Krylov subspace recycling for evolving structures

Krylov subspace recycling is a powerful tool when solving long series of large, sparse linear systems that change only slowly over time. In PDE constrained shape optimization, these appear naturally, as typically hundreds or thousands optimization steps are needed with small changes in the geometry. this setting, however, applying can be difficult task. As geometry evolves, general, so does finite element mesh defined on representing geometry, including numbers nodes and elements connectivity. This especially case if re-meshing techniques used. result, number algebraic degrees freedom system changes, general matrices resulting from discretization size one step to next. Changes connectivity also lead structural matrices. re-meshing, even little, corresponding might differ substantially previous one. Obviously, prevents any straightforward mapping approximate invariant matrix (the focus paper) next; similar problems arise for other selected subspaces. paper, we present an algorithm map current step, meshes. achieved by exploiting coefficient vectors functions mesh, combined interpolation approximation mesh. We demonstrate effectiveness our approach numerically several proof concept studies specific meshing technique.