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.
Steklov eigenvalue optimizer under a diameter constraint Maximizing the Steklov eigenvalues with a diameter constraint
Expanded view of a 13-cell relative-perimeter partition Maximizing the minimal relative perimeter of a partition
Optimized additive-manufacturing supports for three tubes Optimizing supports in additive manufacturing.
Support optimization in additive manufacturing Optimization of the supports in additive manufacturing: various models, numerical computations
Three-dimensional Meissner body of constant width Optimization of various functionals under constant width/diameter and convexity constraints
Packing of 20 spheres in a tetrahedron Computation of Cheeger sets and Circle/Sphere packings via a $\Gamma$-convergence relaxation
Optimal three-cell eigenvalue partition of a cube Optimal partitions for eigenvalues in 3D
Eigenvalue optimizer among shapes of constant width Eigenvalue optimization in the class of shapes of constant width
Automatically detected carbon nanotubes in a microscopy image Automatic detection of carbon nanotubes - image processing (SEMIE 2016, Grenoble)
Critical wave computed by shape optimization Critical waves using a shape optimization approach
Eight-cell min-max partition for Dirichlet eigenvalues Min-max optimal partitions for Dirichlet eigenvalues
Domain with holes maximizing the first Dirichlet eigenvalue Maximization of the first Dirichlet Laplace eigenvalue on domains with holes
Initial and smoothed contours on a triangulated surface Contour smoothing on triangulations - minimization of perimeter - area constraints
Large hexagonal spectral partition Large spectral partitions
Refined 32-cell spectral partition of a sphere Optimal spectral partitions on the sphere
Six-cell perimeter-minimizing partition of a torus Perimeter minimizing equi-areal partitions on surfaces
Ninth Dirichlet eigenvalue optimizer under a volume constraint Optimizing Dirichlet Laplace eigenvalues - volume constraint in 2D ($k \leq 21$)
Fifteenth Dirichlet eigenvalue optimizer under a perimeter constraint Optimizing Dirichlet Laplace eigenvalues - perimeter constraint in 2D ($k \leq 50$)
Three-dimensional second-eigenvalue optimizer under a perimeter constraint Optimizing Dirichlet Laplace eigenvalues - perimeter constraint - $\Gamma$-convergence method 2D and 3D
Shape optimized for a functional of the Steklov spectrum Optimization of functionals depending on the Steklov spectrum
Comparison of numerical Steklov spectrum computations Numerical method based on fundamental solutions - computation Steklov spectrum
Ten-cell spectral partition of an equilateral triangle Minimal spectral partitions on 2D regions
Periodic eight-cell multiphase configuration Numerical computations for the multiphase problem $\min \left( \sum_{i=1}^h \lambda_k(\Omega_i)+m|\Omega_i|\right)$
Regular octagon used in numerical tests of Polya's conjecture Numerical testing for Polya's conjecture - $N \in [5,15]$
Eight-cell anisotropic perimeter partition Numerical optimal partitions for anisotropic perimeters using $\Gamma$-convergence
Seven-cell equal-area perimeter partition of a hexagon Numerical minimal equal area partitions on general regions using $\Gamma$-convergence
Three-dimensional anisotropic isoperimetric optimizer The basic idea behind numerical methods based on $\Gamma$-convergence. Numerical example: the isoperimetric problem.

Created: Jun 2015