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A conjugate gradient method with quasi-Newton approximation

100%
Koko J.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 2
153-165
EN
The conjugate gradient method of Liu and Storey is an efficient minimization algorithm which uses second derivatives information, without saving matrices, by finite difference approximation. It is shown that the finite difference scheme can be removed by using a quasi-Newton approximation for computing a search direction, without loss of convergence. A conjugate gradient method based on BFGS approximation is proposed and compared with existing methods of the same class.
2
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Newton's iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition

100%
Koko J.
International Journal of Applied Mathematics and Computer Science
|
2004
|
tom 14
|
nr 1
13-18
EN
Newton's iteration is studied for the numerical solution of an elliptic PDE with nonlinear boundary conditions. At each iteration of Newton's method, a conjugate gradient based decomposition method is applied to the matrix of the linearized system. The decomposition is such that all the remaining linear systems have the same constant matrix. Numerical results confirm the savings with respect to the computational cost, compared with the classical Newton method with factorization at each step.
3
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Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids

63%
Bresch D., Koko J.
International Journal of Applied Mathematics and Computer Science
|
2006
|
tom 16
|
nr 4
419-429
EN
We present a numerical simulation of two coupled Navier-Stokes flows, using ope-rator-split-ting and optimization-based non-overlapping domain decomposition methods. The model problem consists of two Navier-Stokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numerical experiments are carried out with two coupled fluids; one with an initial linear profile and the other in rest. As expected, the transmission condition generates a recirculation within the fluid in rest.
4
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Mesh r-adaptation for unilateral contact problems

51%
Béal P., Koko J., Touzani R.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
nr 1
9-16
EN
We present a mesh adaptation method by node movement for two-dimensional linear elasticity problems with unilateral contact. The adaptation is based on a hierarchical estimator on finite element edges and the node displacement techniques use an analogy of the mesh topology with a spring network. We show, through numerical examples, the efficiency of the present adaptation method.
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