scholarly journals Schur complement-based domain decomposition preconditioners with low-rank corrections

2016 ◽  
Vol 23 (4) ◽  
pp. 706-729 ◽  
Author(s):  
Ruipeng Li ◽  
Yuanzhe Xi ◽  
Yousef Saad
Keyword(s):  
Domain Decomposition ◽  
Schur Complement ◽  
Low Rank

Fast Domain Decomposition Type Solver for Stiffness Matrices of Reference p-Elements

2013 ◽  
Vol 13 (2) ◽  
pp. 161-183 ◽  
Author(s):  
Vadim Korneev
Keyword(s):  
Finite Difference ◽  
Domain Decomposition ◽  
Elliptic Equations ◽  
Harmonic Functions ◽  
Schur Complement ◽  
P Elements ◽  
Stiffness Matrices ◽  
The Family ◽  
Discrete Harmonic Functions

Abstract. A key component of domain decomposition solvers for hp discretizations of elliptic equations is the solver for internal stiffness matrices of p-elements. We consider an algorithm which belongs to the family of secondary domain decomposition solvers, based on the finite-difference like preconditioning of p-elements, and was outlined by the author earlier. We remove the uncertainty in the choice of the coarse (decomposition) grid solver and suggest the new interface Schur complement preconditioner. The latter essentially uses the boundary norm for discrete harmonic functions induced by orthotropic discretizations on slim rectangles, which was derived recently. We prove that the algorithm has linear arithmetical complexity.

scholarly journals Direct Schur complement method by domain decomposition based on H-matrix approximation

2005 ◽  
Vol 8 (3-4) ◽  
pp. 179-188 ◽  
Author(s):  
Wolfgang Hackbusch ◽  
Boris N. Khoromskij ◽  
Ronald Kriemann
Keyword(s):  
Domain Decomposition ◽  
Schur Complement ◽  
Matrix Approximation

A Domain Decomposition of the Finite Element-Boundary Integral Method for Scattering by Deep Cavities

2011 ◽  
Vol 383-390 ◽  
pp. 2585-2589
Author(s):  
Zhi Wei Cui ◽  
Yi Ping Han ◽  
Wen Juan Zhao
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Domain Decomposition Method ◽  
Schur Complement ◽  
Building Blocks ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Special Method ◽  
Deep Cavities ◽  
Element Boundary

An efficient domain decomposition method (DDM) is employed to improve upon the efficiency and capability of the finite element-boundary integral (FE-BI) method for calculation of electromagnetic (EM) scattering from deep cavities. This method first subdivides the original cavity into many sub-domains along its depth and classifies these sub-domains into a few building blocks. It then employs the substructuring method to deal with the different types of sub-domains. The resulting Schur complement system is solved by a special method which has low memory requirements because the formation of the global Schur complement matrix is not necessary. Numerical results indicate that the presented method is an effective approach for scattering by deep cavities.

scholarly journals Scalable Block Preconditioners for Linearized Navier-Stokes Equations at High Reynolds Number

Algorithms ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 199
Author(s):  
Filippo Zanetti ◽  
Luca Bergamaschi
Keyword(s):  
Stokes Equations ◽  
Schur Complement ◽  
Iterative Solution ◽  
Viscosity Coefficient ◽  
Building Blocks ◽  
Low Rank ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Diffusion Operator ◽  
Advection Diffusion

We review a number of preconditioners for the advection-diffusion operator and for the Schur complement matrix, which, in turn, constitute the building blocks for Constraint and Triangular Preconditioners to accelerate the iterative solution of the discretized and linearized Navier-Stokes equations. An intensive numerical testing is performed onto the driven cavity problem with low values of the viscosity coefficient. We devise an efficient multigrid preconditioner for the advection-diffusion matrix, which, combined with the commuted BFBt Schur complement approximation, and inserted in a 2×2 block preconditioner, provides convergence of the Generalized Minimal Residual (GMRES) method in a number of iteration independent of the meshsize for the lowest values of the viscosity parameter. The low-rank acceleration of such preconditioner is also investigated, showing its great potential.

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