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 …
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 …
[图书][B] Finite and boundary element tearing and interconnecting solvers for multiscale problems
C Pechstein - 2012 - books.google.com
Tearing and interconnecting methods, such as FETI, FETI-DP, BETI, etc., are among the
most successful domain decomposition solvers for partial differential equations. The …
most successful domain decomposition solvers for partial differential equations. The …
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) …
[图书][B] Preconditioning and the conjugate gradient method in the context of solving PDEs
Our times can be characterized by, among many other attributes, the seemingly increasing
speed of everything. Within science, it has led to the publication explosion, which reflects the …
speed of everything. Within science, it has led to the publication explosion, which reflects the …
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 …
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 …
Nonlinear feti-dp and bddc methods
New nonlinear FETI-DP (dual-primal finite element tearing and interconnecting) and BDDC
(balancing domain decomposition by constraints) domain decomposition methods are …
(balancing domain decomposition by constraints) domain decomposition methods are …