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  • 1.
    Araujo-Cabarcas, Juan Carlos
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Campos, Carmen
    Engström, Christian
    Roman, Jose E.
    Computation of scattering resonances in absorptive and dispersive media with applications to metal-dielectric nano-structures2020Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 407, artikel-id 109220Artikel i tidskrift (Refereegranskat)
    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.
    Araujo-Cabarcas, Juan Carlos
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Engström, Christian
    On spurious solutions encountered in Helmholtz scatteringresonance computations in Rd with applications tonano-photonics and acoustics2021Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 429, artikel-id 110024Artikel i tidskrift (Refereegranskat)
    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.

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  • 3.
    Araujo-Cabarcas, Juan Carlos
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Engström, Christian
    Department of Mathematics, Linnaeus University, Sweden.
    Wadbro, Eddie
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Department of Mathematics and Computer Science, Karlstad University, Sweden.
    Shape optimization for the strong routing of light in periodic diffraction gratings2023Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 472, artikel-id 111684Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

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  • 4.
    Berggren, Martin
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Bernland, Anders
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Noreland, Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Acoustic boundary layers as boundary conditions2018Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 371, s. 633-650Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The linearized, compressible Navier-Stokes equations can be used to model acoustic wave propagation in the presence of viscous and thermal boundary layers. However, acoustic boundary layers are notorious for invoking prohibitively high resolution requirements on numerical solutions of the equations. We derive and present a strategy for how viscous and thermal boundary-layer effects can be represented as a boundary condition on the standard Helmholtz equation for the acoustic pressure. This boundary condition constitutes an O (delta) perturbation, where delta is the boundary-layer thickness, of the vanishing Neumann condition for the acoustic pressure associated with a lossless sound-hard wall. The approximate model is valid when the wavelength and the minimum radius of curvature of the wall is much larger than the boundary layer thickness. In the special case of sound propagation in a cylindrical duct, the model collapses to the classical Kirchhoff solution. We assess the model in the case of sound propagation through a compression driver, a kind of transducer that is commonly used to feed horn loudspeakers. Due to the presence of shallow chambers and thin slits in the device, it is crucial to include modeling of visco-thermal losses in the acoustic analysis. The transmitted power spectrum through the device calculated numerically using our model agrees well with computations using a hybrid model, where the full linearized, compressible Navier-Stokes equations are solved in the narrow regions of the device and the inviscid Helmholtz equations elsewhere. However, our model needs about two orders of magnitude less memory and computational time than the more complete model. 

  • 5.
    Cohen, David
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cui, Jianbo
    Hong, Jialin
    Sun, Liying
    Exponential integrators for stochastic Maxwell's equations driven by Itô noise2020Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 410, artikel-id 109382Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This article presents explicit exponential integrators for stochastic Maxwell's equations driven by both multiplicative and additive noises. By utilizing the regularity estimate of the mild solution, we first prove that the strong order of the numerical approximation is ½ for general multiplicative noise. Combining a proper decomposition with the stochastic Fubini's theorem, the strong order of the proposed scheme is shown to be 1 for additive noise. Moreover, for linear stochastic Maxwell's equation with additive noise, the proposed time integrator is shown to preserve exactly the symplectic structure, the evolution of the energy as well as the evolution of the divergence in the sense of expectation. Several numerical experiments are presented in order to verify our theoretical findings.

  • 6.
    Cohen, David
    et al.
    Department of Mathematical Sciences, NTNU.
    Owren, Brynjulf
    Department of Mathematical Sciences, NTNU.
    Raynaud, Xavier
    Department of Mathematical Sciences, NTNU.
    Multi-symplectic integration of the Camassa-Holm equation2008Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 227, nr 11, s. 5492-5512Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The Camassa-Holm equation is rich in geometric structures, it is completely integrable, bi-Hamiltonian, and it represents geodesics for a certain metric in the group of diffeomorphism. Here two new multi-symplectic formulations for the Camassa-Holm equation are presented, and the associated local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretisation of each formulation is exemplified by means of the Euler box scheme. Numerical experiments show that the schemes have good conservative properties, and one of them is designed to handle the conservative continuation of peakon-antipeakon collisions. (c) 2008 Elsevier Inc. All rights reserved.

  • 7.
    Eliasson, Bengt
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik. Theoretische Physik IV, Ruhr-Universität Bochum, Bochum, Germany.
    Outflow boundary conditions for the Fourier transformed three-dimensional Vlasov-Maxwell system2007Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 225, nr 2, s. 1508-1532Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A problem with the solution of the Vlasov equation is its tendency to become filamented/oscillatory in velocity space, which in numerical simulations can give rise to unphysical oscillations and recurrence effects. We present a three-dimensional Vlasov–Maxwell solver (three spatial and velocity dimensions, plus time), in which the Vlasov equation is Fourier transformed in velocity space and the resulting equations solved numerically. By designing absorbing outflow boundary conditions in the Fourier transformed velocity space, the highest Fourier modes in velocity space are removed from the numerical solution. This introduces a dissipative effect in velocity space and the numerical recurrence effect is strongly reduced. The well-posedness of the boundary conditions is proved analytically, while the stability of the numerical implementation is assessed by long-time numerical simulations. Well-known wave-modes in magnetized plasmas are shown to be reproduced by the numerical scheme.

  • 8.
    Johan, Helsing
    et al.
    Lund University, Centre for Mathematical Sciences, Numerical Analysis.
    Wadbro, Eddie
    Lund University, Centre for Mathematical Sciences, Numerical Analysis.
    Laplace’s equation and the Dirichlet–Neumann map: a new mode for Mikhlin’s method2005Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 202, nr 2, s. 391-410Artikel i tidskrift (Refereegranskat)
  • 9.
    Lundow, Per-Håkan
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Markström, Klas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Efficient computation of permanents, with applications to Boson sampling and random matrices2022Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 455, artikel-id 110990Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we first discuss how to compute the permanent efficiently on a parallel computer, followed by algorithms which provide an exponential speed-up for sparse matrices and linear run times for matrices of limited bandwidth. The parallel algorithm has been implemented in a freely available software package, also available in an efficient serial version. As part of the timing runs for this package we set a new world record for the matrix order on which a permanent has been computed. Next we perform a simulation study of several conjectures regarding the distribution of the permanent for random matrices. Here we focus on permanent anti-concentration conjecture, which has been used to find the classical computational complexity of Boson sampling. We find a good agreement with the basic versions of these conjectures, and based on our data we propose refined versions of some of them. For small systems we also find noticeable deviations from a proposed strengthening of a bound for the number of photons in a Boson sampling system.

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  • 10. Markidis, Stefano
    et al.
    Henri, Pierre
    Lapenta, Giovanni
    Rönnmark, Kjell
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Hamrin, Maria
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Meliani, Zakaria
    Laure, Erwin
    The fluid-kinetic particle-in-cell method for plasma simulations2014Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 271, s. 415-429Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A method that solves concurrently the multi-fluid and Maxwell's equations has been developed for plasma simulations. By calculating the stress tensor in the multi-fluid momentum equation by means of computational particles moving in a self-consistent electromagnetic field, the kinetic effects are retained while solving the multi-fluid equations. The Maxwell's and multi-fluid equations are discretized implicitly in time enabling kinetic simulations over time scales typical of the fluid simulations. The Fluid-Kinetic Particle-in-Cell method has been implemented in a three-dimensional electromagnetic code, and tested against the two-stream instability, the Weibel instability, the ion cyclotron resonance and magnetic reconnection problems. The method is a promising approach for coupling fluid and kinetic methods in a unified framework.

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