An Efficient Twofold Iterative Algorithm of Fe-Bi-Mlfma Using Multilevel Inverse-Based Ilu Preconditioning

Abstract

Abstract-It is known that the conventional algorithm (CA) of hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) usually suffers the problem of slow convergence, and the decomposition algorithm (DA) is limited by large memory requirement. An efficient twofold iterative algorithm (TIA) of FE-BI-MLFMA is presented using the multilevel inverse-based incomplete LU (MIB-ILU) preconditioning in this paper. It is shown that this TIA can offer a good balance of efficiency between CPU time and memory requirement. The tree-cotree splitting technique is then employed in the TIA to further improve its efficiency and robustness. A variety of numerical experiments are performed in this paper, demonstrating that the TIA exhibits superior efficiency in memory and CPU time to DA and CA, and greatly improves the computing capability of FE-BI-MLFMA.

Parallel Implementation of Mlfma for Homogeneous Objects With Various Material Properties

“…N . On the other hand, if the object is a perfect electric conductor (PEC), an N × N matrix equation withZ (11) …”

“…. , L, there are N l subdomains and S l field samples with N l S l = O(N ) to compute the interactions in accordance with the factorization in (11). Let the tree structure be parallelized into P processes.…”

“…Accurate discretizations of these objects lead to large matrix equations, even when they are formulated with the surface integral equations. The resulting large-scale problems can be solved iteratively, where the required matrix-vector multiplications are performed efficiently with various acceleration methods, such as the fast Fourier transform (FFT) [6,7], the adaptive integral method [8], and especially the multilevel fast multipole algorithm (MLFMA) [9][10][11][12][13], which has been successfully used to solve many challenging problems in various application areas [1][2][3][4][5]14].…”

Parallel Mom Solution of Jmcfie for Scattering by 3-D Electrically Large Dielectric Objects

“…The Fast Multipole Method (FMM) [9] can reduce the memory requirement and computational complexity to O N 1.5 . The memory requirement and computational complexity can be further reduced to O (N 1ogN ) using the multilevel fast multipole algorithm (MLFMA) [10,11]. Contrary to these fast numerical algorithms, the parallel MOM based on MPI of PC clusters is investigated to solve electromagnetic scattering from 3-D electrically large dielectric objects in this paper.…”

On Openmp Parallelization of the Multilevel Fast Multipole Algorithm

“…Combining integral equation based methods [1][2][3][4][5][6][7][8][9][10] with parallel techniques becomes a new trend in computational electromagnetic (CEM) community because associated applications are always computational resources (including both CPU time and memory) demanding. A series of successes have actually been reached in this area [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”