In this paper, we analyze a hybridizable discontinuous Galerkin method for numerically solving the Stokes equations. The method uses polynomials of degree k for all the components of the approximate solution of the gradient-velocity-pressure formulation. The novelty of the analysis is the use of a new projection tailored to the very structure of the numerical traces of the method. It renders th...

Abstract. In this paper, a modified gradient projection method is proposed to solve the nonlinear constrained optimization problems, where the search direction is obtained by combing feasibility with descent. In addition, it is pointed out that, for linear constrained optimization problems, this method may be simplified and viewed as the modified version to Rosen’s method. The theoretical analy...

A new numerical method to model the dynamic behavior of lipid vesicles under general flows is presented. A gradient-augmented level set method is used to model the membrane motion. To enforce the volumeand surface-incompressibility constraints a four-step projection method is developed to integrate the full Navier-Stokes equations. This scheme is implemented on an adaptive non-graded Cartesian ...

An explicit staggered projection method for the incompressible Navier-Stokes equations with no-slip walls is analyzed and used in simulations to address several issues related to the pressure boundary condition required when the continuity equation is replaced by the standard pressure Poisson equation (PPE), ∇p = ∇ · (−u · ∇u+ f). First, it is shown that a PPE system supplemented with a Neumann...

Approximate projection methods are useful computational tools for solving the equations of timedependent incompressible flow. In this report we will present a new discretization of the approximate projection in an approximate projection method. The discretizations of divergence and gradient will be identical to those in existing approximate projection methodology using cell-centered values of p...

We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label. By harnessing a recent theoretical result on the gradient of mutual information, the above optimization problem can be solved directly using gradient descent,...

It is well known that the gradient-projection algorithm plays an important role in solving constrained convex minimization problems. In this paper, based on Xu’s method [Xu, H. K.: Averaged mappings and the gradient-projection algorithm, J. Optim. Theory Appl. 150, 360-378(2011)], we use the idea of regularization to establish implicit and explicit iterative methods for finding the approximate ...

We present an efficient spectral projected-gradient algorithm for optimization subject to a group `1-norm constraint. Our approach is based on a novel linear-time algorithm for Euclidean projection onto the `1and group `1-norm constraints. Numerical experiments on large data sets suggest that the proposed method is substantially more efficient and scalable than existing methods.