Address
Institut für Numerische und Angewandte Mathematik
Georg-August Universität Göttingen
Lotzestr. 16-18
37083 Göttingen, Germany
Room 221
+49 (0)551 39 27872
m.halla [at] math.uni-goettingen.de
Short CV
- 2022- now PostDoc @ Uni Göttingen
- 2021-2022 PostDoc @ MPI for Solar System Research, Göttingen
- 2020-2021 PostDoc @ Uni Göttingen
- 2019-2020 PostDoc @ MPI for Solar System Research, Göttingen
- 2021 Promotio sub auspiciis Praesidentis rei publicae
- 2019 PhD Defense$\phantom{c}$ @ TU Wien
Research interests
Analysis and numerical methods for partial differential equations
- Wave equations (acoustics, elasticity, electromagnetism, plasmonics, stellar oscillations)
- Eigenvalue problems (holomorphic, non-selfadjoint EVPs; existence, stability and approximation of EVs)
- Transparent boundary conditions (perfectly matched layers, infinite elements; backward, anisotropic waves)
- Compatible discretizations (T-coercivity; Galbrun’s equation, sign-changing coefficients, nonstandard Maxwell problems)
- Target signatures in inverse scattering (transmission EVs, Steklov EVs; linear sampling, inside outside duality)
Research projects
- DFG Project 468728622 Analysis of eigenvalue problems arising in qualitative methods for inverse scattering (2022-2024) url
Events
- Spring School Novel Imaging Techniques with Waves, 11.-14.03.2024, Göttingen, url
- 11th Applied Inverse Problems Conference, 03.-08.09.2023, Göttingen, url
- Minisymposium Eigenvalues in inverse scattering at the 11th Applied Inverse Problems Conference, 03.-08.09.2023, Göttingen, url
- Minisymposium Mathematical aspects of wave propagation in plasmonic structures at the Conference on Mathematics of Wave Phenomena, 14.-18.02.2022, Karlsruhe, url
Publications
Technical reports
[5] A new numerical method for scalar eigenvalue problems in heterogeneous, dispersive, sign-changing materials
M. Halla, T. Hohage, F. Oberender
arXiv:2401.16368
[4] Radial perfectly matched layers and infinite elements for the anisotropic wave equation
M. Halla, M. Kachanovska, M. Wess
arXiv:2401.13483
[3] Convergence analysis of nonconform H(div)-finite elements for the damped time-harmonic Galbrun’s equation
M. Halla
arXiv:2306.03496
[2] On the analysis of waveguide modes in an electromagnetic transmission line
M. Halla, P. Monk
arXiv:2302.11994
[1] A new T-compatibility condition and its application to the discretization of the damped time-harmonic Galbrun’s equation
M. Halla, C. Lehrenfeld, P. Stocker
arXiv:2209.01878
Refereed articles
[13] On the existence and stability of modified Maxwell Steklov eigenvalues
M. Halla
SIAM Journal on Mathematical Analysis, Volume 55, Issue 5, Pages 5445-5463 (2023)
[12] Electromagnetic Steklov eigenvalues: existence and distribution in the self-adjoint case
M. Halla
Research in the Mathematical Sciences, Volume 10, Issue 2, Article 18 (2023)
[11] On the approximation of dispersive electromagnetic eigenvalue problems in two dimensions
M. Halla
IMA Journal of Numerical Analysis, Volume 43, Issue 1, Pages 535-55 (2023)
[10] Radial complex scaling for anisotropic scalar resonance problems
M. Halla
SIAM Journal on Numerical Analysis, Volume 60, Issue 5, Pages 2713-2730 (2022)
[9] On the treatment of exterior domains for the time-harmonic equations of stellar oscillations
M. Halla
SIAM Journal on Mathematical Analysis, Volume 54, Issue 5, Pages 5268-5290 (2022)
[8] On the well-posedness of the damped time-harmonic Galbrun equation and the equations of stellar oscillations
M. Halla, T. Hohage
SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Pages 4068-4095 (2021)
[7] Analysis of radial complex scaling methods: scalar resonance problems
M. Halla
SIAM Journal on Numerical Analysis, Volume 59, Issue 4, Pages 2054-2074, (2021)
[6] Galerkin approximation of holomorphic eigenvalue problems: weak T-coercivity and T-compatibility
M. Halla
Numerische Mathematik, Volume 148, Issue 2, Pages 387-407, (2021)
[5] Electromagnetic Steklov eigenvalues: approximation analysis
M. Halla
ESAIM: Mathematical Modelling and Numerical Analysis, Volume 55, Number 1, Pages 57-76, (2021)
[4] Two scale Hardy space infinite elements for scalar waveguide problems
M. Halla, L. Nannen
Advances in Computational Mathematics, Volume 44, Issue 3, Pages 611-643 (2018)
[3] Convergence of Hardy space infinite elements for Helmholtz scattering and resonance problems
M. Halla
SIAM Journal on Numerical Analysis, Volume 54, Issue 3, Pages 1385–1400 (2016)
[2] Hardy Space Infinite Elements for Time Harmonic Wave Equations with Phase and Group Velocities of Different Signs
M. Halla, T. Hohage, L. Nannen, J. Schöberl
Numerische Mathematik, Volume 133, Issue 1, Pages 103–139 (2016)
[1] Hardy space infinite elements for time-harmonic two-dimensional elastic waveguide problems
M. Halla, L. Nannen
Wave Motion, Volume 59, Pages 94-110 (2015)
Thesis
Analysis of radial complex scaling methods for scalar resonance problems in open systems
M. Halla
PhD Thesis, Technische Universität Wien (2019)