A Combination of Algebraic Multigrid Algorithms with the Conjugate Gradient Technique

2002 ◽  
pp. 101-111
Author(s):  
Qianshun Chang ◽  
Zhaohui Huang
Keyword(s):  
Conjugate Gradient ◽  
Algebraic Multigrid ◽  
Gradient Technique

Algebraic Multigrid Preconditioning for Finite Element Solution of Inhomogeneous Elastic Inclusion Problems in Articular Cartilage

2011 ◽  
Vol 3 (6) ◽  
pp. 729-744
Author(s):  
Zhengzheng Hu ◽  
Mansoor A Haider
Keyword(s):  
Finite Element ◽  
Articular Cartilage ◽  
Analytical Solution ◽  
Conjugate Gradient ◽  
Numerical Solutions ◽  
Elastic Inclusion ◽  
Algebraic Multigrid ◽  
Inclusion Problem ◽  
Inclusion Problems ◽  
Cpu Time

AbstractIn studying biomechanical deformation in articular cartilage, the presence of cells (chondrocytes) necessitates the consideration of inhomogeneous elasticity problems in which cells are idealized as soft inclusions within a stiff extracellular matrix. An analytical solution of a soft inclusion problem is derived and used to evaluate iterative numerical solutions of the associated linear algebraic system based on discretization via the finite element method, and use of an iterative conjugate gradient method with algebraic multigrid preconditioning (AMG-PCG). Accuracy and efficiency of the AMG-PCG algorithm is compared to two other conjugate gradient algorithms with diagonal preconditioning (DS-PCG) or a modified incomplete LU decomposition (Euclid-PCG) based on comparison to the analytical solution. While all three algorithms are shown to be accurate, the AMG-PCG algorithm is demonstrated to provide significant savings in CPU time as the number of nodal unknowns is increased. In contrast to the other two algorithms, the AMG-PCG algorithm also exhibits little sensitivity of CPU time and number of iterations to variations in material properties that are known to significantly affect model variables. Results demonstrate the benefits of algebraic multigrid preconditioners for the iterative solution of assembled linear systems based on finite element modeling of soft elastic inclusion problems and may be particularly advantageous for large scale problems with many nodal unknowns.

An efficient algebraic multigrid preconditioned conjugate gradient solver

2003 ◽  
Vol 192 (20-21) ◽  
pp. 2299-2318 ◽  
Author(s):  
Chihiro Iwamura ◽  
Franco S. Costa ◽  
Igor Sbarski ◽  
Alan Easton ◽  
Nian Li
Keyword(s):  
Conjugate Gradient ◽  
Algebraic Multigrid ◽  
Preconditioned Conjugate Gradient ◽  
Conjugate Gradient Solver

A Modified Conjugate Gradient Method for Frictionless Contact Problems

1983 ◽  
Vol 105 (2) ◽  
pp. 242-246 ◽  
Author(s):  
W. R. Marks ◽  
N. J. Salamon
Keyword(s):  
Finite Element ◽  
Conjugate Gradient ◽  
Solution Method ◽  
Contact Region ◽  
Contact Problems ◽  
Computer Code ◽  
Frictionless Contact ◽  
Elastic Bodies ◽  
Gradient Technique ◽  
Modified Conjugate Gradient Method

The solution of elastic bodies in contact through the application of a conjugate gradient technique integrated with a finite element computer code is discussed. This approach is general, easily applied, and reasonably efficient. Furthermore the solution method is compatible with existing finite element computer programs. The necessary algorithm for use of the technique is described in detail. Numerical examples of two-dimensional frictionless contact problems are presented. It is found that the extent of the contact region and the displacements and stresses throughout the contacting bodies can be economically computed with precision.

An efficient numerical approach for calculating the inverse kinematics for robot manipulators

Robotica ◽  
1985 ◽  
Vol 3 (1) ◽  
pp. 21-26 ◽  
Author(s):  
Jadran Lenarčič
Keyword(s):  
Numerical Methods ◽  
Conjugate Gradient ◽  
Computational Efficiency ◽  
Execution Time ◽  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Computational Procedure ◽  
Numerical Approach ◽  
The Other ◽  
Gradient Technique

SUMMARYThis paper compares three numerical methods for obtaining the joint trajectory of a robot manipulator, which causes movement along the desired Cartesian path. The first solves the kinematic equations, which are given in the Jacobian form, while the other two solve the nonlinear kinematic equations directly by using an iterative computational procedure based on the conjugate gradient technique. The computational efficiency of the proposed methods is estimated in terms of the execution time on a VAX 11/750 minicomputer. It is shown that by using the capacity of microcomputers, these methods could be well used in real-time computation.

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