Scientific machine learning (SciML), an area of research where techniques from machine
learning and scientific computing are combined, has become of increasing importance and …

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 …

Hybrid algorithms, which combine black-box machine learning methods with experience
from traditional numerical methods and domain expertise from diverse application areas, are …

A class of preconditioners based on balancing domain decomposition by constraints
methods is introduced in the Portable, Extensible Toolkit for Scientific Computation (PETSc) …

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 …

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 …

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 …

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 …

A BDDC domain decomposition preconditioner is defined by a coarse component,
expressed in terms of primal constraints, a weighted average across the interface between …

Abstract BDDC and FETI-DP algorithms are developed for three-dimensional elliptic
problems with adaptively enriched coarse components. It is known that these enriched …