On spurious solutions in finite element approximations of resonances in open systems

Araujo-Cabarcas, Juan Carlos; Engström, Christian

doi:10.1016/j.camwa.2017.07.020

Cited by 10 publications

(3 citation statements)

References 44 publications

(60 reference statements)

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“…core modes in Figure 6.) Another issue, well-recognized by many [1,11,16,21] in other resonance computations, is the interference of spurious modes that arise from the discretization of the essential spectrum (and Figure 3 in this paper also provides a glimpse of this issue). In Section 4, we indicate a way to overcome this problem to some extent by using an elliptical contour in our eigensolver.…”

Section: Introductionmentioning

confidence: 86%

“…Although their essential idea is the same as the early works on PML [3,4,5], their work is better appreciated in the following context. While adapting the PML for source problems to eigenproblems, many [1,11,16] preferred a frequency-independent PML over a frequency-dependent PML. This is because for eigenproblems obtained using PML, the "frequency" is related to the unknown eigenvalue, so a frequency-dependent approach results in equations with a nonlinear dependence on the unknown eigenvalue, and hence a nonlinear eigenproblem.…”

Section: Introductionmentioning

confidence: 99%

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Computing leaky modes of optical fibers using a FEAST algorithm for polynomial eigenproblems

Gopalakrishnan¹,

Parker²,

Vandenberge³

2021

Preprint

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An efficient technique to solve polynomial eigenproblems is shown to result in an accurate method for computing leaky modes of optical fibers. The nonlinear eigenproblem arises from a frequency-dependent perfectly matched layer and is solved using a contour integral eigensolver. Extensive computations on an antiresonant fiber with a complex transverse microstructure are reported. Even when employing up to one million degrees of freedom, the fiber model appears to remain in a preasymptotic regime where computed confinement loss values are likely to be off by orders of magnitude. This and other difficulties in computing mode losses, together with some techniques to overcome them, are detailed.

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Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Computing leaky modes of optical fibers using a FEAST algorithm for polynomial eigenproblems

Gopalakrishnan¹,

Parker²,

Vandenberge³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…En una de ellas se pretende utilizar dicho método en la resolución del problema que en [19] se aborda planteando y resolviendo un PEP. En la otra, se colabora con los autores de [5] para la resolución de un problema similar utilizando también dicho solver.…”

Section: Publicacionesunclassified

Implementación paralela de métodos iterativos para la resolución de problemas polinómicos de valores propios

González¹,

Carmén²

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Quiero expresar mi más profundo agradecimiento a José Román, por su excelente trabajo como director y por su dedicación y valiosa aportación a esta tesis. Su gran entrega como investigador ha sido para mí un ejemplo y un estímulo constantes. En segundo lugar, me gustaría mencionar al profesor Daniel Kressner ya que algunos de sus trabajos han sido fuente de inspiración en mayor o menor medida de ideas que considero relevantes para esta tesis. También quiero manifestar mi agradecimiento a Andrés Tomás y Eloy Romero por sus contribuciones a SLEPc, algunas de las cuales han servido de referencia para los desarrollos software realizados en esta tesis. Mi reconocimiento al Ministerio de Educación Cultura y Deporte por la beca otorgada para la realización de esta tesis, y a la Red Española de Supercomputación por los recursos computacionales proporcionados para este trabajo. En elámbito personal, me gustaría agradecer, de nuevo a José Román, el permitirme entrar a formar parte del proyecto SLEPc; a mi compañero de equipo Alejandro Lamas, sus constantes muestras deánimo y su sentido del humor; a los compañeros de Departamento, Fernando Alvarruiz y David Guerrero, la buena disposición que siempre han mostrado para escucharme y ayudarme; finalmente a mi familia, su apoyo continuado e incondicional.

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Computation of scattering resonances in absorptive and dispersive media with applications to metal-dielectric nano-structures

Araújo

Campos

Engström

et al. 2020

Journal of Computational Physics

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In this paper we consider scattering resonance computations in optics when the resonators consist of frequency dependent and lossy materials, such as metals at optical frequencies. The proposed computational approach combines a novel hp-FEM strategy, based on dispersion analysis for complex frequencies, with a fast implementation of the nonlinear eigenvalue solver NLEIGS. Numerical computations illustrate that the pre-asymptotic phase is significantly reduced compared to standard uniform h and p strategies. Moreover, the efficiency grows with the refractive index contrast, which makes the new strategy highly attractive for metal-dielectric structures. The hp-refinement strategy together with the efficient parallel code result in highly accurate approximations and short runtimes on multi processor platforms.

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On spurious solutions in finite element approximations of resonances in open systems

Cited by 10 publications

References 44 publications

Computing leaky modes of optical fibers using a FEAST algorithm for polynomial eigenproblems

Computing leaky modes of optical fibers using a FEAST algorithm for polynomial eigenproblems

Implementación paralela de métodos iterativos para la resolución de problemas polinómicos de valores propios

Computation of scattering resonances in absorptive and dispersive media with applications to metal-dielectric nano-structures

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