Combining machine learning and domain decomposition methods for the solution of partial differential equations—A review
Scientific machine learning (SciML), an area of research where techniques from machine
learning and scientific computing are combined, has become of increasing importance and …
learning and scientific computing are combined, has become of increasing importance and …
Constraint energy minimizing generalized multiscale finite element method
In this paper, we propose Constraint Energy Minimizing Generalized Multiscale Finite
Element Method (CEM-GMsFEM). The main goal of this paper is to design multiscale basis …
Element Method (CEM-GMsFEM). The main goal of this paper is to design multiscale basis …
Machine learning and domain decomposition methods-a survey
Hybrid algorithms, which combine black-box machine learning methods with experience
from traditional numerical methods and domain expertise from diverse application areas, are …
from traditional numerical methods and domain expertise from diverse application areas, are …
PCBDDC: a class of robust dual-primal methods in PETSc
S Zampini - SIAM Journal on Scientific Computing, 2016 - SIAM
A class of preconditioners based on balancing domain decomposition by constraints
methods is introduced in the Portable, Extensible Toolkit for Scientific Computation (PETSc) …
methods is introduced in the Portable, Extensible Toolkit for Scientific Computation (PETSc) …
Adaptive coarse spaces for FETI-DP in three dimensions
An adaptive coarse space approach including a condition number bound for dual primal
finite element tearing and interconnecting (FETI-DP) methods applied to three dimensional …
finite element tearing and interconnecting (FETI-DP) methods applied to three dimensional …
[PDF][PDF] A unified framework for adaptive BDDC
C Pechstein, CR Dohrmann - Electron. Trans. Numer. Anal, 2017 - etna.math.kent.edu
In this theoretical study, we explore how to automate the selection of weights and primal
constraints in BDDC methods for general SPD problems. In particular, we address the three …
constraints in BDDC methods for general SPD problems. In particular, we address the three …
[PDF][PDF] An adaptive choice of primal constraints for BDDC domain decomposition algorithms
JG Calvo, OB Widlund - Electron. Trans. Numer. Anal, 2016 - gwdg.de
An adaptive choice for primal spaces based on parallel sums is developed for BDDC deluxe
methods and elliptic problems in three dimensions. The primal space, which forms the …
methods and elliptic problems in three dimensions. The primal space, which forms the …
A comparison of adaptive coarse spaces for iterative substructuring in two dimensions
A Klawonn, P Radtke… - Electronic Transactions on …, 2016 - etna.ricam.oeaw.ac.at
The convergence rate of iterative substructuring methods generally deteriorates when large
discontinuities occur in the coefficients of the partial differential equations to be solved. In …
discontinuities occur in the coefficients of the partial differential equations to be solved. In …
BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields
A BDDC domain decomposition preconditioner is defined by a coarse component,
expressed in terms of primal constraints, a weighted average across the interface between …
expressed in terms of primal constraints, a weighted average across the interface between …
BDDC and FETI-DP preconditioners with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients
HH Kim, E Chung, J Wang - Journal of Computational Physics, 2017 - Elsevier
Abstract BDDC and FETI-DP algorithms are developed for three-dimensional elliptic
problems with adaptively enriched coarse components. It is known that these enriched …
problems with adaptively enriched coarse components. It is known that these enriched …