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Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
The surge of activity in the resolution of fine scale features in the field of earth sciences over the past decade necessitates the development of robust yet simple algorithms that can tackle the various drawbacks of in silico models…
We consider the common problem setting of an elastic sphere impacting on a flexible beam. In contrast to previous studies, we analyze the modal energy distribution induced by the impact, having in mind the particular application of impact…
Pressure Poisson equation (PPE) reformulations of the incompressible Navier-Stokes equations (NSE) replace the incompressibility constraint by a Poisson equation for the pressure and a suitable choice of boundary conditions. This yields a…
This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods…
Soft robot are celebrated for their propensity to enable compliant and complex robot-environment interactions. Soft robotic manipulators, or slender continuum structure robots have the potential to exploit these interactions to enable new…
We design and analyze a Hybrid High-Order (HHO) method on unfitted meshes to approximate elliptic interface problems. The curved interface can cut through the mesh cells in a very general fashion. As in classical HHO methods, the present…
Elastomeric mechanical metamaterials exhibit unconventional behaviour, emerging from their microstructures often deforming in a highly nonlinear and unstable manner. Such microstructural pattern transformations lead to non-local behaviour…
Magnetic quadrupoles are essential components of particle accelerators like the Large Hadron Collider. In order to study numerically the stability of the particle beam crossing a quadrupole, a large number of particle revolutions in the…
Modeling contact between deformable solids is a fundamental problem in computer animation, mechanical design, and robotics. Existing methods based on $C^0$-discretizations -- piece-wise linear or polynomial surfaces -- suffer from…
This paper presents a novel implicit scheme for the constraint resolution in real-time finite element simulations in the presence of contact and friction. Instead of using the standard motion correction scheme, we propose an iterative…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
Recent developments in high peak-power table-top laser systems reaching highly relativistic light intensities have led to significant advances in laser-driven particle acceleration schemes (mainly the laser wakefield acceleration, LWFA)…
We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations.…
In this paper, we introduce a new reduced basis methodology for accelerating the computation of large parameterized systems of high-fidelity integral equations. Core to our methodology is the use of coarse-proxy models (i.e., lower…
A new preconditioner is developed for high order finite element approximation of linear elastic problems on triangular meshes in two dimensions. The new preconditioner results in a condition number that is bounded independently of the…
Parametric model order reduction (pMOR) is a powerful tool for accelerating finite element (FE) simulations while maintaining parametric dependencies. For geometric parameters, pMOR by matrix interpolation is a well-suited approach because…
Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially…
Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of…
We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of…