2006
DOI: 10.1002/mop.21760
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The application of iterative solvers in discrete dipole approximation method for computing electromagnetic scattering

Abstract: narrowband high-reflectivity Bragg gratings in a novel multimode fiber. Opt Commun 233 (2003), 91-95. 6. J. Lim, Q. Yang, B.E. Jones, and P.R. Jackson, Strain and temperature sensors using multimode optical fiber Bragg gratings and correlation signal processing. ABSTRACT: Several Krylov subspace iterative algorithms are compared as the solvers for the discrete dipole approximation method to analyze the electromagnetic scattering problem. Fast Fourier transform technique is exploited to accelerate the computati… Show more

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Cited by 19 publications
(22 citation statements)
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“…4. Figure 6 shows the convergence histories of GMRES-, BCGSTAB-, TFQMR-, and DRGMRES-NUFFT methods, we refer the readers to [12,15,[29][30][31][32] for the details of the GMRES, BCGSTAB, TFQMR iterative methods. In this case, the dimension of the subspace for both GMRES and DRGMRES is set to be 30, and 8 approximate eigenvectors are used in DRGMRES [27] to improve convergence.…”
Section: Numerical Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…4. Figure 6 shows the convergence histories of GMRES-, BCGSTAB-, TFQMR-, and DRGMRES-NUFFT methods, we refer the readers to [12,15,[29][30][31][32] for the details of the GMRES, BCGSTAB, TFQMR iterative methods. In this case, the dimension of the subspace for both GMRES and DRGMRES is set to be 30, and 8 approximate eigenvectors are used in DRGMRES [27] to improve convergence.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…The MoM requires O(N 2 ) computer memory and O(N 3 ) computation time because of the need to store and invert the MoM matrix [3], where N is the number of unknowns in the problem. An important improvement over the MoM is conjugate gradient -fast Fourier transform method (CG-FFT) [4][5][6][7][8][9][10][11][12][13][14]. It uses conjugate gradient algorithm (CG), one of the Krylov subspace iterative approaches [15], to solve the integral equation, and the required matrix-vector product during the iteration is efficiently evaluated by using the fast Fourier transform (FFT) scheme.…”
Section: Introductionmentioning
confidence: 99%
“…Although a variety of different iterative solvers have been employed by Draine and Flatau (1994), Lumme and Rahola (1994), Flatau (1997), Nebeker, Starr, andHirleman (1998), Rahola (1998), Fan et al (2006, Penttila et al (2007), and , to date no definitive "best" algorithm has been identified. To permit further investigation and to maximize the flexibility and usefulness of the end product, OpenDDA includes: Conjugate Gradients (CG; Hestenes and Stiefel 1952;Shewchuk 1994), Conjugate Gradients Squared (CGS; Sonneveld 1989;Barrett et al 1994), BiConjugate Gradients (BiCG;Fletcher 1975;Barrett et al 1994), BiCG for symmetric systems (BiCG sym ; Freund 1992), Stabilized version of the BiCG (BiCGSTAB; van der Vorst 1992), Restarted, stabilized version of the BiCG (RBiCGSTAB; Sleijpen and Fokkema 1993), Quasiminimal residual with coupled two-term recurrences (QMR; Nachtigal 1991, 1992;Bücker and Sauren 1996), QMR for symmetric systems (QMR sym ; Freund 1992), Transpose-free QMR (TFQMR; Freund 1993) and a variant of BiCGSTAB based on multiple Lanczos starting vectors (ML(n)BiCGSTAB; Yeung and Chan 1999).…”
Section: Iterative Schemesmentioning
confidence: 98%
“…Numerical experiments consistently show that the GMRES algorithm is the best choice [11], and it can be proven that the full (unrestarted) GMRES will evetually converge with any physically meaningfull scatterer and incident field [23]. Most of the practically interesting problems, however, involve…”
mentioning
confidence: 90%
“…[9,10], and boundary integral formulations [1,2,6,7,26]. Whereas the domain integral equation method is lagging behind in this respect [5,11,12,29], reporting convergence and acceleration thereof mainly for low-contrast and/or small objects. One of the difficulties in designing a suitable multiplicative preconditioner for this method is that it needs to be either sparse or have a block-Toeplitz form to be able to compete with local methods in terms of memory and speed.…”
Section: Introductionmentioning
confidence: 99%