Christian Engström

Professor

Institutionen för matematik Fakulteten för teknik

christian.engstrom@lnu.se

0470-70 84 61

070-216 99 42

2045, Hus B, Växjö

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Undervisning

Jag undervisar i kurser inom analys, algebra och beräkningsvetenskap.

Forskning

Partiella differentialekvationer (PDE) är viktiga verktyg för modellering av processer inom vetenskap och teknik. I min forskning utvecklar jag matematisk och numerisk analys som resulterar i robusta och mycket snabba numeriska metoder, vilka kan användas för att bygga digitala tvillingar av vår värld. Nya mycket snabba numeriska metoder utgör en hörnsten i utvecklingen av effektiva maskininlärningsalgoritmer för PDE, optimering med PDE-bivillkor och för osäkerhetskvantifiering.

Resonanser i mekaniska strukturer som hus och broar kan orsaka kraftiga vibrationer som får förödande konsekvenser men resonanser är i andra fall önskvärda, till exempel för att genera en viss ton i ett musikinstrument. I matematiken används spektralteori för att studera resonanser.

I min forskning studerar jag matematik som beskriver resonanser i slutna och öppna system. Jag utvecklar numeriska metoder för dessa problem och studerar tillämpningar inom nano-optik, akustik, värmeledning och mekanik. Jag utvecklar även nya numeriska metoder för tidsberoende och ickelinjära problem.

Jag är under 2022-2027 projektledare det VR-finansierade projektet

Approximation av fraktionella integro-differentialekvationer utan förorening av spektrum

Christian Engström forskar om resonanser.

Mina forskargrupper

Mina pågående forskningsprojekt

Publikationer

Artikel i tidskrift (Refereegranskat)

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: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
Araújo C, J.C., Engström, C. (2021). On spurious solutions encountered in Helmholtz scattering resonance computations in R^d with applications to nano-photonics and acoustics. Journal of Computational Physics. 429. 1-20.
Status: Publicerad
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: Publicerad
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: Publicerad
Engström, C., Torshage, A. (2018). Spectral properties of conservative, dispersive, and absorptive photonic crystals. GAMM - Mitteilungen. 41. 1-16.
Status: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
Engström, C., Grubisic, L. (2015). A subspace iteration algorithm for Fredholm valued functions. Mathematical problems in engineering (Print). 2015. 1-14.
Status: Publicerad
Wadbro, E., Engström, C. (2015). Topology and shape optimization of plasmonic nano-antennas. Computer Methods in Applied Mechanics and Engineering. 293. 155-169.
Status: Publicerad
Engström, C. (2014). Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations. Numerische Mathematik. 126 (3). 413-440.
Status: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
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: Publicerad
Engström, C. (2007). Inverse bounds of two-component composites. SIAM Journal on Applied Mathematics. 68 (3). 666-679.
Status: Publicerad
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: Publicerad
Engström, C. (2007). Structural information of nanocomposites from measured optical properties. Journal of Physics : Condensed Matter. 19 (10).
Status: Publicerad
Engström, C. (2006). Inverse bounds and bulk properties of complex-valued two-component composites. SIAM Journal on Applied Mathematics. 67 (1). 194-213.
Status: Publicerad
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: Publicerad
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: Publicerad

Konferensbidrag (Refereegranskat)

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.

Manuskript (Övrigt vetenskapligt)

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 R^d 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.