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Fireshape: a shape optimization toolbox for Firedrake

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conference contribution
posted on 09.04.2020 by A. Paganini, F. Wechsung
Shape optimization studies how to design a domain such that a shape function is minimized. Ubiquitous in industrial applications, shape optimization is often constrained to partial differential equations (PDEs). One of the main challenges in PDE-constrained shape optimization is the coupling of domain updates and PDE-solvers. Fireshape addresses this challenge by elegantly coupling the finite element library Firedrake and the Rapid Optimization Library (ROL). The main features of Fireshape are: accessibility to users with minimal shape optimization knowledge; decoupled discretization of control and state variables; full access to Firedrake's PDE-solvers; automated derivation of adjoint equations and shape derivatives; different metrics to define shape gradients; access to ROL's optimization algorithms via PyROL. Fireshape is available at https://github.com/fireshape/fireshape. Fireshape's documentation comprises several tutorials and is available at https://fireshape.readthedocs.io/en/latest/.

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