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We introduce a unified optimization framework for geometry processing based on shape constraints. These constraints preserve or prescribe the shape of subsets of the points of a geometric data set, such as polygons, one-ring cells, volume elements, or featu ...
Engineers rely on efficient simulations that provide them with reliable data in order to make proper engineering design decisions. The purpose of this thesis is to design adaptive numerical methods for multiscale problems in this spirit. We consider ellipt ...
The finite cell method (FCM) belongs to the class of immersed boundary methods, and combines the fictitious domain approach with high-order approximation, adaptive integration and weak imposition of unfitted Dirichlet boundary conditions. Its main idea con ...
The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how structure preservation affects the long-time behaviour of num ...
The direct evaluation method tailored to the 4-D singular integrals arising in the second-kind Fredholm surface integral equation formulations is presented. The proposed semi-analytical integration scheme extends the existing singularity cancellation metho ...
We present a coupling of the reduced basis methods and free-form deformations for shape optimization and design of systems modelled by elliptic PDEs. The free-form deformations give a parameterization of the shape that is independent of the mesh, the initi ...
This paper presents a mesh adaptation procedure linked to a finite volume solver, the goal of which is to increase the precision of the numerical simulation of a wing tip vortex flow. The adaptation scheme is applied to hexahedron meshes and hybrid meshes ...
Interest in plasmonic nanostructures has recently multiplied due to their extraordinary optical properties. When resonantly excited, these tiny metallic systems exhibit a strong and localized optical field enhancement. Applications exploiting this effect e ...
We propose certified reduced basis methods for the efficient and reliable evaluation of a general output that is implicitly connected to a given parameterized input through the harmonic Maxwell's equations. The truth approximation and the development of th ...
We propose the reduced basis method for the solution of parametrized optimal control problems described by parabolic partial differential equations in the unconstrained case. The method, which is based on an off-line–on-line decomposition procedure, allows ...
