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3 International Journal of Applied Mathematics and Computer Science

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Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids

Bresch D., Koko J.

International Journal of Applied Mathematics and Computer Science

2006

Vol. 16, no 4

419-429

We present a numerical simulation of two coupled Navier-Stokes flows, using operator-splitting and optimization-based nonoverlapping 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.

Newton's iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition

Koko J.

International Journal of Applied Mathematics and Computer Science

2004

Vol. 14, no 1

13-18

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.

Mesh r-Adaptation for Unilateral Contact Problems

Beal P., Koko J., Touzani R.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no 1

9-16

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.