Solutions of Large-Scale Electromagnetics Problems Using an Iterative Inner-Outer Scheme With Ordinary and Approximate Multilevel Fast Multipole Algorithms

Ergül, Özgür; Malas, Tahir; Gürel, L.

doi:10.2528/pier10061711

Cited by 35 publications

(15 citation statements)

References 27 publications

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“…For these accuracy parameters and the given model of processors, the parallelization efficiency is around 85% leading to 54-fold speedup using 64 processes compared to the corresponding sequential solution [3,25]. Note that problems involving more complicated objects may require effective preconditioners, such as those based on the Schur-complement reduction for penetrable objects [5] and the two-level scheme for PEC objects [36] that are appropriate for MLFMA implementations. For more quantitative assessment of the accuracy and efficiency, Table 4 lists the number of iterations, total time (that is dominated by iterations), memory, and root-mean-square (RMS) error in computational values with respect to analytical values for the sphere problems.…”

Section: Numerical Examplesmentioning

confidence: 99%

Parallel Implementation of Mlfma for Homogeneous Objects With Various Material Properties

Ergül¹

2011

PIER

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Abstract-We present a parallel implementation of the multilevel fast multipole algorithm (MLFMA) for fast and accurate solutions of electromagnetics problems involving homogeneous objects with diverse material properties. Problems are formulated rigorously with the electric and magnetic current combined-field integral equation (JMCFIE) and solved iteratively using MLFMA parallelized with the hierarchical partitioning strategy. Accuracy and efficiency of the resulting implementation are demonstrated on canonical problems involving perfectly conducting, lossless dielectric, lossy dielectric, and double-negative spheres.

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Section: Numerical Examplesmentioning

confidence: 99%

Parallel Implementation of Mlfma for Homogeneous Objects With Various Material Properties

Ergül¹

2011

PIER

Self Cite

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“…Such heavy computation complexity and memory cost are undesirable in many applications, e.g. the reconstruction of largescale induced electric or current density in discontinuous media in computational electromagnetics [19][20][21][22][23][24] or in radar signal research domain [25,26]. Therefore, it is necessary to reduce the computation time and the memory complexity in the G-IPRM.…”

Section: Introductionmentioning

confidence: 99%

A Fast Inverse Polynomial Reconstruction Method Based on Conformal Fourier Transformation

Liu¹,

Liu²,

Zhu³

et al. 2012

PIER

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Abstract-A fast Inverse Polynomial Reconstruction Method (IPRM) is proposed to efficiently eliminate the Gibbs phenomenon in Fourier reconstruction of discontinuous functions. The framework of the fast IPRM is modified by reconstructing the function in discretized elements, then the Conformal Fourier Transform (CFT) and the Chirp Z-Transform (CZT) algorithms are applied to accelerate the evaluation of reconstruction coefficients. The memory cost of the fast IPRM is also significantly reduced, owing to the transformation matrix being discretized in the modified framework. The computation complexity and memory cost of the fast IPRM are O(M N log 2L) and O(M N ), respectively, where L is the number of the discretized elements, M is the degree of polynomials for the reconstruction of each element, and N is the number of the Fourier series. Numerical results demonstrate that the fast IPRM method not only inherits the robustness of the Generalized IPRM (G-IPRM) method, but also significantly reduces the computation time and the memory cost. Therefore, the fast IPRM method is useful for the pseudospectral time domain methods and for the volume integral equation of the discontinuous material distributions.

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“…In recent years, a significant amount of work has been devoted to design fast parallel algorithms that can reduce the O (n 2 ) computational complexity for the M-V product with boundary element equations, like the Fast Multipole Method (FMM) by V. Rokhlin [35], the H-matrix approach by W. Hackbush [25], the Adaptive Cross Approximation by M. Bebendorf [4], and other approaches. Since the pioneering work by Rokhlin and his co-authors, the Fast Multipole Algorithm continues to receive considerable attention in Electromagnetics, see e.g., [20,21,31,32,39].…”

Section: Introductionmentioning

confidence: 99%

Symmetric Inverse-Based Multilevel Ilu Preconditioning for Solving Dense Complex Non-Hermitian Systems in Electromagnetics

Carpentieri¹,

Bollhöfer²

2012

PIER

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Abstract-Boundary element discretizations of exterior Maxwell problems lead to dense complex non-Hermitian systems of linear equations that are difficult to solve from a linear algebra point of view. We show that the recently developed class of inverse-based multilevel incomplete LU factorization has very good potential to precondition these systems effectively. This family of algorithms can produce numerically stable factorizations and exploits efficiently the possible symmetry of the underlying integral formulation. The results are highlighted by calculating the radar-cross-section of a full aircraft, and by a numerical comparison against other standard preconditioners.

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Solutions of Large-Scale Electromagnetics Problems Using an Iterative Inner-Outer Scheme With Ordinary and Approximate Multilevel Fast Multipole Algorithms

Cited by 35 publications

References 27 publications

Parallel Implementation of Mlfma for Homogeneous Objects With Various Material Properties

Parallel Implementation of Mlfma for Homogeneous Objects With Various Material Properties

A Fast Inverse Polynomial Reconstruction Method Based on Conformal Fourier Transformation

Symmetric Inverse-Based Multilevel Ilu Preconditioning for Solving Dense Complex Non-Hermitian Systems in Electromagnetics

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