Christian Engström
ProfessorUndervisning
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
Mina forskargrupper
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AI och maskininlärning för optimering och operationsanalys Under detta forskningstema utvecklar vi både matematisk teori och tillämpningar för artificiell intelligens och maskininlärning inom områden…
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Deterministic and Stochastic Modelling Forskningsområdet Deterministic and Stochastic Modelling inom Linnaeus University Centre for Data Intensive Sciences and Applications (DISA) samlar forskare med…
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Waves, Signals and Systems Forskningen inom vågor, signaler och system handlar främst om akustiska och elektromagnetiska direkta och inversa problem, med tillämpningar inom teknik och industri.
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Vetenskapliga beräkningar och partiella differentialekvationer Under detta forskningstema studeras beräkningsmetoder för partiella differentialekvationer, analys av differential- och…
Mina pågående forskningsprojekt
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Projekt: Effektiva och tillförlitliga beräkningar av spridningsresonanser Beräkningar av spridningsresonanser är inom nanooptik viktiga för utvecklingen av fototermisk cancerterapi, optiska antenner…
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Projekt: Optimering med PDE-bivillkor Partiella differentialekvationer (PDE) används för att modellera ett stort antal fenomen inom vetenskap och teknik. Optimeringsproblem med PDE-bivillkor uppstår…
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Projekt: Spektralteori för obegränsade operatorfunktioner Avancerade tidsberoende material används för att modellera viskoelastiska egenskaper hos trä, vågutbredning av ultraljud och system med…
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Projekt: Vågutbredning och strålningstransport i atmosfären Vågutbredning och strålningstransport i atmosfären är ett modernt forskningsområde med omedelbar anknytning till växthuseffekten och den…
Publikationer
Artikel i tidskrift (Refereegranskat)
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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.
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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.
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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.
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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.
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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.
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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).
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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.
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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.
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Engström, C., Torshage, A. (2018). Accumulation of complex eigenvalues of a class of analytic operator functions. Journal of Functional Analysis. 275 (2). 442-477.
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Engström, C., Torshage, A. (2018). Spectral properties of conservative, dispersive, and absorptive photonic crystals. GAMM - Mitteilungen. 41. 1-16.
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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.
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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.
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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.
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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.
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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.
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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.
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Engström, C., Grubisic, L. (2015). A subspace iteration algorithm for Fredholm valued functions. Mathematical problems in engineering (Print). 2015. 1-14.
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Wadbro, E., Engström, C. (2015). Topology and shape optimization of plasmonic nano-antennas. Computer Methods in Applied Mechanics and Engineering. 293. 155-169.
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Engström, C. (2014). Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations. Numerische Mathematik. 126 (3). 413-440.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Engström, C. (2007). Inverse bounds of two-component composites. SIAM Journal on Applied Mathematics. 68 (3). 666-679.
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Engström, C., Sjöberg, D. (2007). On two numerical methods for homogenization of Maxwell's equations. Journal Electromagnetic Waves and Applications. 21 (13). 1845-1856.
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Engström, C. (2007). Structural information of nanocomposites from measured optical properties. Journal of Physics : Condensed Matter. 19 (10).
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Engström, C. (2006). Inverse bounds and bulk properties of complex-valued two-component composites. SIAM Journal on Applied Mathematics. 67 (1). 194-213.
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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.
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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 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.