17 citations · 76 across the 18 of their papers we have counts for
20 papers
FEM-BEM coupling for the high-frequency Helmholtz problem
Jens Markus Melenk, Ilaria Perugia, Alexander Rieder
We present a wavenumber-explicit analysis of FEM-BEM coupling methods for time-harmonic Helmholtz problems proposed in arXiv:2004.03523 for conforming discretizations and in arXiv:…
Towards optimal hierarchical training of neural networks
Michael Feischl, Alexander Rieder, Fabian Zehetgruber
We propose a hierarchical training algorithm for standard feed-forward neural networks that adaptively extends the network architecture as soon as the optimization reaches a statio…
A -version of convolution quadrature in wave propagation
Alexander Rieder
We consider a novel way of discretizing wave scattering problems using the general formalism of convolution quadrature, but instead of reducing the timestep size (-method), we a…
On interpolation spaces of piecewise polynomials on mixed meshes
Michael Karkulik, Jens Markus Melenk, Alexander Rieder
We consider fractional Sobolev spaces , , on 2D domains and -conforming discretizations by globally continuous piecewise polynomials on a mesh consisting of s…
FEM-BEM coupling in Fractional Diffusion
Markus Faustmann, Alexander Rieder
We derive and analyze a fully computable discrete scheme for fractional partial differential equations posed on the full space . Based on a reformulation using the w…
Fractional Diffusion in the full space: decay and regularity
Markus Faustmann, Alexander Rieder
We consider fractional partial differential equations posed on the full space . Using the well-known Caffarelli-Silvestre extension to as equivalent defini…
An exponentially convergent discretization for space-time fractional parabolic equations using -FEM
Jens Markus Melenk, Alexander Rieder
We consider a space-time fractional parabolic problem. Combining a sinc-quadrature based method for discretizing the Riesz-Dunford integral with -FEM in space yields an exponen…
Mortar coupling of -discontinuous Galerkin and boundary element methods for the Helmholtz equation
Christoph Erath, Lorenzo Mascotto, Jens Markus Melenk +2
We design and analyze a coupling of a discontinuous Galerkin finite element method with a boundary element method to solve the Helmholtz equation with variable coefficients in thre…
Double exponential quadrature for fractional diffusion
Alexander Rieder
We introduce a novel discretization technique for both elliptic and parabolic fractional diffusion problems based on double exponential quadrature formulas and the Riesz-Dunford fu…
Time domain boundary integral equations and convolution quadrature for scattering by composite media (extended preprint)
Alexander Rieder, Francisco-Javier Sayas, Jens Markus Melenk
We consider acoustic scattering in heterogeneous media with piecewise constant wave number. The discretization is carried out using a Galerkin boundary element method in space and…
Metastable Speeds in the Fractional Allen-Cahn Equation
Franz Achleitner, Christian Kuehn, Jens Markus Melenk +1
We study numerically the one-dimensional Allen-Cahn equation with the spectral fractional Laplacian on intervals with homogeneous Neumann boundary conditions. In parti…
FEM-BEM mortar coupling for the Helmholtz problem in three dimensions
Lorenzo Mascotto, Jens Markus Melenk, Ilaria Perugia +1
We present a FEM-BEM coupling strategy for time-harmonic acoustic scattering in media with variable sound speed. The coupling is realized with the aid of a mortar variable that is…
Runge-Kutta approximation for -semigroups in the graph norm with applications to time domain boundary integral equations
Alexander Rieder, Francisco-Javier Sayas, Jens Markus Melenk
We consider the approximation to an abstract evolution problem with inhomogeneous side constraint using -stable Runge-Kutta methods. We derive a priori estimates in norms other…
On superconvergence of Runge-Kutta convolution quadrature for the wave equation
Jens Markus Melenk, Alexander Rieder
The semidiscretization of a sound soft scattering problem modelled by the wave equation is analyzed. The spatial treatment is done by integral equation methods. Two temporal discre…
-FEM for the fractional heat equation
Jens Markus Melenk, Alexander Rieder
We consider a time dependent problem generated by a nonlocal operator in space. Applying a discretization scheme based on -Finite Elements and a Caffarelli-Silvestre extension…
Stable decompositions of -BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D
Michael Karkulik, Jens Markus Melenk, Alexander Rieder
We consider fractional Sobolev spaces , , on a 2D surface . We show that functions in can be decomposed into contributions with local support in a s…
Time-domain boundary integral equation modeling of heat transmission problems
Tianyu Qiu, Alexander Rieder, Francisco-Javier Sayas +1
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoret…
Runge-Kutta convolution quadrature and FEM-BEM coupling for the time dependent linear Schrödinger equation
Jens Markus Melenk, Alexander Rieder
We propose a numerical scheme to solve the time dependent linear Schrödinger equation. The discretization is carried out by combining a Runge-Kutta time-stepping scheme with a fini…
Convolution quadrature for the wave equation with a nonlinear impedance boundary condition
Lehel Banjai, Alexander Rieder
A rarely exploited advantage of time-domain boundary integral equations compared to their frequency counterparts is that they can be used to treat certain nonlinear problems. In th…
Optimal additive Schwarz methods for the -BEM: the hypersingular integral operator in 3D on locally refined meshes
Thomas Führer, Jens Markus Melenk, Dirk Praetorius +1
We propose and analyze an overlapping Schwarz preconditioner for the and boundary element method for the hypersingular integral equation in 3D. We consider surface triangu…