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The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…
Suppose a d-dimensional lattice cube of size n^d is colored in several colors so that no face of its triangulation (subdivision of the standard partition into n^d small cubes) is colored in m+2 colors. Then one color is used at least…
We consider two-level finite element discretization methods for the stream function formulation of the Navier-Stokes equations. The two-level method consists of solving a small nonlinear system on the coarse mesh, then solving a linear…
The expanding applications, utilized by more users, enhance hardware performance and further develop cloud systems for big data processing. This leads to numerous unexplored deep learning applications, especially in advanced computer vision…
An efficient algorithm for computing the terms appearing in the Generalised Kolmogorov Equation (GKE) written for the indefinite plane channel flow is presented. The algorithm, which features three distinct strategies for parallel…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
Two approximation algorithms for solving convex vector optimization problems (CVOPs) are provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously. The first algorithm is an extension of Benson's outer…
In this paper we present an algorithm for computing a matrix representation for a surface in P^3 parametrized over a 2-dimensional toric variety T. This algorithm follows the ideas of [Botbol-Dickenstein-Dohm-09] and it was implemented in…
In Computer Vision, edge detection is one of the favored approaches for feature and object detection in images since it provides information about their objects boundaries. Other region-based approaches use probabilistic analysis such as…
We propose IR2Vec, a Concise and Scalable encoding infrastructure to represent programs as a distributed embedding in continuous space. This distributed embedding is obtained by combining representation learning methods with flow…
Topology optimization is a key methodology in engineering design for finding efficient and robust structures. Due to the enormous size of the design space, evaluating all possible configurations is typically infeasible. In this work, we…
This paper introduces a novel method for the efficient and accurate computation of the volume of a domain whose boundary is given by an orientable hypersurface which is implicitly given as the iso-contour of a sufficiently smooth level-set…
The task of providing effective instruction and facilitating comprehension of resources is a substantial difficulty in the field of Quantum Computing, mostly attributable to the complicated nature of the subject matter. Our research-based…
A canal surface is an envelope of a one parameter family of spheres. In this paper we present an efficient algorithm for computing the implicit equation of a canal surface generated by a rational family of spheres. By using Laguerre and Lie…
This paper extends the author's previous two-dimensional work with Ou and LeVeque to high-resolution finite volume modeling of systems of fluids and poroelastic media in three dimensions, using logically rectangular mapped grids. A method…
Compressible interfacial multiphase flows (CIMF) are essential to different applications, such as liquid fuel injection in supersonic propulsion systems. Since high-level details in CIMF are often difficult to measure in experiments,…
The present article describes the development of a software which was written in visual basic programming language. The software calculates the particle collection efficiency and penetration of a fibrous filter medium for given values of…
An advanced Volume of Fluid (VOF) method is presented that enables performant three-dimensional Direct Numerical Simulations (DNS) of the interaction of two immiscible fluids in a gaseous environment with large topology changes, e.g.,…
We present a high-order method that provides numerical integration on volumes, surfaces, and lines defined implicitly by two smooth intersecting level sets. To approximate the integrals, the method maps quadrature rules defined on…