A parallel and adaptive continuation method for semilinear bifurcation problems

In this paper we propose an efficient continuation method for the following of solution branches of parametrized semilinear elliptic problems. In order to limit the time required for the computation of a whole branch of accurate solutions, we combine a mesh adaptation strategy with parallel programming on a computer network. The first computer is devoted to the continuation on a coarse mesh, the others share out the correction of every roughly generated solution on a sequence of a posteriori refined meshes. A numerical example illustrating the performance of the method is given.

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