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Everything about Domain decomposition methods
Type of numerical method
In mathematics, numerical analysis, and numerical partial differential equations, domain decomposition methods solve a boundary value problem by splitting it into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. A coarse problem with one or few unknowns per subdomain is used to further coordinate the solution between the subdomains globally. The problems on the subdomains are independent, which makes domain decomposition methods suitable for parallel computing. Domain decomposition methods are typically used as preconditioners for Krylov space iterative methods, such as the conjugate gradient method, GMRES, and LOBPCG. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Domain decomposition methodsA 5-minute orientation
- Skim a recent paper: Machine learning and domain decomposition methods - a surveyInfluential work since 2022
- Pick up a classic book: Domain decomposition methods in sciences and engineeringThe most-reprinted book on the subject
- Read the landmark paper: Non-overlapping domain decomposition methods in structural mechanicsCited 173 times
- Go sideways: Additive Schwarz methodA closely related topic
- Go sideways: Numerical methods for partial differential equationsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Non-overlapping domain decomposition methods in structural mechanics
Some Nonoverlapping Domain Decomposition Methods
Isogeometric analysis and domain decomposition methods
Domain decomposition for radial basis meshless methods
Fictitious domain and domain decomposition methods
Domain decomposition methods via boundary integral equations
Parallel efficiency of domain decomposition methods
Domain Decomposition Methods for Domain Composition Purpose: Chimera, Overset, Gluing and Sliding Mesh Methods
🆕 Influential since 2022
Machine learning and domain decomposition methods - a survey
Domain decomposition methods for 3D crack propagation problems using XFEM
New Optimized Robin--Robin Domain Decomposition Methods using Krylov Solvers for the Stokes--Darcy System
Localized model order reduction and domain decomposition methods for coupled heterogeneous systems
Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation
📚 Books worth reading
Domain decomposition methods in sciences and engineeringR. Glowinski · 1997- 📕Domain decomposition preconditioners for the spectral collection methodAlfio Quarteroni · 1988
- 📕Spectral solution of the viscous blunt body problem. II: Multidomain approximationDavid A. Kopriva · 1994
- 📕Newton-Krylov-SchwarzXiao-Chuan Cai · 1995
- 📕Domain decomposition algorithms for first-order system least squares methodsLuca F. Pavarino · 1996
- 📕A conservative staggered-grid Chebyshev multidomain method for compressible flows. II: A semi-structured methodDavid A. Kopriva · 1996
Computer solution of large linear systemsMEURANT, G. Meurant · 1999- 📕Recent advances in scientific computing and applicationsNev.) International Conference on Scientific Computing and Applications (8th 2012 Las Vegas · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Additive Schwarz method In mathematics, the additive Schwarz method, named after Hermann Schwarz, solves a boundary value problem for a partial differential equation approximately…
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- Finite element method Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical…
- Schur complement method In numerical analysis, the Schur complement method, named after Issai Schur, is the basic and the earliest version of non-overlapping domain decomposition…
- Doléans-Dade exponential In stochastic calculus, the Doléans-Dade exponential or stochastic exponential of a semimartingale X is the unique strong solution of the stochastic differentia…
- Fictitious domain method In numerical analysis, the fictitious domain method (FD) is a numerical technique designed to solve partial differential equations on complex geometries…
- Milstein method In mathematics, the Milstein method is a technique for the approximate numerical solution of a stochastic differential equation. It is named after Grigori…
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