We present an approach to parallel variational optical flow computation on standard hardware by domain decomposition. Using an arbitrary partition of the image plane into rectangular subdomains, the global solution to the variational approach is obtained by iteratively combining local solutions which can be efficiently computed in parallel by separate multi-grid iterations for each subdomain. T...

We propose here the use of the variational level set methodology to capture Lagrangian vortex boundaries in 2D unsteady velocity fields. This method reformulates earlier approaches that seek material vortex boundaries as extremum solutions of variational problems. We demonstrate the performance of this technique for two different variational formulations built upon different notions of coherenc...

In this paper, a Galerkin boundary node method (GBNM) is developed for boundary-only analysis of 2D problems in linear elasticity. The GBNM combines the variational form of a boundary integral formulation for the elastic equations with the moving least-squares approximations for generating the trial and test functions. Unlike the boundary node method, the main idea here is to use the Galerkin s...

We study variational problems for curves approximated by B-spline curves. We show that one can obtain discrete Euler-Lagrange equations for the data describing the approximated curves. Our main application is to the occluded curve problem in 2D and 3D. In this case, the aim is to find various aesthetically pleasing solutions as opposed to a solution of a physical problem. The Lagrangians of int...

Recently, it is shown that graph cuts algorithms can be used to solve some variational image restoration problems, especially connected with noise removal and segmentation. For very large size images, the usage for memory and computation increases dramatically. We propose a domain decomposition method with graph cuts algorithms. We show that the new approach costs effective both for memory and ...

In order to reduce the computational effort we develop a method for 3D-to-2D dimensionality reduction of scattering problems in photonics. Contrary to the ‘standard’ Effective Index Method the effective parameters of the reduced problem are always rigorously defined using the variational technique, based on the vectorial 3D Maxwell equations. Results for a photonic crystal slab waveguide show t...

In part I the authors reported on the design of a robust and versatile gradientweighted moving finite element (GWMFE) code in one dimension and on its application to a variety of PDEs and PDE systems. This companion paper does the same for the two-dimensional (2D) case. These moving node methods are especially suited to problems which develop sharp moving fronts, especially problems where one n...

In this paper, we deal with the problem of computing the distance to a surface (a curve in 2D) and consider several distance function approximation methods which are based on solving partial differential equations (PDEs) and finding solutions to variational problems. In particular, we deal with distance function estimation methods related to the Poisson-like equations and generalized double-lay...

This paper describes a simulation method for 2D frequency domain scattering problems in photonics. The technique reduces the spatial dimensionality of the problem by means of global, continuous mode expansion combined with a variational formalism; the resulting equations are solved using a finite element method. Transparent influx boundary conditions and perfectly matched layers are employed at...