Related papers: An energy-preserving Discrete Element Method for e…
We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a…
Usage, manipulation, transport, delivery, and mixing of granular or particulate media, comprised of spherical or polyhedral particles, is commonly encountered in industrial sectors of construction (cement and rock fragments), pharmaceutics…
We propose an efficient method to build a simple discrete element model (DEM) that accurately simulates the oscillation of a continuum beam. The DEM is based on the Timoshenko beam theory of slender cylindrical members and their…
A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…
Energy-preserving numerical methods for solving the Hodge wave equation is developed in this paper. Based on the de Rham complex, the Hodge wave equation can be formulated as a first-order system and mixed finite element methods using…
We analyze the application to elastodynamic problems of mixed finite element methods for elasticity with weak symmetry. Our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without…
This paper deals with the asymptotic behavior and FEM error analysis of a class of strongly damped wave equations using a semidiscrete finite element method in spatial directions combined with a finite difference scheme in the time…
We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following a previous approach employed for linear elastodynamics, the present problem is formulated as a…
Computational modeling is a key resource to gather insight into physical systems in modern scientific research and engineering. While access to large amount of data has fueled the use of Machine Learning (ML) to recover physical models from…
In this article we develop a fully discrete variational scheme that approximates the equations of three dimensional elastodynamics with polyconvex stored energy. The fully discrete scheme is based on a time-discrete variational scheme…
Maintaining conservation laws in the fully discrete setting is critical for accurate long-time behavior of numerical simulations and requires accounting for discrete conservation properties in both space and time. This paper derives…
This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on…
We propose a framework for discrete scientific data compression based on the tensor-train (TT) decomposition. Our approach is tailored to handle unstructured output data from discrete element method (DEM) simulations, demonstrating its…
We present a stability and convergence analysis of the space-time continuous finite element method for the Hamiltonian formulation of the wave equation. More precisely, we prove a continuous dependence of the discrete solution on the data…
This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal…
In this work, a methodology is proposed for formulating general dynamical equations in mechanics under the umbrella of the principle of energy conservation. It is shown that Lagrange's equation, Hamilton's canonical equations, and…
A novel implicit integration scheme for the Discrete Element Method (DEM) based on the variational integrator approach is presented. The numerical solver provides a fully dynamical description that, notably, reduces to an energy…
The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and…