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  • 1.
    Araujo, Juan
    et al.
    Umeå University, Sweden.
    Campos, Carmen
    Universitat Politècnica de València, Spain.
    Engström, Christian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Roman, Jose
    Universitat Politècnica de València, Spain.
    Computation of scattering resonances in absorptive and dispersive media with applications to metal-dielectric nano-structures2020In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 407, p. 1-24, article id 109220Article in journal (Refereed)
    Abstract [en]

    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.

  • 2.
    Araújo C., Juan C.
    et al.
    Umeå University, Sweden.
    Engström, Christian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Wadbro, Eddie
    Umeå University, Sweden;Karlstad University, Sweden.
    Shape optimization for the strong routing of light in periodic diffraction gratings2023In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 472, article id 111684Article in journal (Refereed)
    Abstract [en]

    In the quest for the development of faster and more reliable technologies, the abilityto control the propagation, confinement, and emission of light has become crucial. Thedesign of guide mode resonators and perfect absorbers has proven to be of fundamentalimportance. In this project, we consider the shape optimization of a periodic dielectricslab aiming at efficient directional routing of light to reproduce similar features of a guidemode resonator. For this, the design objective is to maximize the routing efficiency of anincoming 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 mediummodels the wave propagation, and an accurate Robin-to-Robin map models an exteriordomain. We propose an optimal design strategy that consists of representing the dielectricinterface 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 bilinearTransfinite Interpolation formula. This setting admits explicit differentiation with respectto the design variables, from where an exact discrete adjoint method computes thesensitivities. We show in detail how the sensitivities are obtained in the quasi-periodicdiscrete setting. The design strategy employs gradient-based numerical optimization, whichconsists of a BFGS quasi-Newton method with backtracking line search. As a test caseexample, 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. Inall cases, we efficiently reach designs featuring high routing efficiencies that satisfy therequired criteria.

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  • 3.
    Araújo C, Juan Carlos
    et al.
    Umeå University, Sweden.
    Engström, Christian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    On spurious solutions encountered in Helmholtz scattering resonance computations in Rd with applications to nano-photonics and acoustics2021In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 429, p. 1-20, article id 110024Article in journal (Refereed)
    Abstract [en]

    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.

  • 4.
    Eriksson, Sofia
    et al.
    Uppsala University.
    Abbas, Qaisar
    Uppsala University.
    Nordström, Jan
    Linköping University.
    A stable and conservative method for locally adapting the design order of finite difference schemes2011In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, no 11, p. 4216-4231Article in journal (Refereed)
    Abstract [en]

    A procedure to locally change the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be accurate and stable.

    Numerical experiments verify the theoretical accuracy for smooth solutions. In addition, shock calculations are performed, using a scheme where the developed switching procedure is combined with the MUSCL technique.

  • 5.
    Eriksson, Sofia
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Nordström, Jan
    Linköping University, Sweden.
    Finite difference schemes with transferable interfaces for parabolic problems2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 375, p. 935-949Article in journal (Refereed)
    Abstract [en]

    We derive a method to locally change the order of accuracy of finite difference schemes that approximate the second derivative. The derivation is based on summation-by-parts operators, which are connected at interfaces using penalty terms. At such interfaces, the numerical solution has a double representation, with one representation in each domain. We merge this double representation into a single one, yielding a new scheme with unique solution values in all grid points. The resulting scheme is proven to be stable, accurate and dual consistent. (C) 2018 Elsevier Inc. All rights reserved.

  • 6.
    Nordström, Jan
    et al.
    Linköping University.
    Eriksson, Sofia
    Uppsala University.
    Eliasson, Peter
    The Swedish Defense Research Agency.
    Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations2012In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, no 14, p. 4867-4884Article in journal (Refereed)
    Abstract [en]

    We study the influence of different implementations of no-slip solid wall boundary conditions on the convergence to steady-state of the Navier–Stokes equations. The various approaches are investigated using the energy method and an eigenvalue analysis. It is shown that the weak implementation is superior and enhances the convergence to steady-state for coarse meshes. It is also demonstrated that all the stable approaches produce the same convergence rate as the mesh size goes to zero. The numerical results obtained by using a fully nonlinear finite volume solver support the theoretical findings from the linear analysis.

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