Related papers: The BLUES function method applied to partial diffe…
We develop a nonlocal-response generalization to the Green-function surface-integral method (GSIM), also known as the boundary-element method (BEM). This numerically light method can accurately describe the linear hydrodynamic nonlocal…
The alternating direction method of multipliers (ADMM) is a powerful splitting algorithm for linearly constrained convex optimization problems. In view of its popularity and applicability, a growing attention is drawn towards the ADMM in…
A coarse-grained bead-spring-dashpot chain model with the dashpots representing the presence of internal friction, is solved exactly numerically, for the case of chains with more than two beads. Using a decoupling procedure to remove the…
Flexible boundary condition methods couple an isolated defect to a harmonically responding medium through the bulk lattice Green's function; in the case of an interface, interfacial lattice Green's functions. We present a method to compute…
The Active Flux scheme is a finite volume scheme with additional point values distributed along the cell boundary. It is third order accurate and does not require a Riemann solver. Instead, given a reconstruction, the initial value problem…
A nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the…
The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…
The properties of semidilute polymer solutions are investigated at equilibrium and under shear flow by mesoscale simulations, which combine molecular dynamics simulations and the multiparticle collision dynamics approach. In semidilute…
We investigate mathematically a nonlinear approximation type approach recently introduced in [A. Ammar et al., J. Non-Newtonian Fluid Mech., 2006] to solve high dimensional partial differential equations. We show the link between the…
Cell proliferation and diffusion can be modeled through reaction-diffusion systems describing the space-time evolution of a density variable. In this work, we present non-linear transformations of heat equation solutions to model cellular…
Critical points of energy functionals, which are of broad interest, for instance, in physics and chemistry, in solid and quantum mechanics, in material science, or in general diffusion-reaction models arise as solutions to the associated…
We propose a new variational model for non-linear image fusion. Our approach is based on the use of an osmosis energy term related to the one studied in Vogel et al. (2013) and Weickert et al. (2013) The minimization of the proposed…
A second-order face-centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to…
We consider the interplay of thermal fluctuations and shear on the surface of the domains in various systems coarsening under an imposed shear flow. These include systems with nonconserved and conserved dynamics, and a conserved order…
A theoretical model is developed by exploiting the variational technique to investigate the evolution of an optical beam inside an optically pumped graded-index fiber amplifier. The variational analysis is a semi-analytical method that…
Interior point methods solve small to medium sized problems to high accuracy in a reasonable amount of time. However, for larger problems as well as stochastic problems, one needs to use first-order methods such as stochastic gradient…
In this work we develop implicit Active Flux schemes for the scalar advection equation. At every cell interface we approximate the solution by a polynomial in time. This allows to evolve the point values using characteristics and to update…
Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on a curved geometry after a reparametrization invariance…
This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…
In this paper, we present a novel interface-driven adaptive variational procedure using a fully Eulerian description of fluid-structure interaction. The proposed fully-Eulerian procedure involves a fixed background unstructured mesh on…