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Achieng, P., Berntsson, F. & Kozlov, V. (2023). Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain. Journal of Inverse and Ill-Posed Problems, 31(5)
Öppna denna publikation i ny flik eller fönster >>Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain
2023 (Engelska)Ingår i: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 31, nr 5Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We consider the Cauchy problem for the Helmholtz equation with a domain in with N cylindrical outlets to infinity with bounded inclusions in . Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Mazya proposed an alternating iterative method for solving Cauchy problems associated with elliptic, selfadjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We consider the variant proposed by Berntsson, Kozlov, Mpinganzima and Turesson (2018) for bounded domains and derive the necessary conditions for the convergence of the procedure in unbounded domains. For the numerical implementation, a finite difference method is used to solve the problem in a simple rectangular domain in R-2 that represent a truncated infinite strip. The numerical results shows that by appropriate truncation of the domain and with appropriate choice of the Robin parameters mu(0) and mu(1), the Robin-Dirichlet alternating iterative procedure is convergent.

Ort, förlag, år, upplaga, sidor
WALTER DE GRUYTER GMBH, 2023
Nyckelord
Helmholtz equation; Cauchy problem; inverse problem ill-posed problem
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
urn:nbn:se:liu:diva-192481 (URN)10.1515/jiip-2020-0133 (DOI)000940871600001 ()
Tillgänglig från: 2023-03-21 Skapad: 2023-03-21 Senast uppdaterad: 2024-03-18Bibliografiskt granskad
Chepkorir, J., Berntsson, F. & Kozlov, V. (2023). Solving stationary inverse heat conduction in a thin plate. Partial Differential Equations and Applications, 4(6)
Öppna denna publikation i ny flik eller fönster >>Solving stationary inverse heat conduction in a thin plate
2023 (Engelska)Ingår i: Partial Differential Equations and Applications, ISSN 2662-2971, Vol. 4, nr 6Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We consider a steady state heat conduction problem in a thin plate. In the application, it is used to connect two cylindrical containers and fix their relative positions. At the same time it serves to measure the temperature on the inner cylinder. We derive a two dimensional mathematical model, and use it to approximate the heat conduction in the thin plate. Since the plate has sharp edges on the sides the resulting problem is described by a degenerate elliptic equation. To find the temperature in the interior part from the exterior measurements, we formulate the problem as a Cauchy problem for stationary heat equation. We also reformulate the Cauchy problem as an operator equation, with a compact operator, and apply the Landweber iteration method to solve the equation. The case of the degenerate elliptic equation has not been previously studied in this context. For numerical computation, we consider the case where noisy data is present and analyse the convergence.

Nyckelord
Cauchy problem, Stationary heat equation, Degenerate elliptic equation, Landweber iterative method
Nationell ämneskategori
Matematisk analys
Identifikatorer
urn:nbn:se:liu:diva-201113 (URN)10.1007/s42985-023-00267-7 (DOI)
Tillgänglig från: 2024-02-22 Skapad: 2024-02-22 Senast uppdaterad: 2024-02-22Bibliografiskt granskad
Berntsson, F. & Wikström, P. (2023). Thermal tracking of a ladle during production cycles. International Journal for Computational Methods in Engineering Science and Mechanics, 24(6), 406-416
Öppna denna publikation i ny flik eller fönster >>Thermal tracking of a ladle during production cycles
2023 (Engelska)Ingår i: International Journal for Computational Methods in Engineering Science and Mechanics, ISSN 1550-2287, E-ISSN 1550-2295, Vol. 24, nr 6, s. 406-416Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

Temperature control is important for the steel making process. Knowledge of the amount of thermal energy stored in the ladle allows for better predictions of the steel temperature during the process. This has a potential to improve the quality of the steel. In this work, we present a mathematical model of the heat transfer within a ladle during the production process. The model can be used to compute the current, and also the future, thermal status of the ladle. The model is simple and can be solved efficiently. We also present results from numerical simulations intended to illustrate the model.

Ort, förlag, år, upplaga, sidor
TAYLOR & FRANCIS INC, 2023
Nyckelord
Heat equation; steel making ladle; energy simulation; temperature control; industrial application
Nationell ämneskategori
Metallurgi och metalliska material
Identifikatorer
urn:nbn:se:liu:diva-197874 (URN)10.1080/15502287.2023.2253255 (DOI)001058207600001 ()
Tillgänglig från: 2023-09-19 Skapad: 2023-09-19 Senast uppdaterad: 2024-04-09Bibliografiskt granskad
Achieng, P., Berntsson, F., Chepkorir, J. & Kozlov, V. (2021). Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations. Bulletin of the Iranian Mathematical Society, 47, 1681-1699
Öppna denna publikation i ny flik eller fönster >>Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations
2021 (Engelska)Ingår i: Bulletin of the Iranian Mathematical Society, ISSN 1735-8515, Vol. 47, s. 1681-1699Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers k2, in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of k2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.

Ort, förlag, år, upplaga, sidor
Springer, 2021
Nyckelord
Helmholtz equation, Cauchy problem, Inverse problem, Ill-posed problem
Nationell ämneskategori
Matematisk analys
Identifikatorer
urn:nbn:se:liu:diva-170834 (URN)10.1007/s41980-020-00466-7 (DOI)000575739300001 ()2-s2.0-85092146699 (Scopus ID)
Tillgänglig från: 2020-10-26 Skapad: 2020-10-26 Senast uppdaterad: 2024-02-22Bibliografiskt granskad
Berntsson, F., Karlsson, M., Kozlov, V. & Nazarov, S. A. (2018). A Modification to the Kirchhoff Conditions at a Bifurcation and Loss Coefficients.
Öppna denna publikation i ny flik eller fönster >>A Modification to the Kirchhoff Conditions at a Bifurcation and Loss Coefficients
2018 (Engelska)Rapport (Övrigt vetenskapligt)
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.

Förlag
s. 11
Serie
LiTH-MAT-R, ISSN 0348-2960 ; 2018:5
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:liu:diva-147718 (URN)LiTH-MAT-R--2018/05--SE (ISRN)
Tillgänglig från: 2018-05-07 Skapad: 2018-05-07 Senast uppdaterad: 2018-05-07Bibliografiskt granskad
Berntsson, F. & Ohlson, M. (2017). More on Estimation of Banded and Banded Toeplitz Covariance Matrices. Linköping: Linköping University Electronic Press
Öppna denna publikation i ny flik eller fönster >>More on Estimation of Banded and Banded Toeplitz Covariance Matrices
2017 (Engelska)Rapport (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Linköping: Linköping University Electronic Press, 2017. s. 12
Serie
LiTH-MAT-R, ISSN 0348-2960 ; 2017:12
Nationell ämneskategori
Sannolikhetsteori och statistik
Identifikatorer
urn:nbn:se:liu:diva-141051 (URN)LiTH-MAT-R--2017/12--SE (ISRN)
Tillgänglig från: 2017-09-25 Skapad: 2017-09-25 Senast uppdaterad: 2017-10-06Bibliografiskt granskad
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
Öppna denna publikation i ny flik eller fönster >>A one-dimensional model of viscous blood flow in an elastic vessel
2016 (Engelska)Ingår i: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 274, s. 125-132Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
ELSEVIER SCIENCE INC, 2016
Nyckelord
Blood flow; Linear model; Asymptotic analysis; Dimension reduction; Numerical simulation
Nationell ämneskategori
Matematik Maskinteknik
Identifikatorer
urn:nbn:se:liu:diva-124453 (URN)10.1016/j.amc.2015.10.077 (DOI)000367521900013 ()
Tillgänglig från: 2016-02-02 Skapad: 2016-02-01 Senast uppdaterad: 2017-11-30
Evarest, E., Berntsson, F., Singull, M. & Charles, W. (2016). Regime Switching models on Temperature Dynamics. Linköping: Linköping University Electronic Press
Öppna denna publikation i ny flik eller fönster >>Regime Switching models on Temperature Dynamics
2016 (Engelska)Rapport (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Linköping: Linköping University Electronic Press, 2016. s. 24
Serie
LiTH-MAT-R, ISSN 0348-2960 ; 2016:12
Nyckelord
Weather derivatives, Regime switching, temperature dynamics, expectation-maximization, temperature indices
Nationell ämneskategori
Sannolikhetsteori och statistik
Identifikatorer
urn:nbn:se:liu:diva-130586 (URN)LiTH-MAT-R--2016/12--SE (ISRN)
Tillgänglig från: 2016-08-17 Skapad: 2016-08-17 Senast uppdaterad: 2016-08-17Bibliografiskt granskad
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
Öppna denna publikation i ny flik eller fönster >>An accelerated alternating procedure for the Cauchy problem for the Helmholtz equation
2014 (Engelska)Ingår i: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 68, nr 1-2, s. 44-60Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Elsevier, 2014
Nyckelord
Cauchy problem; alternating iterative method; conjugate gradient methods; inverse problem; ill–posed problem
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:liu:diva-105877 (URN)10.1016/j.camwa.2014.05.002 (DOI)000338816300004 ()
Tillgänglig från: 2014-04-11 Skapad: 2014-04-11 Senast uppdaterad: 2017-12-05Bibliografiskt granskad
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
Öppna denna publikation i ny flik eller fönster >>An alternating iterative procedure for the Cauchy problem for the Helmholtz equation
2014 (Engelska)Ingår i: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 22, nr 1, s. 45-62Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Taylor & Francis, 2014
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:liu:diva-77298 (URN)10.1080/17415977.2013.827181 (DOI)000328245900005 ()
Konferens
6th International Conference "Inverse Problems: Modeling and Simulation", 21-26 May 2012, Antalya, Turkey
Tillgänglig från: 2012-05-11 Skapad: 2012-05-11 Senast uppdaterad: 2017-12-07Bibliografiskt granskad
Organisationer
Identifikatorer
ORCID-id: ORCID iD iconorcid.org/0000-0002-2681-8965

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