GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
An Additive Multilevel Optimization Method and Its Application to Unstructured Meshes
Journal of Scientific Computing
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
Journal of Computational Physics
Journal of Computational Physics
Incorporating topological derivatives into level set methods
Journal of Computational Physics
A computational framework for the regularization of adjoint analysis in multiscale PDE systems
Journal of Computational Physics
Variational piecewise constant level set methods for shape optimization of a two-density drum
Journal of Computational Physics
Modeling and simulation of fish-like swimming
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Modelling and shape optimization of an actuator
Structural and Multidisciplinary Optimization
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The aim of this work is to combine penalization and level-set methods to solve inverse or shape optimization problems on uniform cartesian meshes. Penalization is a method to impose boundary conditions avoiding the use of body-fitted grids, whereas level-sets allow a natural non-parametric description of the geometries to be optimized. In this way, the optimization problem is set in a larger design space compared to classical parametric representation of the geometries, and, moreover, there is no need of remeshing at each optimization step. Special care is devoted to the solution of the governing equations in the vicinity of the penalized regions and a method is introduced to increase the accuracy of the discretization. Another essential feature of the optimization technique proposed is the shape gradient preconditioning. This aspect turns out to be crucial since the problem is infinite dimensional in the limit of grid resolution. Examples pertaining to model inverse problems and to shape design for Stokes flows are discussed, demonstrating the effectiveness of this approach.