Accelerated Calderón preconditioning for Maxwell transmission problems

Kleanthous, Antigoni; Betcke, Timo; Hewett, David P.; Escapil-Inchauspé, Paul; Jerez-Hanckes, Carlos; Baran, Anthony J.

doi:10.1016/j.jcp.2022.111099

Cited by 9 publications

(8 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%

“…We discretize the BIEs by approximating the unknowns using div-conforming functions with discrete domain and test spaces, X dom l and X test l , respectively, being finite dimensional subpaces of X(Γ) of dimension N l . For details concerning the stable dual pairing, refer to [34,Section 3.2]. Also, we forgo the error analysis incurred by non-conforming meshes [35].…”

Section: Galerkin Methodsmentioning

confidence: 99%

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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%

Section: Galerkin Methodsmentioning

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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“…However, currently employed single-scattering properties in weather and climate models are not consistent in the sub-mm regions of the electromagnetic spectrum [1,2]. To improve on this situation, we apply BEM to compute efficiently the single-scattering properties (SSPs) of randomly oriented rosette aggregates by applying accelerated matrix solving techniques that reduce the memory costs and solution times of BEM by 99 and 75%, respectively, and this being especially so at the highest size parameters [3,4]. The SSPs of the rosette aggregates are based on models that have consistent masses and orientation-projected areas found in naturally occurring cirrus and ice cloud [5], as well as the assumed mass-dimension relation in the cirrus microphysics scheme in a weather model.…”

Section: Introductionmentioning

confidence: 99%

A new application of the boundary element method to compute the single-scattering properties of complex ice crystals in the microwave

Baran,

Kleanthous,

Betcke

et al. 2024

Radiation Processes in the Atmosphere and Ocean

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The Boundary Element Method (BEM) is being applied to compute the single-scattering properties of randomly oriented complex rosette ice aggregates at the frequencies of 50, 183, 243 and 664 GHz, for the temperatures 190, 230, and 270 K. The rosette aggregates were generated using a Monte Carlo model, and from the statistical runs, 65 aggregates were selected that were within ±30% of an existing mass-dimension relation that is consistent with the Met Office's cirrus microphysics scheme in its weather and climate models. The generated 65 aggregates have maximum dimensions between 10 μm and approximately 1 cm. To compute efficiently their single-scattering properties using BEM, random orientation is approximated by rotating the incident wave about the scatterer rather than the other way around as is done in all other electromagnetic methods. This exploits the BEM linear matrix equation (i.e. Ax=b) by only needing to compute the matrix A once, leaving the less computationally demanding b to change. We show that our representation of random orientation can accurately compute the single-scattering properties of non-axisymmetric particles to within 1 or 2% of T-matrix solutions, and we compare the solutions found for our rosette aggregate models with other commonly used models in the microwave.

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“…To better model the scattering properties of non‐spherical particles, great effort has been invested toward the development of advanced computational methods. These methods generally are composed of two categories: (a) the numerical accurate methods, such as the Invariant Embedding T‐Matrix (II‐TM) methods, the Discrete‐Dipole Approximation method (DDA), Finite‐Difference Time Domain (FDTD) method, and the boundary‐element method (Bi & Yang, 2014; Groth et al., 2015; Kleanthous et al., 2022; Mano, 2000; Mishchenko et al., 1996; Taflove & Umashankar, 1990; Yang & Liou, 1996a; Yurkin et al., 2007) and (b) the geometric‐optics methods, such as the Convectional Geometric‐Optics Method (CGOM), the Improved Geometric Optics Method (IGOM), and physical optics methods (Borovoi & Grishin, 2003; Hesse, 2008; Macke, Mueller, & Raschke, 1996; Yang & Liou, 1996b).…”

Section: Introductionmentioning

confidence: 99%

Toward Better Constrained Scattering Models for Natural Ice Crystals in the Visible Region

Waitz

Wagner

et al. 2023

JGR Atmospheres

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Accelerated Calderón preconditioning for Maxwell transmission problems

Cited by 9 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

A new application of the boundary element method to compute the single-scattering properties of complex ice crystals in the microwave

Toward Better Constrained Scattering Models for Natural Ice Crystals in the Visible Region

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