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Everything about Spectral element method
Formulation of the finite element method
In the numerical solution of partial differential equations, a topic in mathematics, the spectral element method (SEM) is a formulation of the finite element method (FEM) that uses high-degree piecewise polynomials as basis functions. The spectral element method was introduced in a 1984 paper by A. T. Patera. Although Patera is credited with development of the method, his work was a rediscovery of an existing method Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Spectral element methodA 5-minute orientation
- Skim a recent paper: A Review: Applications of the Spectral Finite Element MethodInfluential work since 2022
- Pick up a classic book: Spectral finite element methodThe most-reprinted book on the subject
- Read the landmark paper: Hybrid Multigrid/Schwarz Algorithms for the Spectral Element MethodCited 112 times
- Go sideways: Finite element methodA closely related topic
- Go sideways: Kansa methodA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Hybrid Multigrid/Schwarz Algorithms for the Spectral Element Method
The Spectral Element Method in Structural Dynamics
Adaptive mesh strategies for the spectral element method
A Legendre spectral element method for the Stefan problem
Discontinuous Galerkin spectral element lattice Boltzmann method on triangular element
Photonic Nanojet Analysis by Spectral Element Method
A Spectral-Element Method for Transmission Eigenvalue Problems
Optimization-based limiters for the spectral element method
🆕 Influential since 2022
A Review: Applications of the Spectral Finite Element Method
Investigation and Analysis of Acoustojets by Spectral Element Method
Topology optimization of unsteady flows using the spectral element method
A spectral element-based phase field method for incompressible two-phase flows
A Tetrahedral Spectral Element Method for Thermo-Mechanical Analysis of Electronic Devices
📚 Books worth reading
Spectral finite element methodS. Gopalakrishnan, Srinivasan Gopalakrishnan · 2007
Spectral/hp element methods for computational fluid dynamicsGeorge Karniadakis · 2005- 📕Fourier analysis of finite element preconditioned collocation schemesM. O. Deville · 1990
- 📕Nonconforming mortar element methodsYvon Maday · 1988
Spectral/hp element methods for CFDGeorge Karniadakis · 1999- 📕Spectral/Hp Element Methods for CfdGeorge E. Karniadakis · 1999
- 📕Coupling finite element and spectral methodsChristine Bernardi · 1987
Discrétisations Variationnelles de Problèmes Aux Limites ElliptiquesChristine Bernardi, Yvon Maday · 2004
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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