Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
SIAM Journal on Scientific Computing
Dual-Primal FETI Methods for Three-Dimensional Elliptic Problems with Heterogeneous Coefficients
SIAM Journal on Numerical Analysis
A Preconditioner for Substructuring Based on Constrained Energy Minimization
SIAM Journal on Scientific Computing
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
A Dual-Primal FETI method for incompressible Stokes equations
Numerische Mathematik
Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
SIAM Journal on Scientific Computing
BDDC methods for discontinuous Galerkin discretization of elliptic problems
Journal of Complexity
Three-Level BDDC in Three Dimensions
SIAM Journal on Scientific Computing
A BDDC Algorithm for Mortar Discretization of Elasticity Problems
SIAM Journal on Numerical Analysis
Multispace and multilevel BDDC
Computing
An algebraic theory for primal and dual substructuring methods by constraints
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
A BDDC Method for Mortar Discretizations Using a Transformation of Basis
SIAM Journal on Numerical Analysis
A Three-Level BDDC Algorithm for Mortar Discretizations
SIAM Journal on Numerical Analysis
An Overlapping Schwarz Algorithm for Almost Incompressible Elasticity
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Robust BDDC Preconditioners for Reissner-Mindlin Plate Bending Problems and MITC Elements
SIAM Journal on Numerical Analysis
Journal of Computational Physics
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Balancing domain decomposition by constraints (BDDC) algorithms are constructed and analyzed for the system of almost incompressible elasticity discretized with Gauss-Lobatto-Legendre spectral elements in three dimensions. Initially mixed spectral elements are employed to discretize the almost incompressible elasticity system, but a positive definite reformulation is obtained by eliminating all pressure degrees of freedom interior to each subdomain into which the spectral elements have been grouped. Appropriate sets of primal constraints can be associated with the subdomain vertices, edges, and faces so that the resulting BDDC methods have a fast convergence rate independent of the almost incompressibility of the material. In particular, the condition number of the BDDC preconditioned operator is shown to depend only weakly on the polynomial degree $n$, the ratio $H/h$ of subdomain and element diameters, and the inverse of the inf-sup constants of the subdomains and the underlying mixed formulation, while being scalable, i.e., independent of the number of subdomains and robust, i.e., independent of the Poisson ratio and Young's modulus of the material considered. These results also apply to the related dual-primal finite element tearing and interconnect (FETI-DP) algorithms defined by the same set of primal constraints. Numerical experiments, carried out on parallel computing systems, confirm these results.