| 61. |
- Daneva (Mitradjieva), Maria, et al.
(författare)
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A Comparison of Feasible Direction Methods for the Stochastic Transportation Problem
- 2010
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Ingår i: Computational optimization and applications. - : Springer Science and Business Media LLC. - 0926-6003 .- 1573-2894. ; 46:3, s. 451-466
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Tidskriftsartikel (refereegranskat)abstract
- The feasible direction method of Frank and Wolfe has been claimed to be efficient for solving the stochastic transportation problem. While this is true for very moderate accuracy requirements, substantially more efficient algorithms are otherwise diagonalized Newton and conjugate Frank–Wolfe algorithms, which we describe and evaluate. Like the Frank–Wolfe algorithm, these two algorithms take advantage of the structure of the stochastic transportation problem. We also introduce a Frank–Wolfe type algorithm with multi-dimensional search; this search procedure exploits the Cartesian product structure of the problem. Numerical results for two classic test problem sets are given. The three new methods that are considered are shown to be superior to the Frank–Wolfe method, and also to an earlier suggested heuristic acceleration of the Frank–Wolfe method.
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| 62. |
- Engblom, Stefan
(författare)
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PARALLEL IN TIME SIMULATION OF MULTISCALE STOCHASTIC CHEMICAL KINETICS
- 2009
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Ingår i: Multiscale Modeling & simulation. - : Society for Industrial & Applied Mathematics (SIAM). - 1540-3459 .- 1540-3467. ; 8:1, s. 46-68
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Tidskriftsartikel (refereegranskat)abstract
- A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate equation. A stochastic simulation algorithm is used to obtain an exact realization of the process at the mesoscopic scale (in parallel). The underlying stochastic description is a jump process driven by the Poisson measure. A convergence result in this arguably difficult setting is established, suggesting that a homogenization of the solution is advantageous. We devise a simple but highly general such technique. Three numerical experiments on models representative to the field of computational systems biology illustrate the method. For nonstiff problems, it is shown that the method is able to quickly converge even when stochastic effects are present. For stiff problems, we are instead able to obtain fast convergence to a homogenized solution. Overall, the method builds an attractive bridge between, on the one hand, macroscopic deterministic scales and, on the other hand, mesoscopic stochastic ones. This construction is clearly possible to apply also to stochastic models within other fields.
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| 63. |
- Engström, Christian, et al.
(författare)
-
Complex dispersion relation calculations with the applications to absorptive photonic crystals
- 2010
-
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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| 64. |
- 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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| 65. |
- Engström, Christian
(författare)
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On spectral enclosures for Maxwell’s equations with the Drude-Lorentz model
- 2024
-
Ingår i: Applied Mathematics Letters. - : Elsevier. - 0893-9659 .- 1873-5452. ; 155
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we compare two approaches to derive spectral enclosures for Maxwell’s equations with the Drude–Lorentz model in possibly unbounded domains. The enclosures can be computed in the infinite-dimensional case as well as for the matrix-valued function obtained after a discretization. The enclosures are minimal given only the numerical ranges of the operator coefficients and we compare in the case of purely imaginary poles the derived enclosures with enclosures from the literature.
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| 66. |
- Engström, Christian
(författare)
-
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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| 67. |
- Eriksson, Henrik, et al.
(författare)
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Conjugacy of Coxeter elements
- 2009
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Ingår i: The Electronic Journal of Combinatorics. - 1097-1440 .- 1077-8926. ; 16:2
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Tidskriftsartikel (refereegranskat)abstract
- For a Coxeter group (W, S), a permutation of the set S is called a Coxeter word and the group element represented by the product is called a Coxeter element. Moving the first letter to the end of the word is called a rotation and two Coxeter elements are rotation equivalent if their words can be transformed into each other through a sequence of rotations and legal commutations. We prove that Coxeter elements are conjugate if and only if they are rotation equivalent. This was known for some special cases but not for Coxeter groups in general.
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| 68. |
- Eriksson, J, et al.
(författare)
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Regularization methods for uniformly rank-deficient nonlinear least-squares problems
- 2005
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Ingår i: Journal of Optimization Theory and Applications. - : Springer Science and Business Media LLC. - 0022-3239 .- 1573-2878. ; 127:1, s. 1-26
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Tidskriftsartikel (refereegranskat)abstract
- In solving the nonlinear least-squares problem of minimizing ||f(x)||22, difficulties arise with standard approaches, such as the Levenberg-Marquardt approach, when the Jacobian of f is rank-deficient or very ill-conditioned at the solution. To handle this difficulty, we study a special class of least-squares problems that are uniformly rank-deficient, i.e., the Jacobian of f has the same deficient rank in the neighborhood of a solution. For such problems, the solution is not locally unique. We present two solution tecniques: (i) finding a minimum-norm solution to the basic problem, (ii) using a Tikhonov regularization. Optimality conditions and algorithms are given for both of these strategies. Asymptotical convergence properties of the algorithms are derived and confirmed by numerical experiments. Extensions of the presented ideas make it possible to solve more general nonlinear least-squares problems in which the Jacobian of f at the solution is rank-deficient or ill-conditioned.
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| 69. |
- 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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| 70. |
- Erlander, Sven, 1934-
(författare)
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Cost-Minimizing Choice Behavior in Transportation Planning : A Theoretical Framework fo Logit Models
- 2010
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- This book stems from a desire to understand the underlying assumptions and structureof the choice probability models most often used in transportation planning. The bookinvestigates how far a new way of defining cost minimizing behavior can take us. Allcommonly used choice probability distributions of the logit type – log linear probabilityfunctions – follow from cost minimizing behavior defined in the new way; some newnested models also appear. The new approach provides a deeper understanding of whatis at work in the models. The new way of defining cost minimizing behavior is as follows:cost minimizing behavior pertains if the likelihood (probability) of any independentsample of observations is a decreasing function of the average cost of the sample.Extreme value distributed random variables are not used in the derivation of models. Ameasure of freedom of choice related to the Shannon measure of how much "choice" isinvolved is used to obtain a welfare measure which is equal to composite cost.... more on http://springer.com/978-3-642-11910-1
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