Related papers: A Matlab Implementation of a Flat Norm Motivated P…
We present a new method for obtaining norm bounds for random matrices, where each entry is a low-degree polynomial in an underlying set of independent real-valued random variables. Such matrices arise in a variety of settings in the…
We developed a conformal map technique to analyze the attenuation of edge modes propagating along imperfect boundaries. In systems where the potential energy exhibits conformal invariance, the conformal transformation can straighten the…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…
In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…
We present a simple and efficient MATLAB implementation of the local refinement for polygonal meshes. The purpose of this implementation is primarily educational, especially on the teaching of adaptive virtual element methods.
In this paper, we consider the problem of partitioning a polygon into a set of connected disjoint sub-polygons, each of which covers an area of a specific size. The work is motivated by terrain covering applications in robotics, where the…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
We show how to use the method of orthogonal polynomials for integrating, in the planar approximation, the partition function of one-matrix models with a potential with even or odd vertices, or any combination of them.
In this paper we propose a Local Orthogonal Decomposition method (LOD) for elliptic partial differential equations with inhomogeneous Dirichlet- and Neumann boundary conditions. For this purpose, we present new boundary correctors which…
We discuss how to implement the linear finite element method for solving the Poisson equation. We begin with the data structure to represent the triangulation and boundary conditions, introduce the sparse matrix, and then discuss the…
This paper presents a decomposition method for solving elliptic boundary value problems in one-dimension. The method is an improvement to an existing technique for approximating elliptic systems. It is demonstrated to be computationally…
For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the…
In this paper we present algorithms for an efficient implementation of the Localized Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical simulation of partial differential equations with a continuum of…
One approach to achieving correct finite element assembly is to ensure that the local orientation of facets relative to each cell in the mesh is consistent with the global orientation of that facet. Rognes et al. have shown how to achieve…
This paper examines the theory pertaining to lossless compression of correlated sources located at the edge of a network. Importantly, communication between nodes is prohibited. In particular, a method that combines correlated source coding…
Mesh simplification is the process of reducing the number of vertices, edges and triangles in a three-dimensional (3D) mesh while preserving the overall shape and salient features of the mesh. A popular strategy for this is edge collapse,…
Orthogonal graph drawing has many applications, e.g., for laying out UML diagrams or cableplans. In this paper, we present a new pipeline that draws multigraphs orthogonally, using few bends, few crossings, and small area. Our pipeline…
Automating the solutions of multiple network information theory problems, stretching from fundamental concerns such as determining all information inequalities and the limitations of linear codes, to applied ones such as designing coded…