Adaptive Refinement for Unstructured T-Splines with Linear Complexity

Robust Parallel Adaptive Mesh Refinement Software Library for Unstructured Meshes

Computational Complexity of Adaptive LES with Variable Fidelity Model Refinement

Adaptive methods with both mesh and polynomial order refinements have been used extensively in computational fluid dynamics to achieve optimal accuracy with the minimal computational cost. However hp-refinement by itself is not sufficient for numerical simulation of turbulent flows of engineering interest. For instance, even for the extreme hp-refinement such as spectral DNS, the requirement to...

Non-Linear Model Predictive Control with Adaptive Time-Mesh Refinement

In this paper, we present a novel solution for realtime, Non-Linear Model Predictive Control (NMPC) exploiting a time-mesh refinement strategy. The proposed controller formulates the Optimal Control Problem (OCP) in terms of flat outputs over an adaptive lattice. In common approximated OCP solutions, the number of discretization points composing the lattice represents a critical upper bound for...

Parallel Refinement of Unstructured Meshes

In this paper we describe a parallel h-refinement algorithm for unstructured finite element meshes based on the longest-edge bisection of triangles and tetrahedrons. This algorithm is implemented in PARED, a system that supports the parallel adaptive solution of PDEs. We discuss the design of such an algorithm for distributed memory machines including the problem of propagating refinement acros...

Image compression by linear splines over adaptive triangulations

This paper proposes a new method for image compression. The method is based on the approximation of an image, regarded as a function, by a linear spline over an adapted triangulation, D(Y ), which is the Delaunay triangulation of a small set Y of significant pixels. The linear spline minimizes the distance to the image, measured by the mean square error, among all linear splines over D(Y ). The...