Mixed-order interpolation for the Galerkin coarse-grid approximations in algebraic multigrid solvers

2010 ◽  
Vol 67 (2) ◽  
pp. 175-188 ◽  
Author(s):  
R. Webster
Keyword(s):  
Coarse Grid ◽  
Algebraic Multigrid ◽  
Multigrid Solvers ◽  
Mixed Order

Development of a Novel Mixing Plane Interface Using a Fully Implicit Averaging for Stage Analysis

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Lucian Hanimann ◽  
Luca Mangani ◽  
Ernesto Casartelli ◽  
Thomas Mokulys ◽  
Sebastiano Mauri
Keyword(s):  
Mass Conservation ◽  
Solution Procedure ◽  
Algebraic Multigrid ◽  
Radial Compressor ◽  
Fully Implicit ◽  
Multigrid Solvers ◽  
Algorithm Stability ◽  
Speed Up ◽  
Stage Analysis ◽  
Development And Validation

This paper describes the development and validation steps of a characteristics-based explicit along with a novel fully implicit mixing plane implementation for turbomachinery applications. The framework is an unstructured 3D RANS in-house modified solver, based on open-source libraries. Particular attention was paid to mass-conservation, accurate variables interpolation, and algorithm stability in order to improve robustness and convergence. By introducing a specific interface, allowing the use of algebraic multigrid solvers together with multiprocessor computation, a speed up of the numerical solution procedure was achieved. The validation of both mixing plane algorithms is carried out on an industrial radial compressor and a cold air 1.5 stages axial turbine.

scholarly journals Least-Squares Finite Element Methods and Algebraic Multigrid Solvers for Linear Hyperbolic PDEs

2004 ◽  
Vol 26 (1) ◽  
pp. 31-54 ◽  
Author(s):  
H. De Sterck ◽  
Thomas A. Manteuffel ◽  
Stephen F. McCormick ◽  
Luke Olson
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Finite Element Methods ◽  
Algebraic Multigrid ◽  
Hyperbolic Pdes ◽  
Multigrid Solvers

scholarly journals Accelerating algebraic multigrid solvers on NVIDIA GPUs

2015 ◽  
Vol 70 (5) ◽  
pp. 1162-1181 ◽  
Author(s):  
Hui Liu ◽  
Bo Yang ◽  
Zhangxin Chen
Keyword(s):  
Algebraic Multigrid ◽  
Multigrid Solvers

scholarly journals Coarse-grid selection for parallel algebraic multigrid

1998 ◽  
pp. 104-115 ◽  
Author(s):  
Andrew J. Cleary ◽  
Robert D. Falgout ◽  
Van Emden Henson ◽  
Jim E. Jones
Keyword(s):  
Coarse Grid ◽  
Algebraic Multigrid ◽  
Selection For ◽  
Grid Selection

On the Convergence of System-AMG in Reservoir Simulation

SPE Journal ◽  
2018 ◽  
Vol 23 (02) ◽  
pp. 589-597 ◽  
Author(s):  
Sebastian Gries
Keyword(s):  
Linear Systems ◽  
Reservoir Simulation ◽  
Extreme Case ◽  
Coarse Grid ◽  
Algebraic Multigrid ◽  
Volume Balance ◽  
Coarse Grid Correction ◽  
Speed Up ◽  
Level Problem ◽  
Flexible Framework

Summary System-algebraic multigrid (AMG) provides a flexible framework for linear systems in simulation applications that involve various types of physical unknowns. Reservoir-simulation applications, with their driving elliptic pressure unknown, are principally well-suited to exploit System-AMG as a robust and efficient solver method. However, the coarse grid correction must be physically meaningful to speed up the overall convergence. It has been common practice in constrained-pressure-residual (CPR) -type applications to use an approximate pressure/saturation decoupling to fulfill this requirement. Unfortunately, this can have significant effects on the AMG applicability and, thus, is not performed by the dynamic row-sum (DRS) method. This work shows that the pressure/saturation decoupling is not necessary for ensuring an efficient interplay between the coarse grid correction process and the fine-level problem, demonstrating that a comparable influence of the pressure on the different involved partial-differential equations (PDEs) is much more crucial. As an extreme case with respect to the outlined requirement, linear systems from compositional simulations under the volume-balance formulation will be discussed. In these systems, the pressure typically is associated with a volume balance rather than a diffusion process. It will be shown how System-AMG can still be used in such cases.

scholarly journals Algebraic Multigrid Solvers for Complex-Valued Matrices

2008 ◽  
Vol 30 (3) ◽  
pp. 1548-1571 ◽  
Author(s):  
Scott P. MacLachlan ◽  
Cornelis W. Oosterlee
Keyword(s):  
Algebraic Multigrid ◽  
Multigrid Solvers ◽  
Complex Valued
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