| 1. |
- Fischer, Paul, et al.
(författare)
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Visual time series analysis
- 2012
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Ingår i: Proceedings of COMPSTAT 2012. - 9789073592322 ; , s. 225-234
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Konferensbidrag (refereegranskat)abstract
- We introduce a platform which supplies an easy-to-handle, interactive, extendable,and fast analysis tool for time series analysis. In contrast to other software suits like Maple,Matlab, or R, which use a command-line-like interface and where the user has to memorize/look-up the appropriate commands, our application is select-and-click-driven. It allows to derive manydierent sequences of deviations for a given time series and to visualize them in dierent waysin order to judge their expressive power and to reuse the procedure found.For many transformations or model-ts, the user may choose between manual and automatedparameter selection. The user can dene new transformations and add them to the system. Theapplication contains ecient implementations of advanced and recent techniques for time seriesanalysis including techniques related to extreme value analysis and ltering theory. It has beensuccessfully applied to time series in economics, e.g. reinsurance, and to vibrational stressdata for machinery. The software is web-deployed, but runs on the user's machine, allowingto process sensitive data locally without having to send it away. The software can be accessedunder http://www.imm.dtu.dk/~paf/TSA/launch.html.
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| 2. |
- Araujo-Cabarcas, Juan Carlos, et al.
(författare)
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Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map
- 2018
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Ingår i: Journal of Computational and Applied Mathematics. - Amsterdam : Elsevier. - 0377-0427 .- 1879-1778. ; 330, s. 177-192
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 3. |
- Araujo-Cabarcas, Juan Carlos, et al.
(författare)
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On spurious solutions in finite element approximations of resonances in open systems
- 2017
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Ingår i: Computers and Mathematics with Applications. - : Elsevier. - 0898-1221 .- 1873-7668. ; 74:10, s. 2385-2402
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 4. |
- Araujo-Cabarcas, Juan Carlos, 1981-, et al.
(författare)
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Shape optimization for the strong routing of light in periodic diffraction gratings
- 2023
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Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 472
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Tidskriftsartikel (refereegranskat)abstract
- 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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| 5. |
- Asekritova, Irina, et al.
(författare)
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Diffractive Index Determination by Tikhonov Regularization on Forced String Vibration Data
- 2009
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Ingår i: Mathematical modelling of wave phenomena. - Melville, New York : American Institute of Physics. ; , s. 224-232, s. 224-232
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Konferensbidrag (refereegranskat)abstract
- Wave analysis is efficient for investigating the interior of objects. Examples are ultra sound examination of humans and radar using elastic and electromagnetic waves. A common procedure is inverse scattering where both transmitters and receivers are located outside the object or on its boundary. A variant is when both transmitters and receivers are located on the scattering object. The canonical model is a finite inhomogeneous string driven by a harmonic point force. The inverse problem for the determination of the diffractive index of the string is studied. This study is a first step to the problem for the determination of the mechanical strength of wooden logs. An inverse scattering theory is formulated incorporating two regularizing strategies. The results of simulations using this theory show that the suggested method works quite well and that the regularization methods based on the couple of spaces (L2; H1 ) could be very useful in such problems.
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| 6. |
- Engström, Christian, et al.
(författare)
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Complex dispersion relation calculations with the applications to absorptive photonic crystals
- 2010
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley-Blackwell. - 0029-5981 .- 1097-0207. ; 84, s. 849-863
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Tidskriftsartikel (refereegranskat)abstract
- A high-order discontinuous Galerkin method for calculations of complex dispersion relations of two-dimensional photonic crystals is presented. The medium is characterized by a complex-valued permittivityand we relate for this absorptive system the spectral parameter to the time frequency. We transform thenon-linear eigenvalue problem for a Lorentz material in air into a non-Hermitian linear eigenvalue problemand uses a Krylov space method to compute approximate eigenvalues. Moreover, we study the impact ofthe penalty term numerically and illustrate the high convergence rate of the method.
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| 7. |
- Engström, Christian, et al.
(författare)
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Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications
- 2016
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Ingår i: Computers and Mathematics with Applications. - : Elsevier. - 0898-1221 .- 1873-7668. ; 72:4, s. 952-973
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Tidskriftsartikel (refereegranskat)abstract
- We present a-posteriori analysis of higher order finite element approximations (hp-FEM) for quadratic Fredholm-valued operator functions. Residual estimates for approximations of the algebraic eigenspaces are derived and we reduce the analysis of the estimator to the analysis of an associated boundary value problem. For the reasons of robustness we also consider approximations of the associated invariant pairs. We show that our estimator inherits the efficiency and reliability properties of the underlying boundary value estimator. As a model problem we consider spectral problems arising in analysis of photonic crystals. In particular, we present an example where a targeted family of eigenvalues cannot be guaranteed to be semisimple. Numerical experiments with hp-FEM show the predicted convergence rates. The measured effectivities of the estimator compare favorably with the performance of the same estimator on the associated boundary value problem. We also present a benchmark estimator, based on the dual weighted residual (DWR) approach, which is more expensive to compute but whose measured effectivities are close to one.
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| 8. |
- Engström, Christian
(författare)
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Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations
- 2014
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Ingår i: Numerische Mathematik. - : Springer. - 0029-599X .- 0945-3245. ; 126:3, s. 413-440
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Tidskriftsartikel (refereegranskat)abstract
- Galerkin spectral approximation theory for non-self-adjoint quadratic operator polynomials with periodic coefficients is considered. The main applications are complex band structure calculations in metallic photonic crystals, periodic waveguides, and metamaterials. We show that the spectrum of the considered operator polynomials consists of isolated eigenvalues of finite multiplicity with a nonzero imaginary part. The spectral problem is equivalent to a non-compact block operator matrix and norm convergence is shown for a block operator matrix having the same generalized eigenvectors as the original operator. Convergence rates of finite element discretizations are considered and numerical experiments with the p -version and the h -version of the finite element method confirm the theoretical convergence rates.
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| 9. |
- Eriksson, Sofia, et al.
(författare)
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Finite difference schemes with transferable interfaces for parabolic problems
- 2018
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Ingår i: Journal of Computational Physics. - Linköping : Elsevier. - 0021-9991 .- 1090-2716. ; 375, s. 935-949
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 10. |
- Kaufmann, Thomas, et al.
(författare)
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High-order absorbing boundary conditions for the meshless radial point interpolation method in the frequency domain
- 2013
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Ingår i: International journal of numerical modelling. - : Wiley-Blackwell. - 0894-3370 .- 1099-1204. ; 26:5, s. 478-492
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Tidskriftsartikel (refereegranskat)abstract
- The meshless radial point interpolation method (RPIM) in frequency domain for electromagnetic scattering problems is presented. This method promises high accuracy in a simple collocation approach using radial basis functions. The treatment of high-order non-reflecting boundary conditions for open waveguides is discussed and implemented up to fourth-order. RPIM allows the direct calculation of high-order spatial derivatives without the introduction of auxiliary variables. High-order absorbing boundary conditions offer a choice of absorbing angles for each degree of spatial derivatives. For general applications, a set of these absorbing angles is calculated using global optimization. Numerical experiments show that at the same computational cost, the numerical reflections of the absorbing boundary conditions are much lower than conventional perfectly matched layers, especially at high angles of incidence.
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