Bi-parametric operator preconditioning

Escapil-Inchauspé, Paul; Jerez-Hanckes, Carlos

doi:10.1016/j.camwa.2021.10.012

Cited by 7 publications

(2 citation statements)

References 39 publications

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“…Comprehensive numerical experiments demonstrated good applicability and poly-logarithmic computational requirements of the technique. Further work includes: (i) accelerated preconditioning [34], [38], [41] of tensor equations; (ii) low-rank decomposition to the right-hand side for tensor operator equations, e.g. via pivoted Cholesky factorization [26]; and (iii) extension to heterogeneous scatterers via local multiple traces formulation [42] coupled with OSRC preconditioning [43].…”

Section: Discussionmentioning

confidence: 99%

Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Element Approximation

Escapil-Inchauspé¹,

Jerez-Hanckes²

2020

SIAM J. Sci. Comput.

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Quantifying the effects on electromagnetic waves scattered by objects of uncertain shape is key for robust design, particularly in high precision applications. Assuming small random perturbations departing from a nominal domain, the first-order sparse boundary element method (FOSB) has been proven to directly compute statistical moments with polylogarithmic complexity for a prescribed accuracy, without resorting to computationally intense Monte Carlo simulations. However, implementing the FOSB is not straightforward. To this end, we introduce an easy-to-use with open-source framework to directly apply the technique when dealing with complex objects. Exhaustive computational experiments confirm our claims and demonstrate the technique's applicability as well as provide pathways for further improvement.

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Section: Discussionmentioning

confidence: 99%

Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Element Approximation

Escapil-Inchauspé¹,

Jerez-Hanckes²

2020

SIAM J. Sci. Comput.

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“…Then, one requires suitable preconditioners or regularized BIEs to construct more efficient numerical solvers. This topic has received attention in recent years [3,9,11,12] and some attempts have been carried out to tackle elastic wave problems [4][5][6]29] by considering the composition of the weakly-and hyper-singular boundary integral operators (BIOs). Indeed, including preconditioning techniques into the presented numerical method is relevant but for the sake for brevity will be left as future work.…”

Section: Introductionmentioning

confidence: 99%

Spectral Galerkin method for solving elastic wave scattering problems with multiple open arcs

Jerez-Hanckes¹,

Pinto²,

Yin³

2022

Preprint

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We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin method for solving the associated weakly-and hyper-singular boundary integral equations (BIEs) arising from Dirichlet and Neumann boundary conditions, respectively. Discretization bases of the resulting BIEs employ weighted Chebyshev polynomials that capture the solutions' edge behavior. We show that these bases guarantee exponential convergence in the polynomial degree when assuming analyticity of sources and arcs geometries. Numerical examples demonstrate the accuracy and robustness of the proposed method with respect to number of arcs and wavenumber.

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Local Multiple Traces Formulation for electromagnetics: Stability and preconditioning for smooth geometries

Ayala¹,

Claeys²,

Escapil-Inchauspé³

et al. 2022

Journal of Computational and Applied Mathematics

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Bi-parametric operator preconditioning

Cited by 7 publications

References 39 publications

Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Element Approximation

Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Element Approximation

Spectral Galerkin method for solving elastic wave scattering problems with multiple open arcs

Local Multiple Traces Formulation for electromagnetics: Stability and preconditioning for smooth geometries

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