Live briefing
Everything about Additive Schwarz method
In mathematics, the additive Schwarz method, named after Hermann Schwarz, solves a boundary value problem for a partial differential equation approximately by splitting it into boundary value problems on smaller domains and adding the results. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Additive Schwarz methodA 5-minute orientation
- Skim a recent paper: Additive Schwarz methods for convex optimization with backtrackingInfluential work since 2022
- Pick up a classic book: An additive variant of the Schwarz alternating method for the case of many subregionsThe most-reprinted book on the subject
- Read the landmark paper: Additive Schwarz methods for thep-version finite element methodCited 69 times
- Go sideways: Domain decomposition methodsA closely related topic
- Go sideways: Finite element methodA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Additive Schwarz methods for thep-version finite element method
Unstructured Additive Schwarz--Conjugate Gradient Method for Elliptic Problems with Highly Discontinuous Coefficients
Additive schwarz methods for the H-version boundary element method
An additive Schwarz method for variational inequalities
An Additive Schwarz Method Type Theory for Lions's Algorithm and a Symmetrized Optimized Restricted Additive Schwarz Method
Multilevel additive Schwarz method for the ℎ-𝑝 version of the Galerkin boundary element method
Convergence Analysis of Two-Level Space-Time Additive Schwarz Method for Parabolic Equations
On Convergence of the Additive Schwarz Preconditioned Inexact Newton Method
🆕 Influential since 2022
Additive Schwarz methods for convex optimization with backtracking
Additive Schwarz Methods for Fourth-Order Variational Inequalities
Cache-optimized and low-overhead implementations of additive Schwarz methods for high-order FEM multigrid computations
On the linear convergence of additive Schwarz methods for the p-Laplacian
Accelerated Restricted Additive Schwarz method for asynchronous processing
📚 Books worth reading
An additive variant of the Schwarz alternating method for the case of many subregionsMaksymilian Dryja · 1987
Multilevel additive Schwarz methodsXuejun Zhang · 1991
Additive Schwarz methods for elliptic finite element problems in three dimensionsMaksymilian Dryja · 1991
The Mathematical Theory of Finite Element MethodsSusanne C. Brenner · 2002
Parallel Solution of Partial Differential EquationsPetter Bjørstad · 2000
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Domain decomposition methods In mathematics, numerical analysis, and numerical partial differential equations, domain decomposition methods solve a boundary value problem by splitting…
- Finite element method Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical…
- Neumann–Neumann methods In mathematics, Neumann–Neumann methods are domain decomposition preconditioners named so because they solve a Neumann problem on each subdomain on both…
- Numerical methods for partial differential equations Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations…
- List of numerical analysis topics This is a list of numerical analysis topics. Validated numerics Iterative method Rate of convergence — the speed at which a convergent sequence approaches…
- Numerical methods for ordinary differential equations Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations…
- Spectral method Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The…
- Numerical linear algebra Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which…