Research On Parallel Preconditioner For Multilevel Fast Multipole Method

It is always a hot and difficult problem to accurately and quickly analyze the electromagnetic characteristics(EMC)of targets in the field of computational electromagnetcs.Especially,the demands for electrically large and complex targets are getting higher with the increasing complexity of practical engineering applications.The Method of Moments(Mo M)is widely used in electromagnetic simulations for high accuracy.However,the advantages of the Mo M are spoiled by its expensive demands for memory and computing time,when solving extremely large EM problems.Thus,the scale of solving EMC problems using Mo M is limited.As a fast algorithm of Mo M,Multilevel Fast Multipole Algorithm(MLFMA)can reduce the computing complexity and memory requirement.Furthermore,MLFMA accelerates the matrix vector multiplication and computation speed.However,MLFMA may be confronted with slow convergence or even divergence issues in applications involving complex structures due to the fatc that the condition number of the generated matrix is ill.Fortunately,the precondition method can effectively improve the matrix condition number and accelerate the convergence speed of iterative solution.In view of this,this paper studies the properties of the near interaction matrix of MLFMA,and establishes the pre-conditions by inverting the near interaction matrix integrating with the multifrontal method.Numerical examples show that the proposed precondition method can accelerate the convergence speed and improve the computational efficiency,when simulating electrically large and complex models.In recent years,the fast numerical decomposition algorithm of low-rank matrix has attracted people's attention,which is gradually becoming a research hotspot.For this reason,the matrix compression algorithm is introduced into the construction of precondition in this paper.In addition,the key of the preconditions based on the multifrontal algorithmis to sovle sparse matrix equations.Generally,the sparse matrix is convenient for compression storage and solution Nevertheless,the bottleneck of huge memory demands and expensively consume time will occur with the increase of the simulation scale,in the process of establishing the preconditioned matrix.To solve this bottleneck,the low-rank matrix numerical decomposition algorithm is employed to solve the low-rank compression problem of the near interaction matrix in this paper.Through numerical examples,this method proposed not only accelerates convergence of iterative linear solvers,but also reduces the time of establishing preconditions,and thus,the solving efficiency of MLFMA is greatly improved.