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 …
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 …
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 …
Displacement‐based partitioned equations of motion for structures: Formulation and proof‐of‐concept applications
A new formulation for the displacement‐only partitioned equations of motion for linear
structures is presented, which employs: the partitioned displacement, acceleration, and …
structures is presented, which employs: the partitioned displacement, acceleration, and …
[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 …