Everything about BDDC
Method In numerical analysis
In numerical analysis, BDDC (balancing domain decomposition by constraints) is a domain decomposition method for solving large symmetric, positive definite systems of linear equations that arise from the finite element method. BDDC is used as a preconditioner to the conjugate gradient method. A specific version of BDDC is characterized by the choice of coarse degrees of freedom, which can be values at the corners of the subdomains, or averages over the edges or the faces of the interface between the subdomains. One application of the BDDC preconditioner then combines the solution of local problems on each subdomains with the solution of a global coarse problem with the coarse degrees of freedom as the unknowns. The local problems on different subdomains are completely independent of each other, so the method is suitable for parallel computing. With a proper choice of the coarse degrees of freedom (corners in 2D, corners plus edges or corners plus faces in 3D) and with regular subdomain shapes, the condition number of the method is bounded when increasing the number of subdomains, and it grows only very slowly with the number of elements per subdomain. Thus the number of iterations is bounded in the same way, and the method scales well with the problem size and the number of subdomains. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: BDDCA 5-minute orientation
- Skim a recent paper: Convergence Analysis of BDDC Preconditioners for Composite DG Discretizations of the Cardiac Cell-By-Cell ModelInfluential work since 2022
- Read the landmark paper: FETI-DP, BDDC, and block Cholesky methodsCited 176 times
- Go sideways: FETI-DPA closely related topic
- Go sideways: Balancing domain decomposition methodA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
FETI-DP, BDDC, and block Cholesky methods
Adaptive selection of face coarse degrees of freedom in the BDDC and the FETI-DP iterative substructuring methods
BDDC Algorithms for Incompressible Stokes Equations
BDDC PRECONDITIONERS FOR ISOGEOMETRIC ANALYSIS
Isogeometric BDDC Preconditioners with Deluxe Scaling
BDDC methods for discontinuous Galerkin discretization of elliptic problems
BDDC and FETI-DP without matrices or vectors
Three-Level BDDC in Three Dimensions
🆕 Influential since 2022
Convergence Analysis of BDDC Preconditioners for Composite DG Discretizations of the Cardiac Cell-By-Cell Model
Parallel Newton--Krylov BDDC and FETI-DP Deluxe Solvers for Implicit Time discretizations of the Cardiac Bidomain Equations
Newton–Krylov-BDDC deluxe solvers for non-symmetric fully implicit time discretizations of the bidomain model
Robust and scalable adaptive BDDC preconditioners for virtual element discretizations of elliptic partial differential equations in mixed form
BDDC Deluxe Algorithms for Two-Dimensional H($curl$) Isogeometric Analysis
📚 Books worth reading
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🔗 Related topics
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- Coarse space (numerical analysis) In numerical analysis, coarse problem is an auxiliary system of equations used in an iterative method for the solution of a given larger system of equations…
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