Berntsson, Fredrik
Overview
Works:  29 works in 44 publications in 1 language and 46 library holdings 

Roles:  Author, the 
Classifications:  Q180.S93, 518.64 
Publication Timeline
.
Most widely held works by
Fredrik Berntsson
Sequential solution of the sideways heat equation by windowing of the data by
Fredrik Berntsson(
Book
)
5 editions published between 2001 and 2003 in English and held by 5 WorldCat member libraries worldwide
The sideways heat equation is a onedimensional model of a problem, where one wants to determine the temperature on the surface of a body using interior measurements. More precisely, we consider a heat conduction problem, where temperature and heatflux data are available along the line x = 1 and the solution is sought in the interval 0 = x <1. The problem is illposed in the sense that the solution does not depend continuously on the data. Stability can be restored by replacing the time derivative in the heat equation with a bounded spectral approximation. The cut off level in the spectral approximation acts as a regularization parameter, that controls the degree of smoothness in the solution. In certain applications one wants to solve the sideways heat equation in real time, i.e. to constantly update the solution as new measurements are recorded. For this case sequential solution methods are required
5 editions published between 2001 and 2003 in English and held by 5 WorldCat member libraries worldwide
The sideways heat equation is a onedimensional model of a problem, where one wants to determine the temperature on the surface of a body using interior measurements. More precisely, we consider a heat conduction problem, where temperature and heatflux data are available along the line x = 1 and the solution is sought in the interval 0 = x <1. The problem is illposed in the sense that the solution does not depend continuously on the data. Stability can be restored by replacing the time derivative in the heat equation with a bounded spectral approximation. The cut off level in the spectral approximation acts as a regularization parameter, that controls the degree of smoothness in the solution. In certain applications one wants to solve the sideways heat equation in real time, i.e. to constantly update the solution as new measurements are recorded. For this case sequential solution methods are required
Numerical methods for inverse heat conduction problems by
Fredrik Berntsson(
Book
)
2 editions published in 2001 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2001 in English and held by 4 WorldCat member libraries worldwide
Numerical solution of a Cauchy problem for the Laplace equation by
Fredrik Berntsson(
Book
)
4 editions published in 2000 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 2000 in English and held by 4 WorldCat member libraries worldwide
A spectral method for solving the sideways heat equation by
Fredrik Berntsson(
Book
)
3 editions published in 1999 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1999 in English and held by 3 WorldCat member libraries worldwide
Numerical methods for solving a noncharacteristic Cauchy problem for a parabolic equation by
Fredrik Berntsson(
Book
)
3 editions published in 2001 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 2001 in English and held by 3 WorldCat member libraries worldwide
Wavelet and fourier methods for solving the sideways heat equation by
Lars Eldén(
Book
)
2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide
An alternating iterative procedure for the Cauchy problem for the Helmholtz equation by
Lydie Mpinganzima(
)
2 editions published between 2012 and 2014 in English and held by 2 WorldCat member libraries worldwide
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
2 editions published between 2012 and 2014 in English and held by 2 WorldCat member libraries worldwide
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
Boundary identification for an elliptic equation by
Fredrik Berntsson(
Book
)
2 editions published in 2001 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2001 in English and held by 2 WorldCat member libraries worldwide
Numerical methods for inverse heat conduction problems by
Fredrik Berntsson(
Book
)
1 edition published in 2001 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 2 WorldCat member libraries worldwide
Analysis of DirichletRobin Iterations for Solving the Cauchy Problem for Elliptic Equations by
Pauline Achieng(
)
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
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):10621078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz'ya can be convergent, even for large wavenumbers k 2 , 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 DirichletRobin 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 k 2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
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):10621078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz'ya can be convergent, even for large wavenumbers k 2 , 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 DirichletRobin 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 k 2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters
Numerical methods for inverse heat conduction problems by
Fredrik Berntsson(
Book
)
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
Transient inverse heat conduction problem of quenching a hollow cylinder by one row of water jets(
)
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
Highlights: The GMRES method is applied in quenching process by water jets. Regularization parameter and mesh size are optimized by sensitivity analysis. Temperature cyclic variation is damped from surface to interior of rotary specimen. Time delay of cooling the interior of specimen compared to surface is predicted. Three different boiling curves are defined for a quenched rotary convex surface. Abstract: In this study, a twodimensional linear transition inverse heat conduction problem (IHCP) was solved using the Generalized Minimal Residual Method (GMRES) in quenching process by water jets. The inverse solution method was validated by set of artificial data and solution sensitivity analysis was done on data noise level, regularization parameter, cell size, etc. An experimental study has been carried out on quenching a rotary hollow cylinder by one row of subcooled water jets. The inverse solution approach enabled prediction of surface temperature and heat flux distribution of test specimen in the quenching experiments by using measured internal specimen temperature. Three different boiling curves were defined in the quenching process of a rotary cylinder. Result obtained by the inverse solution showed clear footprint of rotation in surface temperature and heat flux on each revolution of cylinder and temperature variation damping from quenching surface toward interior of specimen
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
Highlights: The GMRES method is applied in quenching process by water jets. Regularization parameter and mesh size are optimized by sensitivity analysis. Temperature cyclic variation is damped from surface to interior of rotary specimen. Time delay of cooling the interior of specimen compared to surface is predicted. Three different boiling curves are defined for a quenched rotary convex surface. Abstract: In this study, a twodimensional linear transition inverse heat conduction problem (IHCP) was solved using the Generalized Minimal Residual Method (GMRES) in quenching process by water jets. The inverse solution method was validated by set of artificial data and solution sensitivity analysis was done on data noise level, regularization parameter, cell size, etc. An experimental study has been carried out on quenching a rotary hollow cylinder by one row of subcooled water jets. The inverse solution approach enabled prediction of surface temperature and heat flux distribution of test specimen in the quenching experiments by using measured internal specimen temperature. Three different boiling curves were defined in the quenching process of a rotary cylinder. Result obtained by the inverse solution showed clear footprint of rotation in surface temperature and heat flux on each revolution of cylinder and temperature variation damping from quenching surface toward interior of specimen
A spectral method for solving the sideways heat equation by
Fredrik Berntsson(
Book
)
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
Solvability of a nonlinear Cauchy problem for an elliptic equation by
Fredrik Berntsson(
)
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
We study a nonlinear operator equation originating from a Cauchy problem for an elliptic equation. The problem appears in applications where surface measurements are used to calculate the temperature below the earth surface. The Cauchy problem is illposed and small perturbations to the used data can result in large changes in the solution. Since the problem is nonlinear certain assumptions on the coefficients are needed. We reformulate the problem as an nonlinear operator equation and show that under suitable assumptions the operator is welldefined. The proof is based on making a change of variables and removing the nonlinearity from the leading term of the equation. As a part of the proof we obtain an iterative procedure that is convergent and can be used for evaluating the operator. Numerical results show that the proposed procedure converges faster than a simple fixed point iteration for the equation in the the original variables
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
We study a nonlinear operator equation originating from a Cauchy problem for an elliptic equation. The problem appears in applications where surface measurements are used to calculate the temperature below the earth surface. The Cauchy problem is illposed and small perturbations to the used data can result in large changes in the solution. Since the problem is nonlinear certain assumptions on the coefficients are needed. We reformulate the problem as an nonlinear operator equation and show that under suitable assumptions the operator is welldefined. The proof is based on making a change of variables and removing the nonlinearity from the leading term of the equation. As a part of the proof we obtain an iterative procedure that is convergent and can be used for evaluating the operator. Numerical results show that the proposed procedure converges faster than a simple fixed point iteration for the equation in the the original variables
SDK for development and testing of onboard applications for M3090 radio modem by
Fredrik Berntsson(
)
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
A onedimensional model of viscous blood flow in an elastic vessel by
Fredrik Berntsson(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
In this paper we present a onedimensional 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
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
In this paper we present a onedimensional 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
Boundary identification for an elliptic equation by
Fredrik Berntsson(
)
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
Numerical methods for inverse heat conduction problems by
Fredrik Berntsson(
Book
)
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
Coefficient identification in PDEs applied to image inpainting by
Fredrik Berntsson(
)
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
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
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
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
Solving the Cauchy problem for the Helmholtz equation using cubic smoothing splines by Mary Nanfuka(
)
1 edition published in 2021 in English and held by 1 WorldCat member library worldwide
We consider the Cauchy problem for the Helmholtz equation defined in a rectangular domain. The Cauchy data are prescribed on a part of the boundary and the aim is to find the solution in the entire domain. The problem occurs in applications related to acoustics and is illposed in the sense of Hadamard. In our work we consider regularizing the problem by introducing a bounded approximation of the second derivative by using Cubic smoothing splines. We derive a bound for the approximate derivative and show how to obtain stability estimates for the method. Numerical tests show that the method works well and can produce accurate results. We also demonstrate that the method can be extended to more complicated domains
1 edition published in 2021 in English and held by 1 WorldCat member library worldwide
We consider the Cauchy problem for the Helmholtz equation defined in a rectangular domain. The Cauchy data are prescribed on a part of the boundary and the aim is to find the solution in the entire domain. The problem occurs in applications related to acoustics and is illposed in the sense of Hadamard. In our work we consider regularizing the problem by introducing a bounded approximation of the second derivative by using Cubic smoothing splines. We derive a bound for the approximate derivative and show how to obtain stability estimates for the method. Numerical tests show that the method works well and can produce accurate results. We also demonstrate that the method can be extended to more complicated domains
more
fewer
Audience Level
0 

1  
General  Special 
Related Identities
 Universitetet i Linköping Matematiska institutionen Publisher
 Linköpings universitet Tekniska fakulteten Publisher
 Eldén, Lars 1944 Author
 Kozlov, Vladimir
 Turesson, BengtOve
 Universitet i Linköping Department of Mathematics
 Regińska, Teresa
 Mpinganzima, Lydie Author
 Linköpings universitet Tekniska högskolan Publisher
 Kozlov, Vladimir 1954
Associated Subjects
Languages