Numerical computations

Below you can find a list containing some numerical computations I performed. You can access a detailed version of each item by clicking on the associated picture.
Maximizing the Steklov eigenvalues with a diameter constraint
Maximizing the minimal relative perimeter of a partition
Optimizing supports in additive manufacturing.
Optimization of the supports in additive manufacturing: various models, numerical computations
Optimization of various functionals under constant width/diameter and convexity constraints
Computation of Cheeger sets and Circle/Sphere packings via a $\Gamma$-convergence relaxation
Optimal partitions for eigenvalues in 3D
Eigenvalue optimization in the class of shapes of constant width
Automatic detection of carbon nanotubes - image processing (SEMIE 2016, Grenoble)
Critical waves using a shape optimization approach
Min-max optimal partitions for Dirichlet eigenvalues
Maximization of the first Dirichlet Laplace eigenvalue on domains with holes
Contour smoothing on triangulations - minimization of perimeter - area constraints
Large spectral partitions
Optimal spectral partitions on the sphere
Perimeter minimizing equi-areal partitions on surfaces
Optimizing Dirichlet Laplace eigenvalues - volume constraint in 2D ($k \leq 21$)
Optimizing Dirichlet Laplace eigenvalues - perimeter constraint in 2D ($k \leq 50$)
Optimizing Dirichlet Laplace eigenvalues - perimeter constraint - $\Gamma$-convergence method 2D and 3D
Optimization of functionals depending on the Steklov spectrum
Numerical method based on fundamental solutions - computation Steklov spectrum
Minimal spectral partitions on 2D regions
Numerical computations for the multiphase problem $\min \left( \sum_{i=1}^h \lambda_k(\Omega_i)+m|\Omega_i|\right)$
Numerical testing for Polya's conjecture - $N \in [5,15]$
Numerical optimal partitions for anisotropic perimeters using $\Gamma$-convergence
Numerical minimal equal area partitions on general regions using $\Gamma$-convergence
The basic idea behind numerical methods based on $\Gamma$-convergence. Numerical example: the isoperimetric problem.

Created: Jun 2015