Related papers: Adaptive Finite Differencing in High Accuracy Elec…
Advances in deep learning have enabled physics-informed neural networks to solve partial differential equations. Numerical differentiation using the finite-difference (FD) method is efficient in physics-constrained designs, even in…
Ab initio molecular dynamics (AIMD) simulations using hybrid density functionals and plane waves are of great interest owing to the accuracy of this approach in treating condensed matter systems. On the other hand, such AIMD calculations…
Large-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing…
This paper presents AFD-STA Net, a neural framework integrating adaptive filtering and spatiotemporal dynamics learning for predicting high-dimensional chaotic systems governed by partial differential equations. The architecture combines:…
In order to accelerate implementation of hyperelastic materials for finite element analysis, we developed an automatic numerical algorithm that only requires the strain energy function. This saves the effort on analytical derivation and…
One of the most popular methods employed in computational electromagnetics is the Finite Difference Time Domain (FDTD) method. We generalise it to a meshless setting using the Radial Basis Function generated Finite Difference (RBF-FD)…
The fourth-order PDE that models the density variation of smectic A liquid crystals presents unique challenges in its (numerical) analysis beyond more common fourth-order operators, such as the classical biharmonic. While the operator is…
V2X (Vehicle-to-everything) communication relies on short messages for short-range transmissions over a fading wireless channel, yet requires high reliability and low latency. Hard-decision decoding sacrifices the preservation of diversity…
To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved…
The finite-difference time-domain (FDTD) method, which is important in photonic hardware design flow, is widely adopted to solve time-domain Maxwell equations. However, FDTD is known for its prohibitive runtime cost, taking minutes to hours…
The efficient encoding of the fermionic Schr\"odinger equation as a spin system Hamiltonian is a long-term problem. I describe an encoding for the fermionic position space Schr\"odinger equation on a finite-volume periodic lattice with a…
Fast power system state estimation (SE) solution is of paramount importance for achieving real-time decision making in power grid operations. Semidefinite programming (SDP) reformulation has been shown effective to obtain the global optimum…
A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method on non-uniform meshes. It is based on the utilization of hierarchical…
The accuracy of atomistic simulations depends on the precision of force fields. Traditional numerical methods often struggle to optimize the empirical force field parameters for reproducing target properties. Recent approaches rely on…
In this paper we develop two conforming finite element methods for a fourth order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in absence of applied magnetic field. Unlike the biharmonic…
Derivative-free optimization (DFO) is vital in solving complex optimization problems where only noisy function evaluations are available through an oracle. Within this domain, DFO via finite difference (FD) approximation has emerged as a…
The design of better exchange-correlation functionals for Density Functional Theory (DFT) is a central challenge of modern electronic structure theory. However, current developments are limited by the mathematical form of the functional,…
A novel hybrid spectral difference/embedded finite volume method is introduced in order to apply a discontinuous high-order method for large scale engineering applications involving discontinuities in the flows with complex geometries. In…
Over the past few years much progress has been made in Computational Fluid Dynamics (CFD) in its ability to accurately simulate the hydrodynamics associated with a deep-V monohull planing craft. This work has focused on not only predicting…
Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a…