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In mathematics, in particular numerical analysis, the FETI method is an iterative substructuring method for solving systems of linear equations from the finite element method for the solution of elliptic partial differential equations, in particular in computational mechanics In each iteration, FETI requires the solution of a Neumann problem in each substructure and the solution of a coarse problem. The simplest version of FETI with no preconditioner in the substructure is scalable with the number of substructures but the condition number grows polynomially with the number of elements per substructure. FETI with a preconditioner consisting of the solution of a Dirichlet problem in each substructure is scalable with the number of substructures and its condition number grows only polylogarithmically with the number of elements per substructure. The coarse space in FETI consists of the nullspace on each substructure.
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In mathematics, a Poincaré–Steklov operator maps the values of one boundary condition of the solution of an elliptic partial differential equation in a domain to the values of another boundary condition. Usually, either of the boundary conditions determines the solution. Thus, a Poincaré–Steklov operator encapsulates the boundary response of the system modelled by the partial differential equation. When the partial differential equation is discretized, for example by finite elements or finite differences, the discretization of the Poincaré–Steklov operator is the Schur complement obtained by eliminating all degrees of freedom inside the domain.
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Angela Kunoth is a German mathematician specializing in the numerical analysis of partial differential equations. She is a professor of mathematics at the University of Cologne, and the editor-in-chief of SIAM Journal on Numerical Analysis.
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Alison Ramage is a British applied mathematician and numerical analyst specialising in preconditioning methods for numerical linear algebra, and their applications to the numerical solution of partial differential equations. She is a reader in the Department of Mathematics and Statistics at the University of Strathclyde.
Klaus Schmitt is an American mathematician doing research in nonlinear differential equations, and nonlinear analysis.
Paola F. Antonietti is an Italian applied mathematician and numerical analyst whose research concerns numerical methods for partial differential equations, and particularly domain decomposition methods, with applications in scientific computing and Applied Sciences such as the computational modelling of neurodegenerative disorders and simulating the propagation of seismic waves. She is Professor of Numerical Analysis at the Polytechnic University of Milan.
References
- 1 2 3 Mihai, Loredana Angela (2005), "A class of alternate strip-based domain decomposition methods for elliptic partial differential Equations", Durham e-Theses (Doctoral), Durham University; see Acknowledgements, p. v
- 1 2 3 "Angela Mihai", Profiles, Cardiff University, retrieved 2023-08-02
- ↑ Mathematicians propose new model to quantify materials uncertainties, Cardiff University, 16 April 2019, retrieved 2023-08-02
- ↑ Angela Mihai at the Mathematics Genealogy Project
- ↑ Dr Angela Mihai elected Vice President of SIAM-UKIE, Cardiff University, 24 May 2023, retrieved 2023-08-02
