Abstract-The programmable graphics processing unit (GPU) is employed to accelerate the unconditionally stable Crank-Nicolson finite-difference time-domain (CN-FDTD) method for the analysis of microwave circuits. In order to efficiently solve the linear system from the CN-FDTD method at each time step, both the sparse matrix vector product (SMVP) and the arithmetic operations on vectors in the bi-conjugate gradient stabilized (Bi-CGSTAB) algorithm are performed with multiple processors of the GPU. Therefore, the GPU based BI-CGSTAB algorithm can significantly speed up the CN-FDTD simulation due to parallel computing capability of modern GPUs. Numerical results demonstrate that this method is very effective and a speedup factor of 10 can be achieved.

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Abstract-A new set of higher order hierarchical basis functions based on curvilinear triangular patch is proposed for expansion of the current in electrical field integral equations (EFIE) solved by method of moments (MoM). The multilevel fast multipole method (MLFMM) is used to accelerate matrix-vector product. An improved sparse approximate inverse (SAI) preconditioner in the higher order hierarchical MLFMM context is constructed based on the nearfield matrix of the EFIE. The quality of the SAI preconditioner can be greatly improved by use of information from higher order hierarchical MLFMM implementation. Numerical experiments with a few electromagnetic scattering problems for open structures are given to show the validity and efficiency of the proposed SAI preconditioner.

Abstract-The efficient algorithm is presented for the analysis of electromagnetic scattering from composite structures with coexisting open and closed conductors.A hybrid combined-field integral equation-the improved electric-field integral equation (CFIE-IEFIE) formulation with the incomplete LU factorization (ILU) preconditioner is proposed.Numerical results are given to demonstrate that the efficiency of our algorithm can be significantly improved when compared with the conventional EFIE formulation and the hybrid CFIE-EFIE formulation.