An effective numerical method based on Legendre polynomials is proposed for the solution of a class of variational problems with suitable boundary conditions. The Ritz spectral method is used for finding the approximate solution of the problem. By utilizing the Ritz method, the given nonlinear variational problem reduces to the problem of solving a system of algebraic equations. The advantage o...

For the 2D Euler equations and related models of geophysical flows, minima of energy–Casimir variational problems are stable steady states of the equations (Arnol’d theorems). The same variational problems also describe sets of statistical equilibria of the equations. This paper uses Lyapunov–Schmidt reduction in order to study the bifurcation diagrams for these variational problems, in the lim...

We study the problem of enabling general 2D and 3D variational constraint representation to be used in conjunction with a feature hierarchy representation, where some of the features may use procedural or other non-constraint based representations. We trace the challenge to a requirement on constraint decomposition algorithms or decomposition-recombination (DR) planners used by most variational...

this study presents a comparative survey of direct methods for solving variational problems. thisproblems can be used to solve various differential equations in physics and chemistry like rateequation for a chemical reaction. there are procedures that any type of a differential equation isconvertible to a variational problem. therefore finding the solution of a differential equation isequivalen...

We present an approach to parallel variational optical flow computation by using an arbitrary partition of the image plane and iteratively solving related local variational problems associated with each subdomain. The approach is particularly suited for implementations on PCclusters because inter-process communication is minimized by restricting the exchange of data to a lower-dimensional inter...

A deformable registration approach for medical images of same dimensionality is proposed. The popular free-form deformations (FFD) setting is utilized to characterize deformations based on a grid of control points. B-splines serve the purpose of interpolating the dense deformation field from a given control point configuration. The central idea is to combine the FFD method with well-understood ...

The ultra weak variational formulation (UWVF) approach has been proposed as an effective method for solving Helmholtz problems with high wave numbers. However, for coarse meshes the method can suffer from instability. In this paper we consider computational aspects of the ultra weak variational formulation for the inhomogeneous Helmholtz problem. We introduce a method to improve the UWVF scheme...

This thesis deals with the reconstruction of images where the measured data are corrupted by Poisson noise and a specific signal-dependent speckle noise, which occurs e.g. in medical ultrasound images. Since both noise types fundamentally differ from the frequently studied additive Gaussian noise in mathematical image processing, adapted variational models are required to handle these types of ...

we establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. a corresponding novel neural network model, which is globally convergent and stable in the sense of lyapunov, is proposed. both theoretical and numerical approaches are considered. numerical simulations for three constrained nonlinear optimization problems a...