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Araujo-Cabarcas, Juan Carlosorcid.org/0000-0002-0143-5554

Open this publication in new window or tab >>Shape optimization for the strong routing of light in periodic diffraction gratings### Araujo-Cabarcas, Juan Carlos

### Engström, Christian

### Wadbro, Eddie

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_some",{id:"formSmash:j_idt204:0:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_otherAuthors",{id:"formSmash:j_idt204:0:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 472, article id 111684Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2023
##### Keywords

Diffraction grating, Helmholtz problem, Light routing, Scattering problem, Shape optimization
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:umu:diva-200659 (URN)10.1016/j.jcp.2022.111684 (DOI)000879217600002 ()2-s2.0-85140226291 (Scopus ID)
#####

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#####

##### Funder

The Kempe Foundations, SMK-1857eSSENCE - An eScience CollaborationSwedish Research Council, 2021-04537
Available from: 2022-11-07 Created: 2022-11-07 Last updated: 2023-09-05Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Department of Computing Science.

Department of Mathematics, Linnaeus University, Sweden.

Umeå University, Faculty of Science and Technology, Department of Computing Science. Department of Mathematics and Computer Science, Karlstad University, Sweden.

In the quest for the development of faster and more reliable technologies, the ability to control the propagation, confinement, and emission of light has become crucial. The design of guide mode resonators and perfect absorbers has proven to be of fundamental importance. In this project, we consider the shape optimization of a periodic dielectric slab aiming at efficient directional routing of light to reproduce similar features of a guide mode resonator. For this, the design objective is to maximize the routing efficiency of an incoming wave. That is, the goal is to promote wave propagation along the periodic slab. A Helmholtz problem with a piecewise constant and periodic refractive index medium models the wave propagation, and an accurate Robin-to-Robin map models an exterior domain. We propose an optimal design strategy that consists of representing the dielectric interface by a finite Fourier formula and using its coefficients as the design variables. Moreover, we use a high order finite element (FE) discretization combined with a bilinear Transfinite Interpolation formula. This setting admits explicit differentiation with respect to the design variables, from where an exact discrete adjoint method computes the sensitivities. We show in detail how the sensitivities are obtained in the quasi-periodic discrete setting. The design strategy employs gradient-based numerical optimization, which consists of a BFGS quasi-Newton method with backtracking line search. As a test case example, we present results for the optimization of a so-called single port perfect absorber. We test our strategy for a variety of incoming wave angles and different polarizations. In all cases, we efficiently reach designs featuring high routing efficiencies that satisfy the required criteria.

Open this publication in new window or tab >>Space weather disturbances in non-stormy times: occurrence of dB/dt spikes during three solar cycles### Hamrin, Maria

### Schillings, Audrey

### Opgenoorth, Hermann J.

### Nesbit-Östman, Sara

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_some",{id:"formSmash:j_idt204:1:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_some",multiple:true}); ### Krämer, Eva

### Araújo, Juan Carlos

### Baddeley, Lisa

### Gunell, Herbert

### Pitkänen, Timo

### Gjerloev, Jesper

### Barnes, R. J.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_otherAuthors",{id:"formSmash:j_idt204:1:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt204_1_j_idt208_j_idt222",{id:"formSmash:j_idt204:1:j_idt208:j_idt222",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_j_idt222",onLabel:"Hide others...",offLabel:"Show others..."}); 2023 (English)In: Journal of Geophysical Research - Space Physics, ISSN 2169-9380, E-ISSN 2169-9402, Vol. 128, no 10, article id e2023JA031804Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

American Geophysical Union (AGU), 2023
##### National Category

Fusion, Plasma and Space Physics
##### Identifiers

urn:nbn:se:umu:diva-215270 (URN)10.1029/2023ja031804 (DOI)2-s2.0-85174460250 (Scopus ID)
#####

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##### Funder

Swedish National Space Board, 81/17Swedish National Space Board, 108/18Swedish National Space Board, 194/19Swedish National Space Board, 118/17Swedish Research Council, 2018-03623Swedish Research Council, 2021-06683
Available from: 2023-10-15 Created: 2023-10-15 Last updated: 2023-10-30Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Physics.

Umeå University, Faculty of Science and Technology, Department of Physics.

Umeå University, Faculty of Science and Technology, Department of Physics.

Umeå University, Faculty of Science and Technology, Department of Physics.

Umeå University, Faculty of Science and Technology, Department of Physics.

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.

Department of Arctic Geophysics, University Centre in Svalbard, Longyearbyen, Norway.

Umeå University, Faculty of Science and Technology, Department of Physics.

Umeå University, Faculty of Science and Technology, Department of Physics. Institute of Space Sciences, Shandong University, Weihai, China.

Johns Hopkins University, Laurel, MD, USA.

Johns Hopkins University, Laurel, MD, USA.

Spatio-temporal variations of ionospheric currents cause rapid magnetic field variations at ground level and Geomagnetically Induced Currents (GICs) that can be harmful for human infrastructure. The risk for large excursions in the magnetic field time derivative, “dB/dt spikes”, is known to be high during geomagnetic storms and substorms. However, less is known about the occurrence of spikes during non-stormy times. We use data from ground-based globally covering magnetometers (SuperMAG database) from the years 1985–2021. We investigate the spike occurrence (|dB/dt| > 100 nT/min) as a function of magnetic local time (MLT), magnetic latitude (Mlat), and the solar cycle phases during non-stormy times (−15 nT ≤ SYM-H < 0). We sort our data into substorm (AL < 200 nT) intervals (“SUB”) and less active intervals between consecutive substorms (“nonSUB”). We find that spikes commonly occur in both SUBs and nonSUBs during non-stormy times (3–23 spikes/day), covering 18–12 MLT and 65°–80° Mlat. This also implies a risk for infrastructure damage during non-stormy times, especially when several spikes occur nearby in space and time, possibly causing infrastructure weathering. We find that spikes are more common in the declining phase of the solar cycle, and that the occurrence of SUB spikes propagates from one midnight to one morning hotspot with ∼10 min in MLT for each minute in universal time (UTC). Finally, we discuss causes for the spikes in terms of spatio-temporal variations of ionospheric currents.

Open this publication in new window or tab >>On spurious solutions encountered in Helmholtz scatteringresonance computations in Rd with applications tonano-photonics and acoustics### Araujo-Cabarcas, Juan Carlos

### Engström, Christian

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_some",{id:"formSmash:j_idt204:2:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_otherAuthors",{id:"formSmash:j_idt204:2:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_otherAuthors",multiple:true}); 2021 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 429, article id 110024Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2021
##### Keywords

plasmon resonance, acoustic scattering resonances, resonance modes, nonlinear eigenvalue problems, Helmholtz problem, pseudospectrum, PML, DtN, leaky modes, resonant states, quasi-normal modes
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:umu:diva-159153 (URN)10.1016/j.jcp.2020.110024 (DOI)000618824400001 ()2-s2.0-85097236464 (Scopus ID)
#####

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##### Funder

Swedish Research Council, 621-2012-3863
##### Note

Umeå University, Faculty of Science and Technology, Department of Computing Science.

In this paper, we consider a sorting scheme for potentially spurious scattering resonant pairs in one- and two-dimensional electromagnetic problems and in three-dimensional acoustic problems. The novel sorting scheme is based on a Lippmann-Schwinger type of volume integral equation and can, therefore, be applied to structures with graded materials as well as to configurations including piece-wise constant material properties. For TM/TE polarized electromagnetic waves and for acoustic waves, we compute first approximations of scattering resonances with finite elements. Then, we apply the novel sorting scheme to the computed eigenpairs and use it to mark potentially spurious solutions in electromagnetic and acoustic scattering resonances computations at a low computational cost. Several test cases with Drude-Lorentz dielectric resonators as well as with graded material properties are considered.

Previously included in manuscript form, with title "Removal of spurious solutions encountered in Helmholtz scattering resonance computations in R^d".

Available from: 2019-05-20 Created: 2019-05-20 Last updated: 2021-09-10Bibliographically approvedOpen this publication in new window or tab >>Shape optimization for the strong directional scattering of dielectric nanorods### Araujo-Cabarcas, Juan Carlos

### Wadbro, Eddie

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_some",{id:"formSmash:j_idt204:3:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_otherAuthors",{id:"formSmash:j_idt204:3:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_otherAuthors",multiple:true}); 2021 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 122, no 15, p. 3683-3704Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

John Wiley & Sons, 2021
##### Keywords

directional scattering, Helmholtz problem, light routing, scattering problem, shape optimization
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:umu:diva-183008 (URN)10.1002/nme.6677 (DOI)000646710100001 ()2-s2.0-85104290944 (Scopus ID)
#####

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##### Funder

The Kempe Foundations, SMK-1857eSSENCE - An eScience Collaboration
Available from: 2021-05-18 Created: 2021-05-18 Last updated: 2022-01-12Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Umeå University, Faculty of Science and Technology, Department of Computing Science. Department of Mathematics and Computer Science, Karlstad University, Karlstad, Sweden.

In this project, we consider the shape optimization of a dielectric scatterer aiming at efficient directional routing of light. In the studied setting, light interacts with a penetrable scatterer with dimension comparable to the wavelength of an incoming planar wave. The design objective is to maximize the scattering efficiency inside a target angle window. For this, a Helmholtz problem with a piecewise constant refractive index medium models the wave propagation, and an accurate Dirichlet-to-Neumann map models an exterior domain. The strategy consists of using a high-order finite element (FE) discretization combined with gradient-based numerical optimization. The latter consists of a quasi-Newton (BFGS) with backtracking line search. A discrete adjoint method is used to compute the sensitivities with respect to the design variables. Particularly, for the FE representation of the curved shape, we use a bilinear transfinite interpolation formula, which admits explicit differentiation with respect to the design variables. We exploit this fact and show in detail how sensitivities are obtained in the discrete setting. We test our strategy for a variety of target angles, different wave frequencies, and refractive indexes. In all cases, we efficiently reach designs featuring high scattering efficiencies that satisfy the required criteria.

Open this publication in new window or tab >>Computation of scattering resonances in absorptive and dispersive media with applications to metal-dielectric nano-structures### Araujo-Cabarcas, Juan Carlos

### Campos, Carmen

### Engström, Christian

### Roman, Jose E.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_some",{id:"formSmash:j_idt204:4:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_otherAuthors",{id:"formSmash:j_idt204:4:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_otherAuthors",multiple:true}); 2020 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 407, article id 109220Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2020
##### Keywords

Plasmon resonance, Resonance modes, Nonlinear eigenvalue problems, Helmholtz problem, PML, Dispersion analysis, leaky modes, resonant states, quasimodes, quasi-normal modes
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:umu:diva-159151 (URN)10.1016/j.jcp.2019.109220 (DOI)000519535500017 ()2-s2.0-85078588641 (Scopus ID)
#####

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##### Note

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

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.

Originally included in thesis in manuscript form

Available from: 2019-05-20 Created: 2019-05-20 Last updated: 2023-03-24Bibliographically approvedOpen this publication in new window or tab >>Reliable hp finite element computations of scattering resonances in nano optics### Araujo-Cabarcas, Juan Carlos

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_some",{id:"formSmash:j_idt204:5:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_otherAuthors",{id:"formSmash:j_idt204:5:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_otherAuthors",multiple:true}); 2019 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Umeå: Umeå Universitet, 2019. p. 35
##### Series

Research report in mathematics, ISSN 1653-0810 ; 67
##### Keywords

Scattering resonances, Helmholtz problems, pseudospectrum, Lippmann-Schwinger equation, finite element methods, nonlinear eigenvalue problems, spurious solutions
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:umu:diva-159154 (URN)978-91-7855-076-0 (ISBN)
##### Public defence

2019-06-13, MA121, MIT-huset, Umeå, 13:00 (English)
##### Opponent

### Ovall, Jeffrey

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##### Supervisors

### Engström, Christian

### Cohen, David

### Larson, Mats G.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_j_idt385",{id:"formSmash:j_idt204:5:j_idt208:j_idt385",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_j_idt385",multiple:true});
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Available from: 2019-05-23 Created: 2019-05-20 Last updated: 2019-05-21Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Eigenfrequencies are commonly studied in wave propagation problems, as they are important in the analysis of closed cavities such as a microwave oven. For open systems, energy leaks into infinity and therefore scattering resonances are used instead of eigenfrequencies. An interesting application where resonances take an important place is in whispering gallery mode resonators.

The objective of the thesis is the reliable and accurate approximation of scattering resonances using high order finite element methods. The discussion focuses on the electromagnetic scattering resonances in metal-dielectric nano-structures using a Drude-Lorentz model for the description of the material properties. A scattering resonance pair satisfies a reduced wave equationand an outgoing wave condition. In this thesis, the outgoing wave condition is replaced by a Dirichlet-to-Neumann map, or a Perfectly Matched Layer. For electromagnetic waves and for acoustic waves, the reduced wave equation is discretized with finite elements. As a result, the scattering resonance problem is transformed into a nonlinear eigenvalue problem.

In addition to the correct approximation of the true resonances, a large number of numerical solutions that are unrelated to the physical problem are also computed in the solution process. A new method based on a volume integral equation is developed to remove these false solutions.

The main results of the thesis are a novel method for removing false solutions of the physical problem, efficient solutions of non-linear eigenvalue problems, and a new a-priori based refinement strategy for high order finite element methods. The overall material in the thesis translates into a reliable and accurate method to compute scattering resonances in physics and engineering.

Department of Mathematics and Statistics, Portland State University, USA.

Institutionen för matematik, Linnéuniversitetet, Sverige.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Open this publication in new window or tab >>Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map### Araujo-Cabarcas, Juan Carlos

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Engström, Christian

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Jarlebring, Elias

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_some",{id:"formSmash:j_idt204:6:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_otherAuthors",{id:"formSmash:j_idt204:6:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_otherAuthors",multiple:true}); 2018 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 330, p. 177-192Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Amsterdam: Elsevier, 2018
##### Keywords

Nonlinear eigenvalue problems, Helmholtz problem, Scattering resonances, Dirichlet-to-Neumann map, Arnoldi's method, Matrix functions
##### National Category

Computational Mathematics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-138325 (URN)10.1016/j.cam.2017.08.012 (DOI)000415783000014 ()2-s2.0-85029359070 (Scopus ID)
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Available from: 2017-08-21 Created: 2017-08-21 Last updated: 2023-03-24Bibliographically approved

Royal Institute of Technology.

We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use of a Dirichlet-to-Neumann map, which accounts for modeling unbounded domains. We consider a variational formulation and show that the spectrum consists of isolated eigenvalues of finite multiplicity that only can accumulate at infinity. The proposed method is based on a high order finite element discretization combined with a specialization of the Tensor Infinite Arnoldi method (TIAR). Using Toeplitz matrices, we show how to specialize this method to our specific structure. In particular we introduce a pole cancellation technique in order to increase the radius of convergence for computation of eigenvalues that lie close to the poles of the matrix-valued function. The solution scheme can be applied to multiple resonators with a varying refractive index that is not necessarily piecewise constant. We present two test cases to show stability, performance and numerical accuracy of the method. In particular the use of a high order finite element discretization together with TIAR results in an efficient and reliable method to compute resonances.

Open this publication in new window or tab >>On spurious solutions in finite element approximations of resonances in open systems### Araujo-Cabarcas, Juan Carlos

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Engström, Christian

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_some",{id:"formSmash:j_idt204:7:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_otherAuthors",{id:"formSmash:j_idt204:7:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_otherAuthors",multiple:true}); 2017 (English)In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 74, no 10, p. 2385-2402Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2017
##### Keywords

Scattering resonances, Lippmann–Schwinger equation, Nonlinear eigenvalue problems, Acoustic resonator, Dielectric resonator, Bragg resonator
##### National Category

Computational Mathematics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-138096 (URN)10.1016/j.camwa.2017.07.020 (DOI)000415908400013 ()2-s2.0-85026531962 (Scopus ID)
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##### Funder

Swedish Research Council, 621-2012-3863
Available from: 2017-08-09 Created: 2017-08-09 Last updated: 2023-03-23Bibliographically approved

In this paper, we discuss problems arising when computing resonances with a finite element method. In the pre-asymptotic regime, we detect for the one dimensional case, spurious solutions in finite element computations of resonances when the computational domain is truncated with a perfectly matched layer (PML) as well as with a Dirichlet-to-Neumann map (DtN). The new test is based on the Lippmann–Schwinger equation and we use computations of the pseudospectrum to show that this is a suitable choice. Numerical simulations indicate that the presented test can distinguish between spurious eigenvalues and true eigenvalues also in difficult cases.