相关论文: Explicit and CPU/GPU parallel energy-preserving sc…

In this paper, we derive two bound-preserving and mass-conserving schemes based on the fractional-step method and high-order compact (HOC) finite difference method for nonlinear convection-dominated diffusion equations. We split the…

The convergence performance of distributed optimization algorithms is of significant importance to solve optimal power flow (OPF) in a distributed fashion. In this paper, we aim to provide some insights on how to partition a power system to…

The coordinated alternating current optimal power flow (ACOPF) for coupled transmission-distribution grids has become crucial to handle problems related to high penetration of renewable energy sources (RESs). However, obtaining all system…

We propose energy-conserving discontinuous Galerkin (DG) methods for symmetric linear hyperbolic systems on general unstructured meshes. Optimal a priori error estimates of order $k+1$ are obtained for the semi-discrete scheme in one…

Increased reliance on graphics processing units (GPUs) for high-intensity computing tasks raises challenges regarding energy consumption. To address this issue, dynamic voltage and frequency scaling (DVFS) has emerged as a promising…

In this paper, we consider the day-ahead operational planning problem of a radial distribution network hosting Distributed Energy Resources (DERs) including rooftop solar and storage-like loads, such as electric vehicles. We present a novel…

Minimization of energy in gradient systems leads to formation of oscillatory and Turing patterns in reaction-diffusion systems. These patterns should be accurately computed using fine space and time meshes over long time horizons to reach…

The recently developed semi-Lagrangian discontinuous Galerkin approach is used to discretize hyperbolic partial differential equations (usually first order equations). Since these methods are conservative, local in space, and able to limit…

Stochastic Klein--Gordon--Schr\"odinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel…

Stochastic Klein--Gordon--Schr\"odinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel…

It is well-known that the Allen-Cahn equation not only satisfies the energy dissipation law but also possesses the maximum bound principle (MBP) in the sense that the absolute value of its solution is pointwise bounded for all time by some…

In this article, we present an interpolative separable density fitting (ISDF) based algorithm to calculate exact exchange in periodic mean field calculations. In the past, decomposing the two-electron integrals into tensor hypercontraction…

We present a fast, unconditionally energy-stable numerical scheme for simulating vesicle deformation under osmotic pressure using a phase-field approach. The model couples an Allen-Cahn equation for the biomembrane interface with a…

In this work, we introduce semi-implicit or implicit finite difference schemes for the continuity equation with a gradient flow structure. Examples of such equations include the linear Fokker-Planck equation and the Keller-Segel equations.…

Decoupling approach presents a novel solution/alternative to the highly time-consuming fluid-thermal-structural simulation procedures when thermal effects and resultant displacements on machine tools are analyzed. Using high dimensional…

Modern graphics processing units (GPUs) provide an unprecedented level of computing power. In this study, we present a high-performance, multi-GPU implementation of the analytical nuclear gradient for Kohn-Sham time-dependent density…

This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…

An effective way to improve energy efficiency is to throttle hardware resources to meet a certain performance target, specified as a QoS constraint, associated with all applications running on a multicore system. Prior art has proposed…

In this paper, two efficient and magnetization norm preserving numerical schemes based on the scalar auxiliary variable (SAV) method are developed for calculating the ground state in micromagnetic structures. The first SAV scheme is based…

The speed of sound in two-phase pipe flow systems is often several orders of magnitude greater than the travelling speed of hydraulic information (volume fractions.) Dynamically simulating such flows requires resolution of acoustic and…