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Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…
Simulating the dynamics of ions near polarizable nanoparticles (NPs) using coarse-grained models is extremely challenging due to the need to solve the Poisson equation at every simulation timestep. Recently, a molecular dynamics (MD) method…
An efficient parallelization approach to simulate optical properties of ensembles of quantum emitters in realistic electromagnetic environments is considered. It relies on balancing computing load of utilized processors and is built into…
In this paper, we explore the concept of metric-driven numerical methods as a powerful tool for solving various types of multiscale partial differential equations. Our focus is on computing constrained minimizers of functionals - or,…
The efficient simulation of fluid-structure interactions at zero Reynolds number requires the use of fast summation techniques in order to rapidly compute the long-ranged hydrodynamic interactions between the structures. One approach for…
We present a comparison of methods for treating the electrostatic interactions of finite, isolated systems within periodic boundary conditions (PBCs), within Density Functional Theory (DFT), with particular emphasis on linear-scaling (LS)…
We present a simple and effective multigrid-based Poisson solver of second-order accuracy in both gravitational potential and forces in terms of the one, two and infinity norms. The method is especially suitable for numerical simulations…
We have developed an adaptive multigrid code for solving the Poisson equation in gravitational simulations. Finer rectangular subgrids are adaptively created in locations where the density exceeds a local level-dependent threshold. We…
This paper describes a novel numerical model aiming at solving moving-boundary problems such as free-surface flows or fluid-structure interaction. This model uses a moving-grid technique to solve the Navier--Stokes equations expressed in…
Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat…
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has been recently proposed able to generate high velocity gradients…
Work presented in this paper describes a general algorithm and its finite element implementation for performing concurrent multiple sub-domain simulations in linear structural dynamics. Using this approach one can solve problems in which…
Periodically driven quantum systems can realize novel phases of matter that are not present in time-independent Hamiltonians. One important application is the engineering of synthetic gauge fields, which opens the realm of topological…
This paper proposes a novel Machine Learning-based approach to solve a Poisson problem with mixed boundary conditions. Leveraging Graph Neural Networks, we develop a model able to process unstructured grids with the advantage of enforcing…
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is…
In this paper, we present an efficient Particle-In-Cell algorithm for the simulation of the three dimensional Vlasov-Poisson system in the presence of a strong external magnetic field. When the intensity of the magnetic field is…
We present a scheme for numerical simulations of collisionless self-gravitating systems which directly integrates the Vlasov--Poisson equations in six-dimensional phase space. By the results from a suite of large-scale numerical…
Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to…