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 …
[图书][B] Lecture notes in computational science and engineering
TJ Barth, M Griebel, DE Keyes, RM Nieminen, D Roose… - 2005 - Springer
The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …
models based on differential equations. Initially, the FEniCS Project consisted of two …
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 …
Automatic spectral coarse spaces for robust finite element tearing and interconnecting and balanced domain decomposition algorithms
N Spillane, DJ Rixen - International Journal for Numerical …, 2013 - Wiley Online Library
We introduce spectral coarse spaces for the balanced domain decomposition and the finite
element tearing and interconnecting methods. These coarse spaces are specifically …
element tearing and interconnecting methods. These coarse spaces are specifically …
FETI-DP methods with an adaptive coarse space
A Klawonn, P Radtke, O Rheinbach - SIAM Journal on Numerical Analysis, 2015 - SIAM
A coarse space is constructed for the dual-primal finite element tearing and interconnecting
(FETI-DP) domain decomposition method applied to highly heterogeneous problems by …
(FETI-DP) domain decomposition method applied to highly heterogeneous problems by …
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) …
A robust two-level overlapping preconditioner for Darcy flow in high-contrast media
In this article, a two-level overlapping domain decomposition preconditioner is developed for
solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media …
solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media …
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 …