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**Control approach to fictitious-domain methods application to fluid dynamics and electro-magnetics.**
*(English)*
Zbl 0768.76042

Fourth international symposium on domain decomposition methods for partial differential equations, Proc. Symp., Moscow/Russ. 1990, 275-309 (1991).

[For the entire collection see Zbl 0758.00010.]

In this method-oriented paper, we would like to discuss an implementation of fictitious domain methods which is based on an optimal control formulation. This approach has very definite advantages since it is based on a least-squares formulation of the boundary condition to be satisfied on the actual boundary; it is then naturally suited for iterative methods such as conjugate gradient, GMRES, etc. The preliminary results have been obtained are encouraging, and there is indeed a large room for improvement, including the investigation of preconditioners more efficient than those presently used which may be slow in some occasions.

In this method-oriented paper, we would like to discuss an implementation of fictitious domain methods which is based on an optimal control formulation. This approach has very definite advantages since it is based on a least-squares formulation of the boundary condition to be satisfied on the actual boundary; it is then naturally suited for iterative methods such as conjugate gradient, GMRES, etc. The preliminary results have been obtained are encouraging, and there is indeed a large room for improvement, including the investigation of preconditioners more efficient than those presently used which may be slow in some occasions.

### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

65N99 | Numerical methods for partial differential equations, boundary value problems |