In this paper, we study some Schwarz methods of Neumann–Neumann type for some vector field problems, discretized with the lowest order Raviart–Thomas and Nédélec finite elements. We consider a hybrid Schwarz preconditioner consisting of a coarse component, which involves the solution of the original problem on a coarse mesh, and local ones, which involve the solution of Neumann problems on the ...

The completeness and versatility of spatial data models and associated operations serve as the foundation of any GIS. The raster data model and the cartographic modeling framework provide the representation and operations for analyzing geographic fields. The current GIS raster data model and cartographic modeling operations are limited in that all the attributes measured at each location in fie...

One of the problems connected with a real-time protein-ligand docking simulation is the need to store series of precomputed electrostatic force fields of a molecule changing in time. A single frame of the force field is a 3D array of floating point vectors and it constitutes approximately 180 MB of data. Therefore requirements on storage grow rapidly if several hundreds of such frames need to b...

This paper presents a new approach for the Radial Basis Function (RBF) interpolation of a vector field. Standard approaches for interpolation randomly select points for interpolation. Our approach uses the knowledge of vector field topology and selects points for interpolation according to the critical points location. We presents the results of interpolation errors on a vector field generated ...

Software development is, mostly, a collaborative process where teams of developers work together in order to produce quality code. Collaboration is, generally, not an issue, as teams work together in the same office or building. However, larger projects may require more people, who might be spread through-out different floors, buildings and different companies. Several systems have been develop...

Traditionally, vector field visualization is concerned with 2D and 3D flows. Yet, many concepts can be extended to general dynamical systems, including the higher-dimensional problem of modeling the motion of finite-sized objects in fluids. In the steady case, the trajectories of these so-called inertial particles appear as tangent curves of a 4D or 6D vector field. These higher-dimensional flo...

This is an expository paper explaining how trees can be used to compute effectively the vector field expressions which arise in nonlinear control theory. It also describe the mathematical structure that sets of trees carry.

In this paper we present and study a new class of regularized kernel methods for learning vector fields, which are based on filtering the spectrum of the kernel matrix. These methods include Tikhonov regularization as a special case, as well as interesting alternatives such as vector valued extensions of L2-Boosting. Our theoretical and experimental analysis shows that spectral filters that yie...

We present an approach for elastic secondary deformations of shapes described as triangular meshes. The deformations are steered by the simulation of a low number of simple mass-spring sets. The result of this simulation is used to define time-dependent divergence-free vector fields whose numerical path line integration gives the new location of each vertex. This way the deformation is guarante...

In quantum groups coproducts of Lie-algebras are twisted in terms of generators of the corresponding universal enveloping algebra. If representations are considered, twists also serve as starproducts that accordingly quantize representation spaces. In physics, requirements turn out to be the other way around. Physics comes up with noncommutative spaces in terms of starproducts that miss a suiti...