Iterative solution of a 3-D scattering problem from arbitrary shaped multidielectric and multiconducting bodies

Soudais, P.

doi:10.1109/8.299597

Cited by 28 publications

(23 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Other authors [1], [2], [4], [8] comment that the number of iterations required for convergence is not greatly altered by a "good" initial guess. Soudias [5] uses the solution from one monostatic angle as the initial guess for the next angle and reports a factor of a two to four reduction in solution time for many monostatic angles.…”

Section: Acceleration Via a Better Initial Guessmentioning

confidence: 99%

“…The iterative method is attempting to find a solution to (5) where is the exact solution to the discretized problem; that is, the solution which a direct approach (in the absence of rounding errors) would obtain.…”

Section: Termination Criteriamentioning

confidence: 99%

“…While they will be shown below to be faster by a large factor for a single solution, that factor would probably be eliminated if many repetitions of the solution were required. There has been some work on analyzing multiple right-hand sides without excessive cost multiples, and some approaches look promising [5], [6]. It is not an issue we address here.…”

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

The complex bi-conjugate gradient solver applied to large electromagnetic scattering problems, computational costs, and cost scalings

Pocock

Walker

1997

IEEE Trans. Antennas Propagat.

View full text Add to dashboard Cite

The complex biconjugate gradient iterative method is applied to an isoparametric boundary integral equation formulation for frequency-domain electromagnetic scattering problems. It is demonstrated to work well on large and geometrically complex examples, including a 20 wavelength slender dipole, the NASA almond, and a resonant cavity. On such problems, with asymmetric curvilinear irregular meshes and nontrivial geometries, the number of iterations required seems to increase rather more than linearly with body size, indicating an overall sixth power cost scaling. This scaling is essentially as for direct methods, but with costs still a small fraction of the direct approach. A method is proposed for the selection of a termination condition designed to avoid seeking the approximate answer too precisely; it typically permits a further halving of costs.

show abstract

Section: Acceleration Via a Better Initial Guessmentioning

confidence: 99%

Section: Termination Criteriamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

The complex bi-conjugate gradient solver applied to large electromagnetic scattering problems, computational costs, and cost scalings

Pocock

Walker

1997

IEEE Trans. Antennas Propagat.

View full text Add to dashboard Cite

show abstract

“…Most of these advanced preconditioners, however, rely on basic iterative methods, such as the Generalized Minimal RESidual method [7] (GMRES) or the Preconditioned Conjugate Gradient [8] (PCG). Still, numerous new or modified iterative methods have been developed to: pipeline reductions [9], [10], avoid synchronizations [11], [12], decrease the number of iterations by means of multiple search directions [13], [14] or Krylov subspace recycling [15], [16]. Iterative methods tailored to tackle efficiently problems with multiple right-hand sides have also blossomed [17]- [19].…”

Section: Introductionmentioning

confidence: 99%

Block Iterative Methods and Recycling for Improved Scalability of Linear Solvers

Jolivet¹,

Tournier

2016

SC16: International Conference for High Performance Computing, Networking, Storage and Analysis

View full text Add to dashboard Cite

“…The new set of linear systems (19) is then solved using a block variant of the flexible inner-outer scheme described above. The outer block solver is a block-GCR [26] and the inner solver a block-GMRES [19]. Most of the linear algebra kernels involved in the algorithms of this section (sum of vectors, dot products calculation) are straightforward to implement in a parallel distributed memory environment.…”

mentioning

confidence: 99%

On the Parallel Solution of Large Industrial Wave Propagation Problems

Giraud

Langou

Sylvand³

2006

J. Comp. Acous.

View full text Add to dashboard Cite

The use of Fast Multipole Methods (FMM) combined with embedded Krylov solvers preconditioned by a sparse approximate inverse is investigated for the solution of large linear systems arising in industrial acoustic and electromagnetic simulations. We use a boundary elements integral equation method to solve the Helmholtz and the Maxwell equations in the frequency domain. The resulting linear systems are solved by iterative solvers using FMM to accelerate the matrix-vector products. The simulation code is developed in a distributed memory environment using message passing and it has out-of-core capabilities to handle very large calculations. When the calculation involves one incident wave, one linear system has to be solved. In this situation, embedded solvers can be combined with approximate inverse preconditioner to design extremely robust algorithms. For radar cross section calculations, several linear systems have to be solved. They involve the same coefficient matrix but different right-hand sides. In this case, we propose a block variant of the single right-hand side scheme. The efficiency, robustness and parallel scalability of our approach are illustrated on a set of large academic and industrial test problems.

show abstract

Iterative solution of a 3-D scattering problem from arbitrary shaped multidielectric and multiconducting bodies

Cited by 28 publications

References 14 publications

The complex bi-conjugate gradient solver applied to large electromagnetic scattering problems, computational costs, and cost scalings

The complex bi-conjugate gradient solver applied to large electromagnetic scattering problems, computational costs, and cost scalings

Block Iterative Methods and Recycling for Improved Scalability of Linear Solvers

On the Parallel Solution of Large Industrial Wave Propagation Problems

Contact Info

Product

Resources

About