Structural shape optimization — a survey
Computer Methods in Applied Mechanics and Engineering
Aerodynamic design via control theory
Journal of Scientific Computing
On the termination of the perfectly matched layer with local absorbing boundary conditions
Journal of Computational Physics
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
Introduction to Shape Optimization: Theory, Approximation, and Computation
Introduction to Shape Optimization: Theory, Approximation, and Computation
Incorporating topological derivatives into level set methods
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Contemporary Architecture and the Digital Design Process
Contemporary Architecture and the Digital Design Process
Curves and Surfaces for Computer Graphics
Curves and Surfaces for Computer Graphics
Shape and topology optimization of an acoustic horn-lens combination
Journal of Computational and Applied Mathematics
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We suggest a boundary shape optimization approach in which the optimization is carried out on the coefficients in a boundary parameterization based on a local, discrete curvature. A fixed mesh is used to numerically solve the governing equations, in which the geometry is represented through inhomogeneous coefficients, similarly as done in the material distribution approach to topology optimization. The method is applied to the optimization of an acoustic horn in two space dimensions. Numerical experiments show that this method can calculate the horn's transmission properties as accurately as a traditional, body-fitted approach. Moreover, the use of a fixed mesh allows the optimization to create shapes that would be difficult to handle with a traditional approach that uses deformations of a body-fitted mesh. The parameterization inherently promotes smooth designs without unduly restriction of the design flexibility. The optimized, smooth horns consistently show favorable transmission properties.