Aktuelle Forschungsfelder

  • Numerische  Analysis
  • Randelementmethoden (BEM)
  • Finite Element Methoden (FEM)
  • Verfahren höherer ordnung und hp-Methoden
  • Integralgleichungen im Zeitbereich
  • Faltungsquadratur
  • Mehrschritt- und Runge-Kutta Methoden für Halbgruppen
  • Fraktionale Differentialoperatoren

Preprints

  • M. Faustmann, A. Rieder, Fractional Diffusion in the full space: decay and regularity, arXiv:2301.05503, 2023
  • M. Karkulik, J. M. Melenk, A. Rieder, On interpolation spaces of piecewise polynomials on mixed meshes, arXiv:2306.16907, 2023
  • A. Rieder, A p-version of convolution quadrature in wave propagation, arXiv:2402.17712, 2024
  • J.M. Melenk, I. Perugia, A.Rieder, FEM-BEM coupling for the high-frequency Helmholtz problem, arXiv:2407.04428, 2024
  • M.Feischl, A.Rieder, F. Zehetgruber, Towards optimal hierarchical training of neural networks, arXiv:2407.02242, 2024

Publikationen (peer reviewed)

  1. Markus Faustmann, Alexander Rieder. FEM-BEM coupling in fractional diffusion. IMA Journal of Numerical Analysis,06 2024.  drae026
    [ DOI | arXiv | http ]
  2. Alexander Rieder. Double exponential quadrature for fractional diffusion. Numer. Math., 153(2-3):359----410, 2023
    [ DOI | arXiv | http ]
  3. Jens Markus Melenk and Alexander Rieder. An exponentially convergent discretization for space–time fractional parabolic equations using hp-FEM. IMA Journal of Numerical Analysis, 10 2022. drac045.
    [ DOI | arXiv | http ]
  4. Christoph Erath, Lorenzo Mascotto, Jens M. Melenk, Ilaria Perugia, and Alexander Rieder. Mortar coupling of hp-discontinuous Galerkin and boundary element methods for the Helmholtz equation. J. Sci. Comput., 92(1):Paper No. 2, 41, 2022.
    [ DOI | arXiv | http ]
  5. Alexander Rieder, Francisco-Javier Sayas, and Jens Markus Melenk. Time domain boundary integral equations and convolution quadrature for scattering by composite media. Math. Comp., 91(337):2165--2195, 2022.
    [ DOI | arXiv | http ]
  6. Franz Achleitner, Christian Kuehn, Jens M. Melenk, and Alexander Rieder. Metastable speeds in the fractional Allen-Cahn equation. Appl. Math. Comput., 408:126329, 2021.
    [ DOI | arXiv | http ]
  7. Jens Markus Melenk and Alexander Rieder. On superconvergence of Runge-Kutta convolution quadrature for the wave equation. Numer. Math., 147(1):157--188, 2021.
    [ DOI | arXiv | http ]
  8. Alexander Rieder, Francisco-Javier Sayas, and Jens Markus Melenk. Rungekutta approximation for c_0-semigroups in the graph norm with applications to time domain boundary integral equations. SN Partial Differential Equations and Applications, 1(6), November 2020.
    [ DOI | arXiv | http ]
  9. Lorenzo Mascotto, Jens M. Melenk, Ilaria Perugia, and Alexander Rieder. FEM-BEM mortar coupling for the Helmholtz problem in three dimensions. Comput. Math. Appl., 80(11):2351--2378, 2020.
    [ DOI | arXiv | http ]
  10. Jens Markus Melenk and Alexander Rieder. hp-FEM for the fractional heat equation. IMA Journal of Numerical Analysis, 04 2020. drz054.
    [ DOI | arXiv | http ]
  11. Michael Karkulik, Jens Markus Melenk, and Alexander Rieder. Stable decompositions of hp-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D. ESAIM Math. Model. Numer. Anal., 54(1):145--180, 2020.
    [ DOI | arXiv | http ]
  12. Tianyu Qiu, Alexander Rieder, Francisco-Javier Sayas, and Shougui Zhang. Time-domain boundary integral equation modeling of heat transmission problems. Numer. Math., 143(1):223--259, 2019.
    [ DOI | arXiv | http ]
  13. Jens Markus Melenk and Alexander Rieder. Runge-Kutta convolution quadrature and FEM-BEM coupling for the time-dependent linear Schrödinger equation. J. Integral Equations Appl., 29(1):189--250, 2017.
    [ DOI | arXiv | http ]
  14. Lehel Banjai and Alexander Rieder. Convolution quadrature for the wave equation with a nonlinear impedance boundary condition. Mathematics of Computation, page 1, 2017.
    [ DOI | arXiv | http ]
  15. T. Führer, J. M. Melenk, D. Praetorius, and A. Rieder. Optimal additive Schwarz methods for the hp-BEM: the hypersingular integral operator in 3D on locally refined meshes. Comput. Math. Appl., 70(7):1583--1605, 2015.
    [ DOI | arXiv | http ]