BDDC and FETI-DP for the Virtual Element Method

Abstract

We build and analyze Balancing Domain Decomposition by Constraint (BDDC) and Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) preconditioners for elliptic problems discretized by the virtual element method (VEM). We prove polylogarithmic condition number bounds, independent of the number of subdomains, the mesh size, and jumps in the diffusion coefficients. Numerical experiments confirm the theory.

References in corpus (5)

• On the Virtual Element Method for Three-Dimensional Elasticity Problems on Arbitrary Polyhedral Meshes
• A Virtual Element Method for elastic and inelastic problems on polytope meshes
• BDDC and FETI-DP under Minimalist Assumptions
• Exponential convergence of the hp Virtual Element Method with corner singularities
• A multigrid algorithm for the $p$-version of the Virtual Element Method

Cited by in corpus (11)

• A three-dimensional Hellinger-Reissner Virtual Element Method for linear elasticity problems
• $C^1$ Virtual Element Method on polyhedral meshes
• A posteriori error estimation and adaptivity in $hp$ virtual elements
• Weakly imposed Dirichlet boundary conditions for 2D and 3D Virtual Elements
• FETI-DP for the three-dimensional Virtual Element Method
• The $p$- and $hp$-versions of the virtual element method for elliptic eigenvalue problems
• Reduced basis stabilization and post-processing for the virtual element method
• Non-conforming harmonic virtual element method: $h$- and $p$-versions
• Parallel solvers for virtual element discretizations of elliptic equations in mixed form
• Auxiliary space preconditioners for virtual element methods on polytopal meshes
• Algebraic Multigrid Methods For Virtual Element Discretizations: A Numerical Study