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

MUMPS is a public domain software package for the multifrontal solution of large sparse
linear systems on distributed memory computers. The matrices can be symmetric positive …

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 …

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 …

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 robust two-level overlap** Schwarz method for scalar elliptic model problems with
highly varying coefficient functions is introduced. While the convergence of standard coarse …

Two-level overlap** Schwarz domain decomposition methods for second-order elliptic
problems in two dimensions are proposed using coarse spaces constructed from the …

Domain decomposition methods are robust and parallel scalable, preconditioned iterative
algorithms for the solution of the large linear systems arising in the discretization of elliptic …

The numerical solution of continuum damage mechanics (CDM) problems suffers from
convergence-related challenges during the material softening stage, and consequently …