Distributed flow algorithms for scalable similarity visualization

We describe simple yet scalable and distributed algorithms for solving the maximum flow problem and its minimum cost flow variant, motivated by problems of interest in objects similarity visualization. We formulate the fundamental problem as a convex-concave saddle point problem. We then show that this problem can be efficiently solved by a first order method or by exploiting faster quasi-Newton steps. Our proposed approach costs at most O(|ε|) per iteration for a graph with |ε| edges. Further, the number of required iterations can be shown to be independent of number of edges for the first order approximation method. We present experimental results in two applications: mosaic generation and color similarity based image layouting. © 2010 IEEE.

A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier-Stokes equations

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier-Stokes model. © 2011 Elsevier Ltd.