Related papers: Fast and Rigorous DC Solution in Finite Element Me…
Power grids vulnerability is a key issue in society. A component failure may trigger cascades of failures across the grid and lead to a large blackout. Complex network approaches have shown a direction to study some of the problems faced by…
The trend in the electric power system is to move towards increased amounts of distributed resources which suggests a transition from the current highly centralized to a more distributed control structure. In this paper, we propose a method…
A model of high temperature superconducting dynamo, a promising type of flux pumps capable of wireless injection of a large DC current into a superconducting circuit, has recently been chosen as an applied superconductivity benchmark…
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
A high order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface are allowed to cut through the background mesh. To…
Direct current (DC) network has been recognized as a promising technique, especially for shipboard power systems (SPSs). Fast resilience control is required for an SPS to survive after faults. Towards this end, this paper proposes the…
A novel multiscale numerical method is developed to accelerate direct simulation Monte Carlo (DSMC) simulations for polyatomic gases with internal energy. This approach applies the general synthetic iterative scheme to stochastic…
Numerical simulation of ultrasonic wave propagation provides an efficient tool for crack identification in structures, while it requires a high resolution and expensive time calculation cost in both time integration and spatial…
Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this…
Robust simulation is essential for reliable operation and planning of transmission and distribution power grids. At present, disparate methods exist for steady-state analysis of the transmission (power flow) and distribution power grid…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
Dimensionality reduction in mechanical vibratory systems poses challenges for distributed structures including geometric nonlinearities, mainly because of the lack of invariance of the linear subspaces. A reduction method based on direct…
Linear Dynamical Systems, both discrete and continuous, are invaluable mathematical models in a plethora of applications such the verification of probabilistic systems, model checking, computational biology, cyber-physical systems, and…
Scenario reduction is an important topic in stochastic programming problems. Due to the random behavior of load and renewable energy, stochastic programming becomes a useful technique to optimize power systems. Thus, scenario reduction gets…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…
In many power system optimization problems, we observe that only a small fraction of the line flow constraints ever become active at the optimal solution, despite variations in the load profile and generation costs. This observation has…
Resilience is emerging as an evolving notion, reflecting a system's ability to endure and adapt to sudden and catastrophic changes and disruptions. This paper spotlights the significance of the quantitative resilience indices of…
The aim of this paper is to propose a systematic way to obtain convergent finite element schemes for the Darcy-Stokes flow problem by combining well-known mixed finite elements that are separately convergent for Darcy and Stokes problems.…
We develop a cut finite element method for the Bernoulli free boundary problem. The free boundary, represented by an approximate signed distance function on a fixed background mesh, is allowed to intersect elements in an arbitrary fashion.…