Concept
Multigrid method
Publications associées (240)
Randomized flexible GMRES with deflated restarting
For a high dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in computational costs as well as numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g. to the generaliz ...
Springer2024A multigrid method for PDE-constrained optimization with uncertain inputs
We present a multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty. The algorithm is based on a collective smoother that at each iteration sweeps over the ...
2023An optimal preconditioned FFT-accelerated finite element solver for homogenization
Till Junge, Ali Falsafi, Martin Ladecký
We generalize and provide a linear algebra-based perspective on a finite element (FE) ho-mogenization scheme, pioneered by Schneider et al. (2017)[1] and Leuschner and Fritzen (2018)[2]. The efficiency of the scheme is based on a preconditioned, well-scale ...
ELSEVIER SCIENCE INC2023Comparing end-tidal CO2, respiration volume per time (RVT), and average gray matter signal for mapping cerebrovascular reactivity amplitude and delay with breath-hold task BOLD fMRI
Cerebrovascular reactivity (CVR), defined as the cerebral blood flow response to a vasoactive stimulus, is an imaging biomarker with demonstrated utility in a range of diseases and in typical development and aging processes. A robust and widely implemented ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2023Spectral Coarse Spaces for the Substructured Parallel Schwarz Method
The parallel Schwarz method (PSM) is an overlapping domain decomposition (DD) method to solve partial differential equations (PDEs). Similarly to classical nonoverlapping DD methods, the PSM admits a substructured formulation, that is, it can be formulated ...
2022