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Berntsson, F., Karlsson, M., Kozlov, V. & Nazarov, S. A. (2018). A Modification to the Kirchhoff Conditions at a Bifurcation and Loss Coefficients.
Open this publication in new window or tab >>A Modification to the Kirchhoff Conditions at a Bifurcation and Loss Coefficients
2018 (English)Report (Other academic)
Abstract [en]

One dimensional models for fluid flow in tubes are frequently used tomodel complex systems, such as the arterial tree where a large numberof vessels are linked together at bifurcations. At the junctions transmission conditions are needed. One popular option is the classic Kirchhoffconditions which means conservation of mass at the bifurcation andprescribes a continuous pressure at the joint.

In reality the boundary layer phenomena predicts fast local changesto both velocity and pressure inside the bifurcation. Thus it is not appropriate for a one dimensional model to assume a continuous pressure. In this work we present a modification to the classic Kirchhoff condi-tions, with a symmetric pressure drop matrix, that is more suitable forone dimensional flow models. An asymptotic analysis, that has beencarried out previously shows that the new transmission conditions hasen exponentially small error.

The modified transmission conditions take the geometry of the bifurcation into account and can treat two outlets differently. The conditions can also be written in a form that is suitable for implementationin a finite difference solver. Also, by appropriate choice of the pressuredrop matrix we show that the new transmission conditions can producehead loss coefficients similar to experimentally obtained ones.

Publisher
p. 11
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2018:5
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-147718 (URN)LiTH-MAT-R--2018/05--SE (ISRN)
Available from: 2018-05-07 Created: 2018-05-07 Last updated: 2018-05-07Bibliographically approved
Berntsson, F. & Ohlson, M. (2017). More on Estimation of Banded and Banded Toeplitz Covariance Matrices. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>More on Estimation of Banded and Banded Toeplitz Covariance Matrices
2017 (English)Report (Other academic)
Abstract [en]

In this paper we consider two different linear covariance structures, e.g., banded and bended Toeplitz, and how to estimate them using different methods, e.g., by minimizing different norms.

One way to estimate the parameters in a linear covariance structure is to use tapering, which has been shown to be the solution to a universal least squares problem. We know that tapering not always guarantee the positive definite constraints on the estimated covariance matrix and may not be a suitable method. We propose some new methods which preserves the positive definiteness and still give the correct structure.

More specific we consider the problem of estimating parameters of a multivariate normal p–dimensional random vector for (i) a banded covariance structure reflecting m–dependence, and (ii) a banded Toeplitz covariance structure.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. p. 12
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2017:12
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-141051 (URN)LiTH-MAT-R--2017/12--SE (ISRN)
Available from: 2017-09-25 Created: 2017-09-25 Last updated: 2017-10-06Bibliographically approved
Berntsson, F., Karlsson, M., Kozlov, V. & Nazarov, S. A. (2016). A one-dimensional model of viscous blood flow in an elastic vessel. Applied Mathematics and Computation, 274, 125-132
Open this publication in new window or tab >>A one-dimensional model of viscous blood flow in an elastic vessel
2016 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 274, p. 125-132Article in journal (Refereed) Published
Abstract [en]

In this paper we present a one-dimensional model of blood flow in a vessel segment with an elastic wall consisting of several anisotropic layers. The model involves two variables: the radial displacement of the vessels wall and the pressure, and consists of two coupled equations of parabolic and hyperbolic type. Numerical simulations on a straight segment of a blood vessel demonstrate that the model can produce realistic flow fields that may appear under normal conditions in healthy blood vessels; as well as flow that could appear during abnormal conditions. In particular we show that weakening of the elastic properties of the wall may provoke a reverse blood flow in the vessel. (C) 2015 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE INC, 2016
Keywords
Blood flow; Linear model; Asymptotic analysis; Dimension reduction; Numerical simulation
National Category
Mathematics Mechanical Engineering
Identifiers
urn:nbn:se:liu:diva-124453 (URN)10.1016/j.amc.2015.10.077 (DOI)000367521900013 ()
Available from: 2016-02-02 Created: 2016-02-01 Last updated: 2017-11-30
Evarest, E., Berntsson, F., Singull, M. & Charles, W. (2016). Regime Switching models on Temperature Dynamics. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Regime Switching models on Temperature Dynamics
2016 (English)Report (Other academic)
Abstract [en]

Two regime switching models for predicting temperature dynamics are presented in this study for the purpose to be used for weather derivatives pricing. One is an existing model in the literature (Elias model) and the other is presented in this paper. The new model we propose in this study has a mean reverting heteroskedastic process in the base regime and a Brownian motion in the shifted regime. The parameter estimation of the two models is done by the use expectation-maximization (EM) method using historical temperature data. The performance of the two models on prediction of temperature dynamics is compared using historical daily average temperature data from five weather stations across Sweden. The comparison is based on the heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. The expected HDDs, CDDs and CAT of the models are compared to the true indices from the real data. Results from the expected HDDs, CDDs and CAT together with their corresponding daily average plots demonstrate that, our model captures temperature dynamics relatively better than Elias model.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. p. 24
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2016:12
Keywords
Weather derivatives, Regime switching, temperature dynamics, expectation-maximization, temperature indices
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-130586 (URN)LiTH-MAT-R--2016/12--SE (ISRN)
Available from: 2016-08-17 Created: 2016-08-17 Last updated: 2016-08-17Bibliographically approved
Berntsson, F., Kozlov, V., Mpinganzima, L. & Turesson, B.-O. (2014). An accelerated alternating procedure for the Cauchy problem for the Helmholtz equation. Computers and Mathematics with Applications, 68(1-2), 44-60
Open this publication in new window or tab >>An accelerated alternating procedure for the Cauchy problem for the Helmholtz equation
2014 (English)In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 68, no 1-2, p. 44-60Article in journal (Refereed) Published
Abstract [en]

In this paper we study the Cauchy problem for the Helmholtz equation. This problem appears in various applications and is severely ill–posed. The modified alternating procedure has been proposed by the authors for solving this problem but the convergence has been rather slow. We demonstrate how to instead use conjugate gradient methods for accelerating the convergence. The main idea is to introduce an artificial boundary in the interior of the domain. This addition of the interior boundary allows us to derive an inner product that is natural for the application and that gives us a proper framework for implementing the steps of the conjugate gradient methods. The numerical results performed using the finite difference method show that the conjugate gradient based methods converge considerably faster than the modified alternating iterative procedure studied previously.

Place, publisher, year, edition, pages
Elsevier, 2014
Keywords
Cauchy problem; alternating iterative method; conjugate gradient methods; inverse problem; ill–posed problem
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-105877 (URN)10.1016/j.camwa.2014.05.002 (DOI)000338816300004 ()
Available from: 2014-04-11 Created: 2014-04-11 Last updated: 2017-12-05Bibliographically approved
Berntsson, F., Kozlov, V., Mpinganzima, L. & Turesson, B.-O. (2014). An alternating iterative procedure for the Cauchy problem for the Helmholtz equation. Paper presented at 6th International Conference "Inverse Problems: Modeling and Simulation", 21-26 May 2012, Antalya, Turkey. Inverse Problems in Science and Engineering, 22(1), 45-62
Open this publication in new window or tab >>An alternating iterative procedure for the Cauchy problem for the Helmholtz equation
2014 (English)In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 22, no 1, p. 45-62Article in journal (Refereed) Published
Abstract [en]

We present a modification of the alternating iterative method, which was introduced by V.A. Kozlov and V. Maz’ya in for solving the Cauchy problem for the Helmholtz equation in a Lipschitz domain. The method is implemented numerically using the finite difference method.

Place, publisher, year, edition, pages
Taylor & Francis, 2014
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-77298 (URN)10.1080/17415977.2013.827181 (DOI)000328245900005 ()
Conference
6th International Conference "Inverse Problems: Modeling and Simulation", 21-26 May 2012, Antalya, Turkey
Available from: 2012-05-11 Created: 2012-05-11 Last updated: 2017-12-07Bibliographically approved
Berntsson, F. & Baravdish, G. (2014). Coefficient identification in PDEs applied to image inpainting. Applied Mathematics and Computation, 242, 227-235
Open this publication in new window or tab >>Coefficient identification in PDEs applied to image inpainting
2014 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 242, p. 227-235Article in journal (Refereed) Published
Abstract [en]

In this paper, we introduce the concept of parameter identification problems, which are inverse problems, as a methodology to inpainting. More specifically, as a first study in this new direction, we generalize the method of harmonic inpainting by studying an elliptic equation in divergence form where we assume that the diffusion coefficient is unknown. As a first step, this unknown coefficient is determined from the information obtained by the known data in the image. Next, we fill in the region with missing data by solving an elliptic equation in divergence form using this obtained diffusion coefficient. An error analysis shows that this approach is promising and our numerical experiments produces better results than the harmonic inpainting.

Place, publisher, year, edition, pages
Elsevier, 2014
Keywords
Image inpainting; Inverse problems; Coefficient identification
National Category
Mathematics Civil Engineering
Identifiers
urn:nbn:se:liu:diva-110691 (URN)10.1016/j.amc.2014.05.051 (DOI)000340563000020 ()
Available from: 2014-09-24 Created: 2014-09-19 Last updated: 2017-12-05Bibliographically approved
Berntsson, F., Kozlov, V. A., Mpinganzima, L. & Turesson, B.-O. (2014). Numerical Solution of the Cauchy Problem for the Helmholtz Equation. Linköping University Electronic Press
Open this publication in new window or tab >>Numerical Solution of the Cauchy Problem for the Helmholtz Equation
2014 (English)Report (Other academic)
Abstract [en]

The Cauchy problem for the Helmholtz equation appears in applications related to acoustic or electromagnetic wave phenomena. The problem is ill–posed in the sense that the solution does not depend on the data in a stable way. In this paper we give a detailed study of the problem. Specifically we investigate how the ill–posedness depends on the shape of the computational domain and also on the wave number. Furthermore, we give an overview over standard techniques for dealing with ill–posed problems and apply them to the problem.

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2014. p. 16
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2014:04
Keywords
Helmholtz equation, Cauchy Problem, Ill-Posed, Regularization, Numerical Methods.
National Category
Computational Mathematics Mathematics
Identifiers
urn:nbn:se:liu:diva-105707 (URN)LiTH-MAT-R--2014/04--SE (ISRN)
Available from: 2014-04-03 Created: 2014-04-03 Last updated: 2014-04-11Bibliographically approved
Berntsson, F., Kozlov, V., Mpinganzima, L. & Turesson, B.-O. (2014). Robin–Dirichlet algorithms for the Cauchy problem for the Helmholtz equation.
Open this publication in new window or tab >>Robin–Dirichlet algorithms for the Cauchy problem for the Helmholtz equation
2014 (English)Manuscript (preprint) (Other academic)
Abstract [en]

The Cauchy problem for the Helmholtz equation is considered. It was demonstrated in a previous paper by the authors that the alternating algorithm suggested by V.A. Kozlov and V.G. Maz’ya does not converge for large wavenumbers in the Helmholtz equation. We prove here that if we alternate Robin and Dirichlet boundary conditions instead of Neumann and Dirichlet boundary conditions, then the algorithm will converge. We present also another algorithm based on the same idea, which converges for large wavenumbers. Numerical implementations obtained using the finite difference method are presented. Numerical results illustrate that the algorithms suggested in this paper, produce a convergent iterative sequences.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-105876 (URN)
Available from: 2014-04-11 Created: 2014-04-11 Last updated: 2014-04-11Bibliographically approved
Chen, L., Berntsson, F., Zhang, Z., Wang, P., Wu, J. & Xu, T. (2014). Seismically constrained thermo-rheological structure of the eastern Tibetan margin: Implication for lithospheric delamination. Tectonophysics, 627, 122-134
Open this publication in new window or tab >>Seismically constrained thermo-rheological structure of the eastern Tibetan margin: Implication for lithospheric delamination
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2014 (English)In: Tectonophysics, ISSN 0040-1951, E-ISSN 1879-3266, Vol. 627, p. 122-134Article in journal (Refereed) Published
Abstract [en]

The eastern Tibetan margin bordered by the Longmen Shan range exhibits significant lateral differences in the lithospheric structure and thermal state. To investigate the roles of these differences in mountain building, we construct a thermo-rheological model along a wide-angle seismic profile across the eastern Tibetan margin based on recent seismic and thermal observations. The thermal modeling is constrained by the surface heat flow data and crustal P wave velocity model. The construction of the theological envelopes is based on rock mechanics results, and involves two types of rheology: a weak case where the lower crust is felsic granulite and the lithospheric mantle is wet peridotite, and a strong case where the lower crust is mafic granulite and the lithospheric mantle is dry peridotite. The results demonstrate: (1) one high-temperature anomaly exists within the uppermost mantle beneath eastern Tibet, indicating that the crust in eastern Tibet is remarkably warmer than that in the Sichuan basin, and (2) the rheological strength of the lithospheric mantle beneath eastern Tibet is considerably weaker than that beneath the Sichuan basin. The rheological profiles are in accord with seismicity distribution. By combining these results with the observed crustal/lithospheric architecture, Pn velocity distribution and magmatism in the eastern Tibetan margin, we suggest that the delamination of a thickened lithospheric mantle root beneath eastern Tibet is responsible for the growth of the eastern Tibetan margin.

Place, publisher, year, edition, pages
Elsevier, 2014
Keywords
Lithosphere rheology; Temperature; Seismic velocity; Eastem Tibetan margin; Delamination
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-109593 (URN)10.1016/j.tecto.2013.11.005 (DOI)000339535000012 ()
Available from: 2014-08-21 Created: 2014-08-21 Last updated: 2017-12-05Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-2681-8965

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