| 1. |
- Anderson, Rachele, et al.
(author)
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Inference for time-varying signals using locally stationary processes
- 2019
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In: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427. ; 347, s. 24-35
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Journal article (peer-reviewed)abstract
- Locally Stationary Processes (LSPs) in Silverman’s sense, defined by the modulation in time of a stationary covariance function, are valuable in stochastic modelling of time-varying signals. However, for practical applications, methods to conduct reliable parameter inference from measured data are required. In this paper, we address the lack of suitable methods for estimating the parameters of the LSP model, by proposing a novel inference method. The proposed method is based on the separation of the two factors defining the LSP covariance function, in order to take advantage of their individual structure and divide the inference problem into two simpler sub-problems. The method’s performance is tested in a simulation study and compared with traditional sample covariance based estimation. An illustrative example of parameter estimation from EEG data, measured during a memory encoding task, is provided.
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| 2. |
- Araujo-Cabarcas, Juan Carlos, et al.
(author)
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Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map
- 2018
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In: Journal of Computational and Applied Mathematics. - Amsterdam : Elsevier. - 0377-0427 .- 1879-1778. ; 330, s. 177-192
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Journal article (peer-reviewed)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. |
- Arjmand, Doghonay, et al.
(author)
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Temporal upscaling in micromagnetism via heterogeneous multiscale methods
- 2019
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In: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427 .- 1879-1778. ; 345, s. 99-113
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Journal article (peer-reviewed)abstract
- We consider a multiscale strategy addressing the disparate scales in the Landau–Lifschitz equations in micromagnetism. At the microscopic scale, the dynamics of magnetic moments are driven by a high frequency field. On the macroscopic scale we are interested in simulating the dynamics of the magnetisation without fully resolving the microscopic scales.The method follows the framework of heterogeneous multiscale methods and it has two main ingredients: a micro- and a macroscale model. The microscopic model is assumed to be known exactly whereas the macromodel is incomplete as it lacks effective quantities. The two models use different temporal and spatial scales and effective parameter values for the macromodel are computed on the fly, allowing for improved efficiency over traditional one-scale schemes.For the analysis, we consider a single spin under a high frequency field and show that effective quantities can be obtained accurately with step-sizes much larger than the size of the microscopic scales required to resolve the microscopic features. Numerical results both for a single magnetic particle as well as a chain of interacting magnetic particles are given to validate the theory.
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| 4. |
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| 5. |
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| 6. |
- Baeumer, B., et al.
(author)
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Boundary conditions for fractional diffusion
- 2018
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In: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427. ; 336, s. 408-424
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Journal article (peer-reviewed)abstract
- This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady state solutions. Absorbing and reflecting boundary conditions are considered, and illustrated through several examples. Reflecting boundary conditions involve fractional derivatives. The Caputo fractional derivative is shown to be unsuitable for modeling fractional diffusion, since the resulting boundary value problem is not positivitypreserving.
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| 7. |
- Baeumer, Boris, et al.
(author)
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Reprint of: Boundary conditions for fractional diffusion
- 2018
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In: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427. ; 339, s. 414-430
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Journal article (peer-reviewed)abstract
- This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady state solutions. Absorbing and reflecting boundary conditions are considered, and illustrated through several examples. Reflecting boundary conditions involve fractional derivatives. The Caputo fractional derivative is shown to be unsuitable for modeling fractional diffusion, since the resulting boundary value problem is not positivity preserving.
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| 8. |
- Beilina, Larisa, 1970, et al.
(author)
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Globally convergent and adaptive finite element methods in imaging of buried objects from experimental backscattering radar measurements
- 2015
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In: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427. ; 289, s. 371-391
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Journal article (peer-reviewed)abstract
- We consider a two-stage numerical procedure for imaging of objects buried in dry sand using time-dependent backscattering experimental radar measurements. These measurements are generated by a single point source of electric pulses and are collected using a microwave scattering facility which was built at the University of North Carolina at Charlotte. Our imaging problem is formulated as the inverse problem of the reconstruction of the spatially distributed dielectric constant, which is an unknown coefficient in Maxwell’s equations.
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| 9. |
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| 10. |
- Gaudreau, Philippe, et al.
(author)
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Improvements to the cluster Newton method for underdetermined inverse problems
- 2015
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In: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427 .- 1879-1778. ; 283, s. 122-141
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Journal article (peer-reviewed)abstract
- The Cluster Newton method (CN method) has proved to be very efficient at finding multiple solutions to underdetermined inverse problems. In the case of pharmacokinetics, underdetermined inverse problems are often given extra constraints to restrain the variety of solutions. In this paper, we propose a new algorithm based on the two parameters of the Beta distribution for finding a family of solutions which best fit the extra constraints. This allows for a much greater control on the variety of solutions that can be obtained with the CN method. In addition, this algorithm facilitates the task of obtaining pharmacologically feasible parameters. Moreover, we also make some improvements to the original CN method including an adaptive margin of error for the perturbation of the target values and the use of an analytical Jacobian in the resolution of the forward problem.
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