10 citations · 11 across the 11 of their papers we have counts for
12 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…
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…
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…
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…
Optimized Schwarz methods for heterogeneous heat transfer problems
Martin J. Gander, Liu-Di Lu, Tingting Wu
We present here nonoverlapping optimized Schwarz methods applied to heat transfer problems with heterogeneous diffusion coefficients. After a Laplace transform in time, we derive t…
Discontinuous Galerkin time integration for second-order differential problems: formulations, analysis, and analogies
Gabriele Ciaramella, Martin J. Gander, Ilario Mazzieri
We thoroughly investigate Discontinuous Galerkin (DG) discretizations as time integrators for second-order oscillatory systems, considering both second-order and first-order formul…
Time parallelization for hyperbolic and parabolic problems
Martin J. Gander, Shu-Lin Wu, Tao Zhou
Time parallelization, also known as PinT (Parallel-in-Time) is a new research direction for the development of algorithms used for solving very large scale evolution problems on hi…
Natural damping of time-harmonic waves and its influence on Schwarz methods
Martin J. Gander, Hui Zhang
The influence of various damping on the performance of Schwarz methods for time-harmonic waves is visualized by Fourier analysis.
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)\backslashπ…
A Parareal algorithm without Coarse Propagator?
Martin J. Gander, Mario Ohlberger, Stephan Rave
The Parareal algorithm was invented in 2001 in order to parallelize the solution of evolution problems in the time direction. It is based on parallel fine time propagators called F…
Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning
Faycal Chaouqui, Martin J. Gander, Pratik M. Kumbhar +1
Substructured domain decomposition (DD) methods have been extensively studied, and they are usually associated with nonoverlapping decompositions. We introduce here a substructured…