Regularized conjugate gradient method for skew-symmetric indefinite system of linear equations and applications

2007 ◽  
Vol 187 (2) ◽  
pp. 1484-1494
Author(s):  
Jinhai Chen ◽  
Zuhe Shen
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Linear Equations ◽  
System Of Linear Equations

Application of Jacobi - Conjugate Gradient Method in the Two-Dimensional Magnetotelluric Forward

2013 ◽  
Vol 416-417 ◽  
pp. 2123-2127
Author(s):  
Chong Li Zhu
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Linear Equations ◽  
Hessian Matrix ◽  
Simulation Method ◽  
Coefficient Matrix ◽  
Fine Grid ◽  
Solution Efficiency

Using the finite element method and all kinds of numerical simulation method, A large-scale system of linear equations is solved eventually,the solution method of the system of equations largely determines the solution efficiency and precision of numerical calculation. The Jacobi iteration preconditioning conjugate gradient method is adopted, Both overcome the coefficient matrix pathological characteristics and the characteristics of slow convergence speed ,and avoid the disadvantages such as Newton's method to store and Hessian matrix is calculated and inversed,improve forward modeling calculation speed and accuracy. Guarantee for solving numerical stability and efficiency ,of the thick grid combined with verification, the algorithm is feasible and it is verified by coarse grid combine with fine grid.

Thermal Floorplan Base on Conjugate Gradient Solver in HotSpot

2014 ◽  
Vol 608-609 ◽  
pp. 908-912
Author(s):  
Zhong Hua Jiang ◽  
Ning Xu ◽  
Chun Xiang Wu
Keyword(s):  
Linear System ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Decomposition Method ◽  
Sparse Matrix ◽  
Linear Equations ◽  
Sparse Linear Systems ◽  
Vlsi Physical Design ◽  
Conjugate Gradient Solver

In this paper, we introduce an effective iterative method to solve the thermal linear system in HotSpot thermal floorplan, the iterative Conjugate Gradient Method is suitable to solve the traditional sparse matrix linear equations. We define a class of dummy sparse linear systems in iterative thermal floorplan algorithm, the iterative methods for linear system can be extended to apply to other iterative framework algorithm. We apply the conjugate gradient method to solve the thermal model in floorplan of VLSI physical design. The experiments' result shows that thermal floorplan using Conjugate gradient method is effective. The running time of our incremental conjugate gradient thermal solver with Jocabi Precondition is approximate 0.59 comparing with LU decomposition method.

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