Homotopy for Shape Optimization
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In this work we propose a homotopy method for shape optimization problems. Here, Newton's method provides quick convergence if the initial guess is close to the solution. However, we do not necessarily have a good initial guess of the solution. We choose a problem, which is easy to solve or where we know the solution, and connect the solutions of a specific path. Following this path (using Newton's method) will finally lead to the desired solution. Finally, the resulting algorithms are substantiated by numerical examples.
