces,eliminating the virtual interface between adjacent sub-regions.The singularity of field iterative process between connected sub-regions is modified,and the convergence in outer iterative process of FBF-DDM is studied.The parallel implementation of FBF-DDM is also realized by MPI+Open MP hybrid programming.Finally,the scattering problem of complex electrically large aircraft is simulated successfully.(5)Since most targets in practical engineering problems are in half-space environments,such as ground-air and sea-air,the electromagnetic field integral equation suitable for PEC targets in free-space and half-space is constructed by using the dyadic Green's function of planar layered media,which is based on the principle of electromagnetic field equivalence.Then,the IE-DDM and FBF-DDM are extended to half-space environment and the scattering problem of ship with 100-wavelengths,which successfully calculated the problems up to 2million unknowns.In general,this thesis has conducted in-depth research on the Mo M from the perspective of parallel optimization and electromagnetic algorithm respectively,aiming to expand the application scope of the Mo M in practical engineering.