In this paper, we present a novel volumetric mesh representation suited for parallel computing on modern GPU architectures. The data structure is based on a compact, ternary sparse matrix storage of boundary operators. Boundary operators correspond to the first-order top-down relations of k-faces to their (k−1)-face facets. The compact, ternary matrix storage format is based on compressed spars...

For the convection-diiusion equation in two dimensions we derive the cell orientated discretization which is based on the method of lines leading to diierential-algebraic equations and their time integration by implicit methods. This approach is well-suited in convection-dominated cases. The eeciency of the method depends on the solution of the arising linear systems mainly. Motivated by the de...

In this short paper we discuss how the position scale half-space ofwavelet analysis may be cut into different regions. We discuss conditions under which they are independent in the sense that the Töplitz operators associated with their characteristic functions commute modulo smoothing operators. This shall be used to define microlocal classes of distributions having a well defined behavior alon...

Generalization may be defined as a controlled reduction and simplifica tion of geographical data. Despite the knowledge of basic generalization operators, the automation of generalization remains a complex issue. Ac tually the change in resolution induces numerous spatial conflicts and the use of generalization operators such as smoothing or aggregation may ac cidentally degrade geographical da...

Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, ...

Various geometric operators have been playing an important role in surface processing. For example, many shape analysis algorithms have been developed based on eigenfunctions of the Laplace–Beltrami operator (LBO), which is defined based on the first fundamental form of the surface. In this paper, we introduce two new geometric operators based on the second fundamental form of the surface, name...

We present several theoretical contributions which allow Lie groups to be fit to high dimensional datasets. Transformation operators are represented in their eigen-basis, reducing the computational complexity of parameter estimation to that of training a linear transformation model. A transformation specific “blurring” operator is introduced that allows inference to escape local minima via a sm...

The paper presents a convergence analysis of a multigrid solver for a system of linear algebraic equations resulting from the disretization of a convection-diffusion problem using a finite element method. We consider piecewise linear finite elements in combination with a streamline diffusion stabilization . We analyze a multigrid method that is based on canonical inter-grid transfer operators, ...

This article describes a method for reducing the shape distortions due to scale-space smoothing that arise in the computation of 3-D shape cues using operators (derivatives) defined from scale-space representation. More precisely, we are concerned with a general class of methods for deriving 3-D shape cues from a 2-D image data based on the estimation of locally linearized deformations of brigh...