Related papers: Inter/extrapolation-based multirate schemes -- a d…
We propose a novel method for the efficient and accurate iterative solution of frequency domain integral equations (IEs) that are used for large/multi-scale electromagnetic scattering problems. The proposed method uses a novel…
The controller design of the so-called "difference algebraic equation" (DAE) systems that are frequently shown in industrial processes, tend to be challenging because of the combination of algebraic equations and high state dimensions. In…
We compare three approaches to posing the index 3 set of differential algebraic equations (DAEs) associated with the constrained multibody dynamics problem formulated in absolute coordinates. The first approach works directly with the…
This paper investigates iterative methods for solving bi-level optimization problems where both inner and outer functions have a composite structure. We establish novel theoretical results, including the first analysis that provides…
In 5G smart cities, edge computing is employed to provide nearby computing services for end devices, and the large-scale models (e.g., GPT and LLaMA) can be deployed at the network edge to boost the service quality. However, due to the…
Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to…
We introduce, analyze and test a new interpolation operator for use with continuous data assimilation (DA) of evolution equations that are discretized spatially with the finite element method. The interpolant is constructed as an…
As is well-known, the advantage of the high-order compact difference scheme (H-OCD) is unconditionally stable and convergent with the order $O(\tau^2+h^4)$ under the maximum norm. In this article, a new numerical gradient scheme based on…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…
Solving initial value problems and boundary value problems of Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions…
In engineering, it is a common desire to couple existing simulation tools together into one big system by passing information from subsystems as parameters into the subsystems under influence. As executed at fixed time points, this data…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
Singularly perturbed systems (SPSs) are prevalent in engineering applications, where numerically solving their initial value problems (IVPs) is challenging due to stiffness arising from multiple time scales. Classical explicit methods…
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…
Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…
Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims at resolving the statistics of the slowest dynamics. This…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
Constrained mechanical systems occur in many applications, such as modeling of robots and other multibody systems. In this case, the motion is governed by a system of differential-algebraic equations (DAE), often with large and sparse…
We consider quadrature formulas of high order in time based on Radau-type, L-stable implicit Runge-Kutta schemes to solve time dependent stiff PDEs. Instead of solving a large nonlinear system of equations, we develop a method that performs…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…