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Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...
Harmonic tension–compression tests at 0.1, 0.5 and 1 Hz on hydrated bovine periodontal ligament (PDL) were numerically simulated. The process was modeled by finite elements (FE) within the framework of poromechanics, with the objective of isolating the con ...
Explicit stabilized methods for stiff ordinary differential equations have a long history. Proposed in the early 1960s and developed during 40 years for the integration of stiff ordinary differential equations, these methods have recently been extended to ...
Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrat ...
In finite element simulations dedicated to the modelling of microstructure evolution, the mesh has to be fine enough to: (i) accurately describe the geometry of the constituents; (ii) capture local strain gradients stemming from the heterogeneity in materi ...
We present a method to obtain the frequency spectrum of a signal with a nonlinear dynamical system. The dynamical system is composed of a pool of adaptive frequency oscillators with negative mean-field coupling. For the frequency analysis, the synchronizat ...
A high-order implicit-explicit additive Rung-Kutta time integrator is implemented in a particle-in-cell method based on a high-order discontinuous Galerkin Maxwell solver for the simulation of plasmas. The method enforces Gauss law by a hyperbolic divergen ...
Background The ambition of most molecular biologists is the understanding of the intricate network of molecular interactions that control biological systems. As scientists uncover the components and the connectivity of these networks, it becomes possible t ...
Forged components exhibit good mechanical strength, particularly in terms of high cycle fatigue properties. This is due to the specific microstructure resulting from large plastic deformation as in a forging process. The goal of this study is to account fo ...
Despite the popularity of high-order explicit Runge-Kutta (ERK) methods for integrating semi-discrete systems of equations, ERK methods suffer from severe stability-based time step restrictions for very stiff problems. We implement a discontinuous Galerkin ...