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We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the…
We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…
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…
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…
We present a novel approach to robust pose graph optimization based on Graduated Non-Convexity (GNC). Unlike traditional GNC-based methods, the proposed approach employs an adaptive shape function using B-spline to optimize the shape of the…
Geometric optimization problems are at the core of many applications in geometry processing. The choice of a representation fitting an optimization problem can considerably simplify solving the problem. We consider the Nonlinear…
An effective method for generating linear equations of maximal symmetry in their much general normal form is obtained. In the said normal form, the coefficients of the equation are differential functions of the coefficient of the term of…
Most problems in gravitational lensing require numerical solutions. The most frequent types of problems are (1) finding multiple images of a single source and classifying the images according to their properties like magnification or…
This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surface from the scattered near-field Cauchy data generating by point sources and…
We present a practical approach to solving distance-based optimization problems using optical computing hardware. The objective is to minimize an energy function defined as the weighted sum of squared differences between measured distances…
This article develops a solution for an inverse problem through the generalized method of lines. We consider a Laplace equation on a domain with internal and external boundaries with standard Dirichlet boundary conditions. Also, we specify…
A general class of Newton algorithms on Gra{\ss}mann and Lagrange-Gra{\ss}mann manifolds is introduced, that depends on an arbitrary pair of local coordinates. Local quadratic convergence of the algorithm is shown under a suitable condition…
Solving structured systems of linear equations in a non-centralized fashion is an important step in many distributed optimization and control algorithms. Fast convergence is required in manifold applications. Known decentralized algorithms,…
In this paper we derive a variational formulation for a linear curved beam which is natively expressed in global Cartesian coordinates. During derivation the beam midline is assumed to be implicitly described by a vector distance function…
An important topic of interest in imaging is the construction of protocols that are not diffraction limited. This can be achieved in a variety of ways, including classical superresolution techniques or quantum entanglement-based protocols.…
We consider capillary surfaces that are constructed by bounded generating curves. This class of surfaces includes radially symmetric and lower dimensional fluid-fluid interfaces. We use the arc-length representation of the differential…
We propose a general and versatile framework that significantly speeds-up graphical model optimization while maintaining an excellent solution accuracy. The proposed approach relies on a multi-scale pruning scheme that is able to…
Curve and surface fairing is crucial in computer-aided geometric design, influencing product quality, physical performance, and aesthetics. Traditional methods often apply global modifications, lacking fine-grained control. This paper…
This work aims at the precise and efficient computation of the x-ray projection of an image represented by a linear combination of general shifted basis functions that typically overlap. We achieve this with a suitable adaptation of ray…
In this paper we present a method for direct evaluation of generalized B-splines (GB-splines) via the local representation of these curves as piecewise functions. To accomplish this we introduce a local structure that makes GB-spline curves…