Preconditioned iterative methods for solving dense linear systems from electromagnetic scattering applications

We consider preconditioned iterative solution of large dense linear systems, where the coefficient matrix is a large, dense, and complex valued matrix arising from discretizing the integral equations of electromagnetic scattering. For some scattering structures this matrix can be poorly conditioned and may be difficult to solve by using iterative methods.; Our research goal is to design and develop mathematical and computing algorithms to solve this matrix equation fast and efficiently by using only limited computer resources (CPU time and memory). Therefore, the main purpose of this study is to develop the robust and efficient preconditioners, which will be used in conjunction with Krylov subspace iterative methods, for solving a large dense linear system from electromagnetic scattering problems.; We solve the electromagnetic wave equations using several Krylov iterative methods with the incomplete lower-upper (ILU) triangular factorization with a dual dropping strategy (ILUT) preconditioner, the sparse approximate inverse (SAI) preconditioner, and the two-level (TL) preconditioner in the context of a multilevel fast multipole algorithm (MLFMA). The novelty of this work is that the preconditioners are constructed using the near part block diagonal submatrices generated from the MLFMA. That is, the sparse matrix, which is the part of the original dense matrix, is used for constructing the robust and efficient preconditioners for the dense matrix. The dense coefficient matrix is never explicitly needed in constructing any preconditioners studied this work.; Experimental results show that these types of preconditioners reduce the number of Krylov subspace iterations substantially. The preconditioned iteration scheme also maintains the computational complexity of the MLFMA, and consequently reduces the total CPU time. Under limited computer resources, the fast and accurate information of the electromagnetic materials, due to the employment of the high performance preconditioned solvers, may increase the economic competitiveness in which the CPU time and the memory storage are substantially reduced.; Hence, this dissertation research work may make significant impact on large scale scientific and engineering computations, and eventually on designing better electro-magnetic devices and products.