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Everything about Multigrid method
Method of solving differential equations
In numerical analysis, a multigrid method is an algorithm for solving differential equations using a hierarchy of discretizations. They are an example of a class of techniques called multiresolution methods, very useful in problems exhibiting multiple scales of behavior. For example, many basic relaxation methods exhibit different rates of convergence for short- and long-wavelength components, suggesting these different scales be treated differently, as in a Fourier analysis approach to multigrid. MG methods can be used as solvers as well as preconditioners. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Multigrid methodA 5-minute orientation
- Skim a recent paper: Multigrid Method for Solving Inverse Problems for Heat EquationInfluential work since 2022
- Pick up a classic book: Multigrid finite element methods for electromagnetic field modelingThe most-reprinted book on the subject
- Read the landmark paper: Multigrid Method for Maxwell's EquationsCited 317 times
- Go sideways: Numerical methods for partial differential equationsA closely related topic
- Go sideways: Relaxation (iterative method)A closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Multigrid Method for Maxwell's Equations
The hierarchical basis multigrid method
Multigrid method for fractional diffusion equations
Multigrid Monte Carlo method. Conceptual foundations
An Implicit Multigrid Method for Turbulent Combustion
Multigrid method for electronic structure calculations
A multigrid method for eigenvalue problem
On the Algebraic Multigrid Method
🆕 Influential since 2022
Multigrid Method for Solving Inverse Problems for Heat Equation
Parallel multigrid method for solving inverse problems
Anisotropic modeling with geometric multigrid preconditioned finite-element method
Agglomeration-Based Geometric Multigrid Schemes for the Virtual Element Method
A parallel geometric multigrid method for adaptive topology optimization
📚 Books worth reading
Multigrid finite element methods for electromagnetic field modelingYu Zhu, Zhu, Yu · 2004- 📕Application of multi-grid methods for solving the Navier-Stokes equationsA. O. Demuren · 1989
- 📕An LU-SSOR scheme for the Euler and Navier-Stokes equationsSeokkwan Yoon · 1986
- 📕Three-dimensional multigrid algorithms for the flux-split Euler equationsW. Kyle Anderson · 1988
Practical Fourier analysis for multigrid methodsR. Wienands, Roman Wienands · 2004- 📕On the multilevel solution algorithm for Markov chainsGraham Horton · 1997
- 📕Canonical-variables multigrid method for steady-state Euler equationShlomo Ta'asan · 1994
- 📕The solution of radiation transport equations with adaptive finite elementsLinda Stals · 2001
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- 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…
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- Iterative method In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate…
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- Convergent matrix In linear algebra, a convergent matrix is a matrix that converges to the zero matrix under matrix exponentiation. When successive powers of a matrix T…
- Spectral method Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The…