Related papers: Kinetic Solvers with Adaptive Mesh in Phase Space
Implicit solvers present strong limitations when used on supercomputing facilities and in particular for adaptive mesh-refinement codes. We present a new method for implicit adaptive time-stepping on adaptive mesh refinement-grids. We…
Recently, neural networks have been extensively employed to solve partial differential equations (PDEs) in physical system modeling. While major studies focus on learning system evolution on predefined static mesh discretizations, some…
We propose two variants of the overlapping additive Schwarz method for the finite element discretiza- tion of the elliptic problem in 3D with highly heterogeneous coefficients. The methods are efficient and simple to construct using the…
Component Modal Synthesis (CMS) is a reduced order modelling method widely used for large-scale complex systems. It can effectively approximate system-level models through component synthesis, in which the repetitive geometrical components…
We present a new adaptive resolution technique for efficient particle-based multiscale molecular dynamics (MD) simulations. The presented approach is tailor-made for molecular systems where atomistic resolution is required only in spatially…
To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME)…
In this paper, a stochastic alternating direction method of multipliers (ADMM) is proposed for a class of nonsmooth composite and stochastic convex optimization problems in Hilbert space, motivated by optimization problems constrained by…
A new topography adapted mesh generation process tailored to simulate Atmospheric Boundary Layer (ABL) flows on complex terrains is presented. The mesher is fully automatic given: the maximum and minimum surface mesh size, the size of the…
The Adaptive Resolution Scheme (AdResS) is a hybrid scheme that allows one to treat a molecular system with different levels of resolution depending on the location of the molecules. The construction of a Hamiltonian based on the this idea…
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…
The Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve the equations of continuum electrostatics for large biomolecular assemblages that has provided impact in the study of a broad range of chemical, biological, and…
We investigate artificial compressibility (AC) techniques for the time discretization of the incompressible Navier-Stokes equations. The space discretization is based on a lowest-order face-based scheme supporting polytopal meshes, namely…
Understanding the dynamic behavior of biomolecules is fundamental to elucidating biological function and facilitating drug discovery. While Molecular Dynamics (MD) simulations provide a rigorous physical basis for studying these dynamics,…
This article proposes a new statistical numerical method to address gas kinetics problems obeying the Boltzmann equation. This method is inspired from some Monte-Carlo algorithms used in linear transport physics, where virtual particles are…
In this work, we introduce the novel application of the adaptive mesh refinement (AMR) technique in the global stability analysis of incompressible flows. The design of an accurate mesh for transitional flows is crucial. Indeed, an…
Molecular dynamics (MD) simulation is widely used to study protein conformations and dynamics. However, conventional simulation suffers from being trapped in some local energy minima that are hard to escape. Thus, most computational time is…
We introduce an $r-$adaptive algorithm to solve Partial Differential Equations using a Deep Neural Network. The proposed method restricts to tensor product meshes and optimizes the boundary node locations in one dimension, from which we…
We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field during materials processing. Our numerical approach uses the systematic renormalization-group formulation of the phase field…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…