10 papers
Dirichlet-Neumann waveform relaxation for heterogeneous heat equations: continuous and time discrete L2 analysis
Niklas Kotarsky, Philipp Birken, Martin J. Gander +1
We consider two coupled linear heat equations on different spatial domains that interact through a lower dimensional interface. This models conjugate heat transfer. The problem is…
A Parareal Algorithm with Low-Rank Coarse Solvers
Martin J. Gander, Mario Ohlberger, Stephan Rave
We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from truncated SVD approximations of the transfe…
Fourier Analysis of Finite Difference Schemes for the Helmholtz Equation in 1D with Dirichlet Conditions: Sharp Estimates and Relative Errors
Martin J. Gander, Hui Zhang, Haiyang Zhou
We consider the Dirichlet problem of the indefinite Helmholtz equation in 1D, in , , , with a constant wavenumber $k\in(0,\infty)\backslashÏ…
Optimized Schwarz Waveform Relaxation for the Damped Wave Equation
Gerardo Cicalese, Gabriele Ciaramella, Ilario Mazzieri +1
The performance of Schwarz Waveform Relaxation is critically dependent on the choice of transmission conditions. While classical absorbing conditions work well for wave propagation…
Hierarchical Coarse Basis by Randomised SVD: the Helmholtz Problem
Martin J. Gander, Yao-Lin Jiang, Hui Zhang
The oscillatory waves require sufficient degrees of freedom to resolve. That restriction usually applies also to coarse problems for Schwarz methods. The resulting coarse problem i…
On an efficient line smoother for the p-multigrid γ-cycle
José Pablo Lucero Lorca, Duane Rosenberg, Isidora Jankov +2
As part of the development of a Poisson solver for the spectral element discretization used in the GeoFluid Object Workbench (GeoFLOW) code, we propose a solver for the linear syst…