Numerical homogenization beyond scale separation

R Altmann, P Henning, D Peterseim - Acta Numerica, 2021 - cambridge.org
Numerical homogenization is a methodology for the computational solution of multiscale
partial differential equations. It aims at reducing complex large-scale problems to simplified …

A parallel implementation of a two-level overlap** Schwarz method with energy-minimizing coarse space based on Trilinos

A Heinlein, A Klawonn, O Rheinbach - SIAM Journal on Scientific Computing, 2016 - SIAM
We describe a new implementation of a two-level overlap** Schwarz preconditioner with
energy-minimizing coarse space (GDSW: generalized Dryja--Smith--Widlund) and show …

The multiscale finite element method for nonlinear continuum localization problems at full fine-scale fidelity, illustrated through phase-field fracture and plasticity

LH Nguyen, D Schillinger - Journal of Computational Physics, 2019 - Elsevier
The residual-driven iterative corrector scheme recently presented by the authors for linear
problems has opened a pathway to achieve the best possible fine-mesh accuracy in the …

Hybrid localized spectral decomposition for multiscale problems

AL Madureira, M Sarkis - SIAM Journal on Numerical Analysis, 2021 - SIAM
We consider a finite element method for elliptic equations with heterogeneous and possibly
high-contrast coefficients based on primal hybrid formulation. We assume minimal regularity …

An adaptive GDSW coarse space for two-level overlap** Schwarz methods in two dimensions

A Heinlein, A Klawonn, J Knepper… - … Decomposition Methods in …, 2018 - Springer
We propose robust coarse spaces for two-level overlap** Schwarz preconditioners, which
are extensions of the energy minimizing coarse space known as GDSW (Generalized Dryja …

A model-updating approach based on the component mode synthesis method and perturbation analysis

T Wang, H He, W Yan, GP Chen - Journal of Sound and Vibration, 2018 - Elsevier
A model-updating approach based on an improved free-interface component mode
synthesis method is proposed. First, the equivalent higher-order matrix of the system is …

Fast-convergent two-level restricted additive Schwarz methods based on optimal local approximation spaces

A Strehlow, C Ma, R Scheichl - ar** Schwarz preconditioners and multiscale discretizations with applications to fluid-structure interaction and highly heterogeneous problems
A Heinlein - 2016 - kups.ub.uni-koeln.de
Accurate simulations of transmural wall stresses in artherosclerotic coronary arteries may
help to predict plaque rupture. Therefore, a robust and efficient numerical framework for …

Parallel adaptive FETI‐DP using lightweight asynchronous dynamic load balancing

A Klawonn, MJ Kühn… - International Journal for …, 2020 - Wiley Online Library
Summary A parallel FETI‐DP domain decomposition method using an adaptive coarse
space is presented. The implementation builds on a recently introduced adaptive FETI‐DP …