Parallel multiplicative Schwarz preconditioner for solving nonselfadjoint elliptic problems

2020 ◽  
pp. 1-19
Author(s):  
Ruyi Zhang ◽  
Shishun Li
Keyword(s):  
Elliptic Problems ◽  
Schwarz Preconditioner

scholarly journals On Discontinuous Galerkin Methods for Elliptic Problems with Discontinuous Coefficients

2003 ◽  
Vol 3 (1) ◽  
pp. 76-85 ◽  
Author(s):  
Maksymilian Dryja
Keyword(s):  
Rate Of Convergence ◽  
Discontinuous Galerkin ◽  
Error Bound ◽  
Discontinuous Galerkin Methods ◽  
Elliptic Problems ◽  
Discontinuous Coefficients ◽  
Galerkin Methods ◽  
Additive Schwarz ◽  
Discrete Problems ◽  
Schwarz Preconditioner

AbstractDiscontinuous Galerkin methods for elliptic problems with discontinuous coefficients are discussed. First the error bound of the methods is analyzed. Then a multilevel additive Schwarz preconditioner for one of the discrete problems is designed and analyzed. Although the preconditioner is not optimal it is very well suited for parallel computations and its rate of convergence is independent of the jumps of coefficients.

scholarly journals Robust Iterative Solvers for Gao Type Nonlinear Beam Models in Elasticity

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. Borsos ◽  
János Karátson
Keyword(s):  
Finite Element ◽  
Newton Method ◽  
Newton's Method ◽  
Numerical Experiments ◽  
Elliptic Problems ◽  
Iterative Solvers ◽  
Finite Element Solution ◽  
Element Solution ◽  
Nonlinear Beam ◽  
Quasi Newton

Abstract The goal of this paper is to present various types of iterative solvers: gradient iteration, Newton’s method and a quasi-Newton method, for the finite element solution of elliptic problems arising in Gao type beam models (a geometrical type of nonlinearity, with respect to the Euler–Bernoulli hypothesis). Robust behaviour, i.e., convergence independently of the mesh parameters, is proved for these methods, and they are also tested with numerical experiments.

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