MFEM: A modular finite element methods library

R Anderson, J Andrej, A Barker, J Bramwell… - … & Mathematics with …, 2021 - Elsevier
MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite
element methods that features arbitrary high-order finite element meshes and spaces …

[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 …

BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields

DS Oh, O Widlund, S Zampini, C Dohrmann - Mathematics of Computation, 2018 - ams.org
A BDDC domain decomposition preconditioner is defined by a coarse component,
expressed in terms of primal constraints, a weighted average across the interface between …

Adaptive selection of primal constraints for isogeometric BDDC deluxe preconditioners

LB Da Veiga, LF Pavarino, S Scacchi, OB Widlund… - SIAM Journal on …, 2017 - SIAM
Isogeometric analysis has been introduced as an alternative to finite element methods in
order to simplify the integration of computer-aided design (CAD) software and the …

Multilevel balancing domain decomposition by constraints deluxe algorithms with adaptive coarse spaces for flow in porous media

S Zampini, X Tu - SIAM Journal on Scientific Computing, 2017 - SIAM
Multilevel balancing domain decomposition by constraints (BDDC) deluxe algorithms are
developed for the saddle point problems arising from mixed formulations of Darcy flow in …

Robust and scalable adaptive BDDC preconditioners for virtual element discretizations of elliptic partial differential equations in mixed form

F Dassi, S Zampini, S Scacchi - Computer Methods in Applied Mechanics …, 2022 - Elsevier
Abstract The Virtual Element Method (VEM) is a recent numerical technology for the solution
of partial differential equations on computational grids constituted by polygonal or …

Hierarchical matrix approximations of Hessians arising in inverse problems governed by PDEs

I Ambartsumyan, W Boukaram, T Bui-Thanh… - SIAM Journal on …, 2020 - SIAM
Hessian operators arising in inverse problems governed by partial differential equations
(PDEs) play a critical role in delivering efficient, dimension-independent convergence for …

Block FETI–DP/BDDC preconditioners for mixed isogeometric discretizations of three-dimensional almost incompressible elasticity

O Widlund, S Zampini, S Scacchi, L Pavarino - Mathematics of Computation, 2021 - ams.org
A block FETI–DP/BDDC preconditioner for mixed formulations of almost incompressible
elasticity is constructed and analyzed; FETI–DP (Finite Element Tearing and Interconnecting …

BDDC deluxe algorithms for two-dimensional H (curl) isogeometric analysis

OB Widlund, S Scacchi, LF Pavarino - SIAM Journal on Scientific Computing, 2022 - SIAM
Isogeometric analysis has been introduced as an alternative to finite elements to simplify the
integration of computer-aided design and the discretization of variational problems of …

Balancing domain decomposition by constraints algorithms for curl-conforming spaces of arbitrary order

S Zampini, P Vassilevski, V Dobrev, T Kolev - … Decomposition Methods in …, 2018 - Springer
Abstract We construct Balancing Domain Decomposition by Constraints methods for the
linear systems arising from arbitrary order, finite element discretizations of the H (curl) model …