相关论文: Fast Parallel Frequency Sweeping Algorithms for Ro…
Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…
A numerical method for the direct numerical simulation of incompressible wall turbulence in rectangular and cylindrical geometries is presented. The distinctive feature resides in its design being targeted towards an efficient…
In this paper, we propose multicontinuum splitting schemes for multiscale problems, focusing on a parabolic equation with a high-contrast coefficient. Using the framework of multicontinuum homogenization, we introduce spatially smooth…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
The increasing penetration of renewable energy resources and utilization of energy storage systems pose new challenges in maintaining power system's stability. Specifically, the cost function of regulation no longer remains smooth, which…
This paper deals with the problem of efficient sampling from a stochastic differential equation, given the drift function and the diffusion matrix. The proposed approach leverages a recent model for probabilities \cite{rudi2021psd} (the…
When using Laguerre and Hermite spectral methods to numerically solve PDEs in unbounded domains, the number of collocation points assigned inside the region of interest is often insufficient, particularly when the region is expanded or…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
We present a new time-stepping algorithm for nonlinear PDEs that exhibit scale separation in time. Our scheme combines asymptotic techniques (which are inexpensive but can have insufficient accuracy) with parallel-in-time methods (which,…
In this paper, the stability of fractional differential equations (FDEs) with unknown parameters is studied. FDEs bring many advantages to model the physical systems in the nature or man-made systems in the industry. Because this…
Machine learning models, and deep neural networks in particular, are increasingly deployed in risk-sensitive domains such as healthcare, environmental forecasting, and finance, where reliable quantification of predictive uncertainty is…
Parametric linear programming is a central operation for polyhedral computations, as well as in certain control applications.Here we propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.This type…
This article offers sharp spatial and temporal mean-square regularity results for a class of semi-linear parabolic stochastic partial differential equations (SPDEs) driven by infinite dimensional fractional Brownian motion with the Hurst…
The aim of our work is to provide a simple homogenization and discrete-to-continuum procedure for energy driven problems involving stochastic rapidly-oscillating coefficients. Our intention is to extend the periodic unfolding method to the…
Transient stability simulation of a large-scale and interconnected electric power system involves solving a large set of differential algebraic equations (DAEs) at every simulation time-step. With the ever-growing size and complexity of…
In this paper, we apply the Feature Space Decomposition (FSD) method developed in [LS24, GLS25, LSSW26, ALSS26] to obtain, under fairly general conditions, matching upper and lower bounds for the population excess risk of spectral methods…
Phase unwrapping is a key problem in many coherent imaging systems, such as synthetic aperture radar (SAR) interferometry. A general formulation for redundant integration of finite differences for phase unwrapping (Costantini et al., 2010)…
We present analytical and numerical results on the joint dynamics of two coupled Duffing oscillators with nonlinearity of opposite signs (hardening and softening). In particular, we focus on the existence and stability of synchronized…
Parallel-across-the method time integration can provide small scale parallelism when solving initial value problems. Spectral deferred corrections (SDC) with a diagonal sweeper, which is closely related to iterated Runge-Kutta methods…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of…