Related papers: Dynamic coupling of a finite element solver to lar…
We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for…
In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
In recent years, a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on non-matching or overlapping meshes. Examples of such methods include the fictitious…
This article surveys research on the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's C-grid finite difference scheme to the finite element…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…
Chemical accuracy serves as an important metric for assessing the effectiveness of the numerical method in Kohn--Sham density functional theory. It is found that to achieve chemical accuracy, not only the Kohn--Sham wavefunctions but also…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
The finite element method is widely used in simulations of various fields. However, when considering domains whose extent differs strongly in different spatial directions a finite element simulation becomes computationally very expensive…
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…
In simulations of crystals, unlike liquids or gases, it may happen that the properties of the studied system depend not only on the volume of the simulation cell but also on its shape. For such cases it is desirable to change the shape of…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
Damping of structures and systems is often dominated by frictional dissipation in connections, the prediction of which remains a longstanding scientific challenge. Previous studies have shown that the actual topography of contact interfaces…
Long ranged electrostatic interactions are time consuming to calculate in molecular dynamics and Monte-Carlo simulations. We introduce an algorithmic framework for simulating charged particles which modifies the dynamics so as to allow…
We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in [40], enables the use of separate meshes to…
Recent developments dedicated to the building of multiscale mechanical and chemical constitutive laws for energetic molecular crystals are presented and discussed. In particular, various tools have been specifically incorporated in…