Related papers: Fast and Rigorous DC Solution in Finite Element Me…
This paper develops high-accuracy methods for numerically solving optimal control problems subject to nonsmooth differential equations with set-valued step functions. A notable subclass of these systems are Filippov systems. The set-valued…
In this paper we present an advanced numerical method to simulate a real life challenging industrial problem that consists of the non-destructive testing in steam generators. We develop a finite element technique that handles the big data…
We propose a new coding scheme, called the delayed coding (DC) scheme, for channels with insertion, deletion, and substitution (IDS) errors. The proposed scheme employs delayed encoding and non-iterative detection and decoding strategies to…
This work presents a practical finite element modeling strategy, the Crack Element Method (CEM), for simulating the dynamic crack propagation in two-dimensional structures. The method employs an element-splitting algorithm based on the…
Accurately modeling power distribution grids is crucial for designing effective monitoring and decision making algorithms. This paper addresses the partial observability issue of data-driven distribution modeling in order to improve the…
We study the convergence and the stability of fictitious dynamical methods for electrons. First, we show that a particular damped second-order dynamics has a much faster rate of convergence to the ground-state than first-order steepest…
The problem of optimal control of power distribution systems is becoming increasingly compelling due to the progressive penetration of distributed energy resources in this specific layer of the electrical infrastructure. Distribution…
The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…
In the present article we investigate optical near fields in semiconductor lasers. We perform finite element simulations for two different laser types, namely a super large optical waveguide (SLOW) laser, which is an edge emitter, and a…
Pairwise compatibility measure (CM) is a key component in solving the jigsaw puzzle problem (JPP) and many of its recently proposed variants. With the rapid rise of deep neural networks (DNNs), a trade-off between performance (i.e.,…
Conventional AC Power Flow (ACPF) solvers like Newton-Raphson (NR) face significant computational and convergence challenges in modern, large-scale power systems. This paper proposes a novel, two-stage hybrid method that integrates a…
To address the power system hardening problem, traditional approaches often adopt robust optimization (RO) that considers a fixed set of concerned contingencies, regardless of the fact that hardening some components actually renders…
Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty…
We propose a novel decomposition framework for the distributed optimization of Difference Convex (DC)-type nonseparable sum-utility functions subject to coupling convex constraints. A major contribution of the paper is to develop for the…
A computer simulation has to be fast to be helpful, if it is employed to study the behavior of a multicomponent dynamic system. This paper discusses modeling concepts and algorithmic techniques useful for creating such fast simulations.…
The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…
The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time. To this end, algorithmically, the standard adaptive finite…
In contrast with the diffusion equation which smoothens the initial data to $C^\infty$ for $t>0$ (away from the corners/edges of the domain), the subdiffusion equation only exhibits limited spatial regularity. As a result, one generally…
Finding strongly connected components (SCCs) and the diameter of a directed network play a key role in a variety of discrete optimization problems, and subsequently, machine learning and control theory problems. On the one hand, SCCs are…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…