Related papers: Curvilinear coordinate Generalized Source Method f…
The generalized winding number is an essential part of the geometry processing toolkit, allowing to quantify how much a given point is inside a surface, even when the surface has boundaries and noise. We propose a new universal method to…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
The ability of curved gratings as sectors of concentric circular gratings to couple linearly polarized light into focused surface plasmons is investigated by theory, simulation and experiment. Curved gratings, as sectors of concentric…
We propose a novel method to generate a small set of ruled surfaces that do not collide with the input shape for linear hot-wire rough machining. Central to our technique is a new observation: the ruled surfaces constructed by vertical…
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
Computing offsets of curves on parametric surfaces is a fundamental yet challenging operation in computer aided design and manufacturing. Traditional analytical approaches suffer from time-consuming geodesic distance queries and complex…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
Implementing the modal method in the electromagnetic grating diffraction problem delivered by the curvilinear coordinate transformation yields a general analytical solution to the 1D grating diffraction problem in a form of a T-matrix.…
We present a new mimetic finite difference method for diffusion problems that converges on grids with \textit{curved} (i.e., non-planar) faces. Crucially, it gives a symmetric discrete problem that uses only one discrete unknown per curved…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
We propose a new exact approach to the generalized graph layering problem that is based on a particular quadratic assignment formulation. It expresses, in a natural way, the associated layout restrictions and several possible objectives,…
We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable…
We generalize the technique of [Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains, SIAM J. Sci. Comput. 34, pp. A497--A519 (2012)] to elliptic problems with mixed boundary conditions and elliptic…
We propose a family of curvature-based regularization terms for deep generative model learning. Explicit coordinate-invariant formulas for both intrinsic and extrinsic curvature measures are derived for the case of arbitrary data manifolds…
A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
The availability of a robust and efficient routine for calculating light curves of a finite source magnified due to bending its light by the gravitational field of an intervening binary lens is essential for determining the characteristics…