Interior point tracking in shape evolving unstructured finite element meshes

An algorithm is presented for the tracking of interior points in a shape evolving unstructured FE mesh. Evolution of the boundary shape may be associated with a governing equation, as in moving boundary problems, or may be prescribed, as in structural shape optimisation. In the latter SSO case the point tracking algorithm may be used in conjunction with a FD approximation to determine geometric sensitivities: in this case the boundary deformation is a small perturbation. For meshes undergoing gross deformations of the boundary an incremental method is used. Reversibility tests are undertaken to assess the robustness and accuracy of the algorithm and examples are given to illustrate the general utility of the method.

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