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The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
We present an energy-preserving mechanic formulation for dynamic quasi-brittle fracture in an Eulerian-Lagrangian formulation, where a second-order phase-field equation controls the damage evolution. The numerical formulation adapts in…
$T, p$ flash calculations determine the correct number of phases at phase equilibrium and their compositions for fixed temperature and pressure. They are essential for chemical process simulation and optimization. The convex envelope method…
Phase equilibrium calculations are an essential part of numerical simulations of multi-component multi-phase flow in porous media, accounting for the largest share of the computational time. In this work, we introduce a GPUenabled, fast,…
A common problem in physics and engineering is the calculation of the minima of energy functionals. The theory of Sobolev gradients provides an efficient method for seeking the critical points of such a functional. We apply the method to…
Differential equations (DEs) are used as numerical models to describe physical phenomena throughout the field of engineering and science, including heat and fluid flow, structural bending, and systems dynamics. While there are many other…
In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical…
In spirit of the principle of least action, which means that when a perturbation is applied to a physical system its reaction is such that it modifies its state to "agree" with the perturbation by "minimal" change of its initial state. In…
In this work, we present a transition-state optimization protocol based on the Mode-Tracking algorithm [J. Chem. Phys. 118 (2003) 1634]. By calculating only the eigenvector of interest instead of diagonalizing the full Hessian matrix and…
This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power…
We develop computational methods for approximating the solution of a linear multi-term matrix equation in low rank. We follow an alternating minimization framework, where the solution is represented as a product of two matrices, and…
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
The accurate modelling and simulation of electric devices involving ferromagnetic materials requires the appropriate consideration of magnetic hysteresis. We discuss the systematic incorporation of the energy-based vector hysteresis model…
We study merchant energy production modeled as a compound switching and timing option. The resulting Markov decision process is intractable. State-of-the-art approximate dynamic programming methods applied to realistic instances of this…
With the growing popularity of electric vehicles (EVs), maintaining power grid stability has become a significant challenge. To address this issue, EV scheduling control strategies have been developed to manage vehicle-to-grid (V2G) in…
Thermomechanical stress induced by through-silicon vias (TSVs) plays an important role in the performance and reliability analysis of 2.5D/3D ICs. While the finite element method (FEM) adopted by commercial software can provide accurate…
The modeling of cracks has been an intensely researched topic for decades - both from the mechanical as well as from the mathematics point of view. As far as the modeling of sharp cracks/interfaces is concerned, the resulting free boundary…
The problem of finding an electric vehicle route that optimizes both driving time and energy consumption can be modeled as a bicriterion path problem. Unfortunately, the problem of finding optimal bicriterion paths is NP-complete. This…
This work presents a critical overview of the effects of different aspects of model formulation on crack path selection in quasi-static phase field fracture. We consider different evolution methods, mechanics formulations, fracture…
This paper outlines an energy-minimization finite-element approach to the modeling of equilibrium configurations for nematic liquid crystals in the presence of internal and external electric fields. The method targets minimization of system…