Row scaling as a preconditioner for some nonsymmetric linear systems with discontinuous coefficients

DOI10.1016/j.cam.2010.05.021zbMath1196.65066OpenAlexW2076329633MaRDI QIDQ989153

Rachel Gordon, Dan Gordon

Publication date: 27 August 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2010.05.021

zbMATH Keywords

algorithmconvergencenumerical examplesdiscontinuous coefficientsdomain decompositionpreconditioningGMRESlinear equationsgeometric scaling\(L_p\)-normdiagonal scalingBi-CGSTABelliptic convection-diffusion equationGRSnonsymmetric equations

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Iterative numerical methods for linear systems (65F10) Finite difference methods for boundary value problems involving PDEs (65N06) Preconditioners for iterative methods (65F08)

Related Items (5)

CADD: a seamless solution to the domain decomposition problem of subdomain boundaries and cross-points ⋮ Convection-adapted BEM-based FEM ⋮ Eulerian incompressible smoothed particle hydrodynamics on multiple GPUs ⋮ Parallel solution of high frequency Helmholtz equations using high order finite difference schemes ⋮ CARP-CG: A robust and efficient parallel solver for linear systems, applied to strongly convection dominated PDEs

Uses Software

• CARP-CG
• LAPACK
• AztecOO
• ILUT
• Aztec

Cites Work

• CARP-CG: A robust and efficient parallel solver for linear systems, applied to strongly convection dominated PDEs
• An efficient preconditioned CG method for the solution of a class of layered problems with extreme contrasts in the coefficients
• Scaling symmetric positive definite matrices to prescribed row sums.
• Interface relaxation methods for elliptic differential equations
• Scaling of matrices to achieve specified row and column sums
• Matrices which can be optimally scaled
• Condition numbers and equilibration of matrices
• Solution Methods for Nonsymmetric Linear Systems with Large off-Diagonal Elements and Discontinuous Coefficients
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Some New Bounds on the Condition Numbers of Optimally Scaled Matrices
• On a Characterization of the Best $l_2 $-Scaling of a matrix
• Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations
• Unstructured Additive Schwarz--Conjugate Gradient Method for Elliptic Problems with Highly Discontinuous Coefficients
• Scaling Matrices to Prescribed Row and Column Maxima
• Scaling improves stability of preconditioned CG-like solvers for FE consolidation equations
• ILUT: A dual threshold incomplete LU factorization
• A geometric approach to quadratic optimization: an improved method for solving strongly underdetermined systems in CT
• On the Effects of Scaling of the Peaceman-Rachford Method
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