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We develop a new approach to tackle communication constraints in a distributed learning problem with a central server. We propose and analyze a new algorithm that performs bidirectional compression and achieves the same convergence rate as…
A coupled boundary spectral element method (BSEM) and spectral element method (SEM) formulation for the propagation of small-amplitude water waves over variable bathymetries is presented in this work. The wave model is based on the…
Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices…
Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…
Constraints in power consumption and computational power limit the skill of operational numerical weather prediction by classical computing methods. Quantum computing could potentially address both of these challenges. Herein, we present…
Molecular simulation technologies have afforded researchers a unique look into the nanoscale interactions driving physical processes. However, a limitation for molecular dynamics (MD) simulations is that they must be performed on…
Anomalous diffusion is often modelled in terms of the subdiffusion equation, which can involve a weakly singular source term. For this case, many predominant time stepping methods, including the correction of high-order BDF schemes [{\sc…
Newly developed coupled-cluster (CC) methods enable simulations of ionization potentials and spectral functions of molecular systems in a wide range of energy scales ranging from core-binding to valence. This paper discusses results…
The weakly compressible smoothed particle hydrodynamics (WCSPH) method has been employed to simulate various physical phenomena involving fluids and solids. Various methods have been proposed to implement the solid wall, inlet/outlet, and…
The Lattice Boltzmann Method (LBM) is widely recognized as an efficient algorithm for simulating fluid flows in both single-phase and multi-phase scenarios. In this research, a quantum Carleman Linearization formulation of the Lattice…
A general derivation is proposed for several boundary conditions arisen in the lattice Boltzmann simulations of various physical problems. Pair-wise moment conservations are proposed to enforce the boundary conditions with given macroscopic…
Hybrid quantum mechanical-molecular mechanical (QM/MM) simulations are widely used in enzyme simulation. Over ten convergence studies of QM/MM methods have revealed over the past several years that key energetic and structural properties…
The shrinking core model describes the reaction of a spherical solid particle with a surrounding fluid. In this work, we revisit the SCM by deriving it from the underlying physical processes and performing a careful non-dimensionalisation,…
Quantum computers hold promise to circumvent the limitations of conventional computing for difficult molecular problems. However, the accumulation of quantum logic errors on real devices represents a major challenge, particularly in the…
Hybrid quantum mechanics / molecular mechanics (QM/MM) models successfully describe the properties of biological macromolecules. However, most QM/MM methodologies are constrained to unrealistic gas phase models, thus limiting their…
Fluid simulations, especially at high Reynolds numbers, are computationally expensive on classical computers, making them promising application targets for quantum computing. Recent studies have combined the lattice Boltzmann method (LBM)…
The implementation and validation of the adaptive buffered force QM/MM method in two popular packages, CP2K and AMBER are presented. The implementations build on the existing QM/MM functionality in each code, extending it to allow for…
It is well known that the number of particles should be scaled up to enable industrial scale simulation. The calculations are more computationally intensive when the motion of the surrounding fluid is considered. Besides the advances in…
We present a novel parametric finite element approach for simulating the surface diffusion of curves and surfaces. Our core strategy incorporates a predictor-corrector time-stepping method, which enhances the classical first-order temporal…
The Kinetic-Diffusion Monte Carlo (KDMC) method is a powerful tool for simulating neutral particles in fusion reactors. It is a hybrid fluid-kinetic method that is significantly faster than pure kinetic methods at the cost of a small bias…