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Adaptive isogeometric methods for the solution of partial diifferential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to apply the multi-level construction of hierarchical spline ...
Several methods are proposed to manipulate and pattern liquid metal films into elastic conductors but all lack precise control over the film thickness and roughness, thereby limiting its uniformity, stability, and reproducibility. Here, an approach relying ...
In this thesis, we study systems of linear and/or non-linear stochastic heat equations and fractional heat equations in spatial dimension 1 driven by space-time white noise. The main topic is the study of hitting probabilities for the solutions to these ...
We propose a data-driven artificial viscosity model for shock capturing in discontinuous Galerkin methods. The proposed model trains a multi-layer feedforward network to map from the element-wise solution to a smoothness indicator, based on which the artif ...
Many daily life tasks require precise control when making contact with surfaces. Ensuring a smooth transition from free motion to contact is crucial as incurring a large impact force may lead to unstable contact with the robot bouncing on the surface, i.e. ...
Surface roughness is relevant to all the phenomena and processes that take place at the interface between two bodies, like adhesion, contact, friction, and wear. Understanding the relation between surface roughness evolution and wear is therefore key in se ...
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap technique. In addition t ...
Dealing with strong shocks while retaining numerical dissipation of reasonably low level has been one of the major challenges for high order methods like discontinuous Galerkin. In the literature, various shock capturing models have been designed based on ...
We present a novel method for convex unconstrained optimization that, without any modifications, ensures: (i) accelerated convergence rate for smooth objectives, (ii) standard convergence rate in the general (non-smooth) setting, and (iii) standard converg ...
We present a novel method for convex unconstrained optimization that, without any modifications, ensures: (i) accelerated convergence rate for smooth objectives, (ii) standard convergence rate in the general (non-smooth) setting, and (iii) standard converg ...
