Abstract. In this work, we are interested in a class of problems of great importance in many areas of industry and engineering. It is the invese problem for the biharmonic equation. It consists to complete the missing data on the inaccessible part from the measured data on the accessible part of the boundary. To solve this ill-posed problem, we opted for the alternative iterative method developed by Kozlov, Mazya and Fomin which is a convergent method for the elliptical Cauchy problems in general. The numerical implementation of the iterative algorithm is based on the application of the boundary element method (BEM) for a sequence of mixed well-posed direct problems. Numerical results are performed for a square domain showing the effectiveness of the algorithm by BEM to produce accurate and stable numerical results
This paper is interested at the Cauchy problem for Laplace's equation, which is to recover both Dirichlet and Neumann conditions on the inaccessible part of the boundary (inner part) of an annular domain from the over specified conditions on the accessible one (outer part). This work is an extension of the proposed algorithm for a unit circle [1] to annular domain, where, we describe an alternating formulation of the KMF algorithm proposed by Kozlov, Mazya and Fomin, and its relationship with the standard formulation. The new KMF algorithm ameliorates the accuracy of the solution and reduces the number of iterations required to achieve convergence. In the last part, the discussion of the error estimation of solution is presented and some numerical tests, using the software Freefem are given to show the efficiency of the proposed method.
This work concerns the use of the iterative algorithm (KMF algorithm) proposed by Kozlov, Mazya and Fomin to solve the Cauchy problem for Laplace's equation. This problem consists to recovering the lacking data on some part of the boundary using the over specified conditions on the other part of the boundary. We describe an alternating formulation of the KMF algorithm and its relationship with a classical formulation. The implementation of this algorithm for a regular domain is performed by the finite element method using the software Freefem. The numerical tests developed show the effectiveness of the proposed algorithm since it allows to have more accurate results as well as reducing the number of iterations needed for convergence.
General TermsAlgorithms, computational mathematics.
In this work, we are interested in improving the performance of genetic algorithm (GA) to solve the Asymmetric Traveling Salesman Problem (ATSP). Several approaches have been developed with genetic algorithms based on the adaptation and improvement of different standard genetic operators. We proposes a new GA adopting immigration strategies to maitain diversity and to perform more the genetic algorithm. Experimental results on series of standard instances of ATSP show that the proposed structured memory immigration scheme in GA effectively improves the performance of GAs.
The asymmetric traveling salesman problem (ATSP) is a combinatorial problem of great importance where the cost matrix is not symmetric, which complicates its resolution. The genetic algorithms (GAs) are a meta-heuristics methods used to solve transportation problems that have proved their effectiveness to obtain good results. However, improvements can be made by adapting the crossover operator as a primordial operator in GAs. In this work, we propose an adapted XIM crossover operator for the ATSP in order to improve the optimal solution obtained by GAs. Numerical simulations are performed and discussed for different series of standard instances showing the improvement of the optimal solution by the proposed genetic operator.
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