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Fredrik Berntsson

Associate Professor, Docent

I am interested in computers, and software, as tools for mathematical computations, or for simulating physical processes. An important aspect is the mathematical analysis of computational methods with respect to stability and accuracy.

I am interested in using computers to perform computations or simulate physical systems. The areas I am interested in are linear algebra, functional analysis, and partial differential equations. In my research I mostly study problems from different application areas, including inverse heat conduction, image processing, and biomechanics. I also teach various courses in scientific computing, linear algebra, and programming.

Link to my profile at ResearchGate

Publications

2026

Jean Pierre Ngendahayo, Minani Froduald, Johan Thim, Fredrik Berntsson (2026) Solving an inverse heat conduction problem with phase transitions using Tikhonov regularization RESEARCH IN MATHEMATICS, Vol. 13, Article 2670816 (Article in journal) https://dx.doi.org/10.1080/27684830.2026.2670816

2025

Pauline Achieng, Fredrik Berntsson, Vladimir Kozlov (2025) Reconstructing of the radiation condition and solution for a variable coefficient Helmholtz equation in a semi-infinite strip from Cauchy data on an interior segment Journal of Mathematical Analysis and Applications, Vol. 541, Article 128684 (Article in journal) https://dx.doi.org/10.1016/j.jmaa.2024.128684

2024

Martin Deosborns, Henry Kasumba, Juma Kasozi, Fredrik Berntsson (2024) Optimal Actuator Design for Control of Vibrations Induced by Pedestrian-Bridge Interactions MATHEMATICS IN APPLIED SCIENCES AND ENGINEERING, Vol. 5, p. 85-184 (Article in journal) https://dx.doi.org/10.5206/mase/16958
Pauline Achieng, Fredrik Berntsson, Vladimir Kozlov (2024) Reconstruction of the Radiation Condition and Solution for the Helmholtz Equation in a Semi-infinite Strip from Cauchy Data on an Interior Segment Computational Methods in Applied Mathematics, Vol. 24, p. 813-828 (Article in journal) https://dx.doi.org/10.1515/cmam-2022-0244

2023

Jennifer Chepkorir, Fredrik Berntsson, Vladimir Kozlov (2023) Solving stationary inverse heat conduction in a thin plate Partial Differential Equations and Applications, Vol. 4, Article 50 (Article in journal) https://dx.doi.org/10.1007/s42985-023-00267-7

Research

Factory producing steel.

Simulationsoftware ensures quality in steel production

Through a simulation program developed by researchers at MAI and SSAB can high quality steel be produced. The program ensures that the ironmaking ladles used during production are at the right temperature, which affects the quality of the steel.
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Inverse and Ill-posed Problems

Inverse problems appear when looking for the cause of an observed effect. Difficulties include lack of uniqueness and instability with respect to errors in the observed data. Special mathematical techniques are used for solving such problems.
Human blood cells with one red cell in front.

Mathematical Modelling of the Blood Circulatory System

Mathematical models of the circulatory system can be used in order to better understand the system and so help diagnose blood-vascular diseases and other problems while also enabling planning for the treatment of these diseases.

Numerical Solutions of Time-Dependent Partial Differential Equations

Well-posedness of the governing partial differential equations lead to effective and accurate numerical methods for the analysis of physical processes in science and engineering.

Publications

2026

Jean Pierre Ngendahayo, Minani Froduald, Johan Thim, Fredrik Berntsson (2026) Solving an inverse heat conduction problem with phase transitions using Tikhonov regularization RESEARCH IN MATHEMATICS, Vol. 13, Article 2670816 (Article in journal) https://dx.doi.org/10.1080/27684830.2026.2670816

2025

Pauline Achieng, Fredrik Berntsson, Vladimir Kozlov (2025) Reconstructing of the radiation condition and solution for a variable coefficient Helmholtz equation in a semi-infinite strip from Cauchy data on an interior segment Journal of Mathematical Analysis and Applications, Vol. 541, Article 128684 (Article in journal) https://dx.doi.org/10.1016/j.jmaa.2024.128684

2024

Martin Deosborns, Henry Kasumba, Juma Kasozi, Fredrik Berntsson (2024) Optimal Actuator Design for Control of Vibrations Induced by Pedestrian-Bridge Interactions MATHEMATICS IN APPLIED SCIENCES AND ENGINEERING, Vol. 5, p. 85-184 (Article in journal) https://dx.doi.org/10.5206/mase/16958
Pauline Achieng, Fredrik Berntsson, Vladimir Kozlov (2024) Reconstruction of the Radiation Condition and Solution for the Helmholtz Equation in a Semi-infinite Strip from Cauchy Data on an Interior Segment Computational Methods in Applied Mathematics, Vol. 24, p. 813-828 (Article in journal) https://dx.doi.org/10.1515/cmam-2022-0244

2023

Jennifer Chepkorir, Fredrik Berntsson, Vladimir Kozlov (2023) Solving stationary inverse heat conduction in a thin plate Partial Differential Equations and Applications, Vol. 4, Article 50 (Article in journal) https://dx.doi.org/10.1007/s42985-023-00267-7
Pauline Achieng, Fredrik Berntsson, Vladimir Kozlov (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, Vol. 31 (Article in journal) https://dx.doi.org/10.1515/jiip-2020-0133
Martin Deosborns Arop, Henry Kasumba, Juma Kasozi, Fredrik Berntsson (2023) Optimal Actuator Placement for Control of Vibrations Induced by Pedestrian-Bridge Interactions MATHEMATICS IN APPLIED SCIENCES AND ENGINEERING, Vol. 4, p. 172-195 (Article in journal) https://dx.doi.org/10.5206/mase/15949
Fredrik Berntsson, Patrik Wikström (2023) Thermal tracking of a ladle during production cycles International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 24, p. 406-416 (Article in journal) https://dx.doi.org/10.1080/15502287.2023.2253255

2022

Mary Nanfuka, Fredrik Berntsson, John Mango (2022) Solving the Cauchy problem for the Helmholtz equation using cubic smoothing splines Journal of Applied Mathematics and Computing, Vol. 68, p. 1335-1350 (Article in journal) https://dx.doi.org/10.1007/s12190-021-01572-3
Mary Nanfuka, Fredrik Berntsson, Godwin Kakuba (2022) Solving a Cauchy problem for the heat equation using cubic smoothing splines Applicable Analysis, Vol. 101, p. 4882-4897 (Article in journal) https://dx.doi.org/10.1080/00036811.2021.1876224

Organisation

Illustrative picture representing mathematics

Applied Mathematics (TIMA)

Applied mathematics is used to study advanced methods for modeling in technology as well as natural and social sciences. The division conducts research in computational mathematics, mathematical statistics and optimization.
Fractal Plant

Department of Mathematics (MAI)

The department conducts research in computational mathematics, mathematics and applied mathematics, mathematical statistics, and optimization. We provide courses to students in most degree programmes in mathematics, science and engineering.
Studenthuset on Campus Valla in Linköping

About LiU

Linköping University, LiU, offers innovative education and boundary-crossing research. The students are among the most desirable in the labour market and international rankings consistently place LiU as a leading global university.