Current research fields

  • Numerical  Analysis
  • Boundary element methods (BEM)
  • Finite element methods (FEM)
  • Higher order procedures and hp methods
  • Integral equations in the time domain
  • Convolution quadrature
  • Multi-step and Runge-Kutta methods for semigroups
  • Fractional differential operators

Preprints

  • M. Faustmann, A. Rieder, FEM-BEM coupling in Fractional Diffusion, arXiv:2302.11279 (accepted at IMA J. Numer. Analysis), 2023
  • 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

Publications (peer reviewed)

  1. Alexander Rieder. Double exponential quadrature for fractional diffusion. Numer. Math., 153(2-3):359----410, 2023
    [ DOI | arXiv | http ]
  2. 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 ]
  3. 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 ]
  4. 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 ]
  5. 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 ]
  6. 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 ]
  7. 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 ]
  8. 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 ]
  9. Jens Markus Melenk and Alexander Rieder. hp-FEM for the fractional heat equation. IMA Journal of Numerical Analysis, 04 2020. drz054.
    [ DOI | arXiv | http ]
  10. 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 ]
  11. 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 ]
  12. 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 ]
  13. 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 ]
  14. 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 ]