Christian Engström
ProfessorTeaching
I teach courses in analysis, algebra, and computational science.
Research
Partial differential equations (PDEs) are important tools for modeling processes in science and technology. In my research, I develop mathematical and numerical analysis that results in robust and very fast numerical methods, which can be used to build digital twins of our world. New, very fast numerical methods are a cornerstone in the development of efficient machine learning algorithms for PDE, optimization with PDE constraints, and uncertainty quantification.
Resonances in mechanical structures such as houses and bridges can cause strong vibrations that have devastating consequences, but resonances are in other cases desirable, for example, to generate a certain tone in a musical instrument. In mathematics, spectral theory is used to study resonances.
In my research, I study mathematics that describes resonances in closed and open systems. I develop numerical methods for these problems and study applications in nano-optics, acoustics, thermal conduction, and mechanics. I also develop new numerical methods for time-dependent and non-linear problems.
During 2022-2027 I am project manager the VR-funded project
Pollution-free approximation techniques for fractional integro-differential equations
My research groups
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Computational Mathematics for Predictive Digital Twins (PreDiTwin) In recent years, remarkable progress in mathematics, process-based modeling, data science, and sensor technology has opened up…
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Deterministic and Stochastic Modelling The research field Deterministic and Stochastic Modelling within Linnaeus University Centre for Data Intensive Sciences and Applications (DISA) brings together…
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Scientific Computing and Partial Differential Equations Within this research theme, we study numerical methods for partial differential equations, analysis of differential and pseudo-differential…
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Waves, Signals and Systems The research in waves, signals and systems deals primarily with acoustic and electromagnetic direct and inverse problems, with engineering and industrial applications.
My ongoing research projects
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Project: Efficient and reliable computations of scattering resonances Scattering resonance computations in nano-optics are important in the development of photothermal cancer therapy, optical…
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Project: Optimization with PDE constraints Partial differential equations (PDEs) are used to model a multitude of phenomena in science and engineering. PDE-constrained optimization problems arise in…
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Project: Pollution-free approximation techniques for fractional integro-differential equations In the project, mathematical theory and software are developed to calculate resonances without the risk…
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Project: Spectral properties of unbounded operator functions Advanced time-dependent materials are used to model viscoelastic properties of wood, wave propagation of ultrasound, and systems with…
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Project: Wave propagation and radiative transfer in the atmosphere Wave propagation and radiative transfer in the atmosphere is a modern research area with immediate connection to the greenhouse…
Publications
Article in journal (Refereed)
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Engström, C., Torshage, A. (2024). Spectral properties of a class of operator functions with applications to the Moore-Gibson-Thompson equation with memory. Journal of Mathematical Analysis and Applications. 532 (2).
Status: Published -
Engström, C. (2024). On spectral enclosures for Maxwell’s equations with the Drude-Lorentz model. Applied Mathematics Letters. 155.
Status: Published -
Engström, C., Giani, S., Grubišić, L. (2023). Numerical solution of distributed-order time-fractional diffusion-wave equations using Laplace transforms. Journal of Computational and Applied Mathematics. 425.
Status: Published -
Araújo C., J.C., Engström, C., Wadbro, E. (2023). Shape optimization for the strong routing of light in periodic diffraction gratings. Journal of Computational Physics. 472.
Status: Published -
Giani, S., Engström, C., Grubišić, L. (2023). khp-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory. Journal of Computational and Applied Mathematics. 429.
Status: Published -
Engström, C., Giani, S., Grubišić, L. (2022). A spectral projection based method for the numerical solution of wave equations with memory. Applied Mathematics Letters. 127.
Status: Published -
Engström, C., Giani, S., Grubisic, L. (2022). Higher Order Composite DG approximations of Gross–Pitaevskii ground state : benchmark results and experiments. Journal of Computational and Applied Mathematics. 400.
Status: Published -
Engström, C. (2021). Spectra of Gurtin-Pipkin type of integro-differential equations and applications to waves in graded viscoelastic structures. Journal of Mathematical Analysis and Applications. 499 (2).
Status: Published -
Araújo C, J.C., Engström, C. (2021). On spurious solutions encountered in Helmholtz scattering resonance computations in Rd with applications to nano-photonics and acoustics. Journal of Computational Physics. 429. 1-20.
Status: Published -
Araujo, J., Campos, C., Engström, C., Roman, J. (2020). Computation of scattering resonances in absorptive and dispersive media with applications to metal-dielectric nano-structures. Journal of Computational Physics. 407. 1-24.
Status: Published -
Engström, C., Torshage, A. (2018). Accumulation of complex eigenvalues of a class of analytic operator functions. Journal of Functional Analysis. 275 (2). 442-477.
Status: Published -
Engström, C., Torshage, A. (2018). Spectral properties of conservative, dispersive, and absorptive photonic crystals. GAMM - Mitteilungen. 41. 1-16.
Status: Published -
Araujo-Cabarcas, J.C., Engström, C., Jarlebring, E. (2018). Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map. Journal of Computational and Applied Mathematics. 330. 177-192.
Status: Published -
Engström, C., Langer, H., Tretter, C. (2017). Rational eigenvalue problems and applications to photonic crystals. Journal of Mathematical Analysis and Applications. 445 (1). 240-279.
Status: Published -
Engström, C., Torshage, A. (2017). On equivalence and linearization of operator matrix functions with unbounded entries. Integral equations and operator theory. 89 (4). 465-492.
Status: Published -
Engström, C., Torshage, A. (2017). Enclosure of the numerical range of a class of non-selfadjoint rational operator functions. Integral equations and operator theory. 88 (2). 151-184.
Status: Published -
Araujo-Cabarcas, J.C., Engström, C. (2017). On spurious solutions in finite element approximations of resonances in open systems. Computers and Mathematics with Applications. 74 (10). 2385-2402.
Status: Published -
Engström, C., Giani, S., Grubisic, L. (2016). Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications. Computers and Mathematics with Applications. 72 (4). 952-973.
Status: Published -
Engström, C., Grubisic, L. (2015). A subspace iteration algorithm for Fredholm valued functions. Mathematical problems in engineering (Print). 2015. 1-14.
Status: Published -
Wadbro, E., Engström, C. (2015). Topology and shape optimization of plasmonic nano-antennas. Computer Methods in Applied Mechanics and Engineering. 293. 155-169.
Status: Published -
Engström, C. (2014). Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations. Numerische Mathematik. 126 (3). 413-440.
Status: Published -
Kaufmann, T., Engström, C. (2013). High-order absorbing boundary conditions for the meshless radial point interpolation method in the frequency domain. International journal of numerical modelling. 26 (5). 478-492.
Status: Published -
Effenberger, C., Kressner, D., Engström, C. (2012). Linearization techniques for band structure calculations in absorbing photonic crystals. International Journal for Numerical Methods in Engineering. 89 (2). 180-191.
Status: Published -
Kaufmann, T., Yu, Y., Engström, C., Chen, Z., Fumeaux, C. (2012). Recent developments of the meshless radial point interpolation method for time‐domain electromagnetics. International journal of numerical modelling. 25 (5-6). 468-489.
Status: Published -
Wang, M., Engström, C., Schmidt, K., Hafner, C. (2011). On high-order FEM applied to canonical scattering problems in plasmonics. Journal of Computational and Theoretical Nanoscience. 8 (8). 1564-1572.
Status: Published -
Engström, C. (2010). On a method to reduce uncertainties in bulk property measurements of two-component composites. IEEE transactions on microwave theory and techniques. 58 (2). 434-439.
Status: Published -
Kaufmann, T., Engström, C., Fumeaux, C., Vahldieck, R. (2010). Eigenvalue-analysis and longtime-stability of resonant structures for the meshless radial point interpolation method in time-domain. IEEE transactions on microwave theory and techniques. 58 (12). 3399-3408.
Status: Published -
Engström, C. (2010). On the spectrum of a holomorphic operator-valued function with applications to absorptive photonic crystals. Mathematical Models and Methods in Applied Sciences. 20 (8). 1319-1341.
Status: Published -
Engström, C., Wang, M. (2010). Complex dispersion relation calculations with the applications to absorptive photonic crystals. International Journal for Numerical Methods in Engineering. 84. 849-863.
Status: Published -
Engström, C., Hafner, C., Schmidt, K. (2009). Computations of lossy Bloch waves in two-dimensional photonic crystals. Journal of Computational and Theoretical Nanoscience. 6 (3). 775-783.
Status: Published -
Engström, C., Richter, M. (2009). On the spectrum of an operator pencil with applications to wave propagation in periodic and frequency dependent materials. SIAM Journal on Applied Mathematics. 70 (1). 231-247.
Status: Published -
Engström, C. (2007). Inverse bounds of two-component composites. SIAM Journal on Applied Mathematics. 68 (3). 666-679.
Status: Published -
Engström, C., Sjöberg, D. (2007). On two numerical methods for homogenization of Maxwell's equations. Journal Electromagnetic Waves and Applications. 21 (13). 1845-1856.
Status: Published -
Engström, C. (2007). Structural information of nanocomposites from measured optical properties. Journal of Physics : Condensed Matter. 19 (10).
Status: Published -
Engström, C. (2006). Inverse bounds and bulk properties of complex-valued two-component composites. SIAM Journal on Applied Mathematics. 67 (1). 194-213.
Status: Published -
Engström, C. (2005). Bounds on the effective tensor and structural parameters for anisotropic two-phase composite material. Journal of Physics D : Applied Physics. 38. 3695-3702.
Status: Published -
Sjöberg, D., Engström, C., Kristensson, G., Wall, D., Wellander, N. (2005). A Floquet-Bloch decomposition of Maxwell's equations, applied to homogenization. Multiscale Modeling & simulation. 4 (1). 149-171.
Status: Published
Conference paper (Refereed)
- Kaufmann, T., Engström, C., Fumeaux, C. (2011). Adaptive meshless methods in electromagnetic modeling : a gradient-based refinement strategy. European Microwave Week 2011: "Wave to the Future", EuMW 2011, Conference Proceedings - 41st European Microwave Conference, EuMC 2011. 559-562.
- Kaufmann, T., Fumeaux, C., Engström, C. (2011). A comparison of three meshless algorithms : Radial point interpolation, non-symmetric and symmetric Kansa method. 2011 IEEE MTT-S International Microwave Symposium Digest.
- Kaufmann, T., Engström, C., Fumeaux, C. (2010). Residual-based adaptive refinement for meshless eigenvalue solvers. The International Conference on Electromagnetics in Advanced Applications (ICEAA'10). 244-247.
- Kaufmann, T., Engström, C., Fumeaux, C. (2010). Characterization of an adaptiverenement algorithm for a meshless eigenvalue solver based on radial basis functions. 2010 Electromagnetic Compatibility Symposium – Melbourne. 17-20.
- Engström, C. (2010). On a high-order discontinuous Galerkin method applied to canonical scattering problems. International Symposium on Electromagnetic Theory : EMTS, 2010 URSI. 752-755.
- Kaufmann, T., Fumeaux, C., Engström, C., Vahldieck, R. (2009). Meshless eigenvalue analysis for resonant structures based on the radial point interpolation method. Microwave conference : 2009, APMC, Asia, Pasific. 818-821.
- Engström, C. (2005). Bounds on effective anisotropic material parameters. ICEAA 2005 - 9th International Conference on Electromagnetics in Advanced Applications and EESC 2005 - 11th European Electromagnetic Structures Conference. 745-748.
- Engström, C., Sjöberg, D. (2004). A Comparison of two numerical methods for homogenization of Maxwell's equations. Computational Electromagnetics- Methods and Applications (EMB04), Gothenburg, Sweden, October 18-19, 2004. 50-57.
- Engström, C., Sjöberg, D. (2004). Numerical methods for homogenization of Maxwell's equations. URSI 2004 International Symposium on Electromagnetic Theory. 987-989.
- Sjöberg, D., Kristensson, G., Engström, C. (2003). Validity of homogenization using Bloch waves. ICEAA 2003 - International Conference on Electromagnetics in Advanced Applications. 455-458.
- Engström, C., Kristensson, G., Sjöberg, D., Wall, D., Wellander, N. (2003). Homogenization of the Maxwell equations using Floquet-Bloch decomposition. Mathematical and numerical waves 2003 : aspect of wave propagation. 412-416.
Manuscript (preprint) (Other academic)
- Engström, C. (2020). Spectra of Gurtin-Pipkin type of integro-differential equations and applications to waves in graded viscoelastic structures.
- Araujo Cabarcas, J.C., Compos, C., Engström, C., Roman, J. (2019). Computation of scattering resonances in absorptive and dispersive mediawith applications to metal-dielectric nano-structures.
- Araújo Cabarcas, J.C., Engström, C. (2019). On spurious solutions encountered in Helmholtz scattering resonance computations in Rd with applications to nano-photonics and acoustics. 32.
- Araujo Caracas, J.C., Engström, C., Jarlebring, E. (2016). Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map.