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Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…
Graph embedding techniques are pivotal in real-world machine learning tasks that operate on graph-structured data, such as social recommendation and protein structure modeling. Embeddings are mostly performed on the node level for learning…
In this paper, we discuss an adaptive hybrid stress finite element method on quadrilateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid…
Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
The computational modeling of high-speed flows (e.g. hypersonic) and space plasmas is characterized by a plethora of complex physical phenomena, in particular involving strong oblique shocks, bow shocks and/or shock waves boundary layer…
Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…
Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…
We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of…
An adaptive scheme to generate reduced-order models for parametric nonlinear dynamical systems is proposed. It aims to automatize the POD-Greedy algorithm combined with empirical interpolation. At each iteration, it is able to adaptively…
We present a novel, physically-based morphing technique for elastic shapes, leveraging the differentiable material point method (MPM) with space-time control through per-particle deformation gradients to accommodate complex topology…
Computing the stiffness matrix for the finite element discretization of the nonlocal Laplacian on unstructured meshes is difficult, because the operator is nonlocal and can even be singular. In this paper, we focus on the $C^0$-piecewise…
This paper introduces a deep learning method for solving an elliptic hemivariational inequality (HVI). In this method, an expectation minimization problem is first formulated based on the variational principle of underlying HVI, which is…
Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal…
As estimators of location parameters, univariate trimmed means are well known for their robustness and efficiency. They can serve as robust alternatives to the sample mean while possessing high efficiencies at normal as well as heavy-tailed…
One of the main challenges in numerically solving partial differential equations is finding a discretisation for the computational domain that balances the accurate representation of the underlying field with computational efficiency.…
The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods…
Numerical solution of equations governing time domain simulations in computational electromagnetics, is usually based on grid methods in space and on explicit schemes for the time evolution. A predefined grid in the problem domain and a…
We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary…
In this article we consider two-grid finite element methods for solving semilinear interface problems in d space dimensions, for d=2 or d=3. We first describe in some detail the target problem class with discontinuous diffusion…