Numerical Mathematics-theory Methods and Applications 

About: Numerical Mathematics-theory Methods and Applications is an academic journal published by Cambridge University Press. The journal publishes majorly in the area(s): Finite element method & Multigrid method. It has an ISSN identifier of 1004-8979. Over the lifetime, 449 publications have been published receiving 3835 citations. The journal is also known as: NM-TMA & Numerical mathematics: theory, methods and applications.

pde2path - A Matlab Package for Continuation and Bifurcation in 2D Elliptic Systems

Abstract: pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components, on general two dimensional domains, and with rather general boundary conditions. The package is based on the FEM of the Matlab pdetoolbox, and is explained by a number of examples, including Bratu’s problem, the Schnakenberg model, Rayleigh-Benard convection, and von Karman plate equations. These serve as templates to study new problems, for which the user has to provide, via Matlab function files, a description of the geometry, the boundary conditions, the coefficients of the PDE, and a rough initial guess of a solution. The basic algorithm is a one parameter arclength-continuation with optional bifurcation detection and branch-switching. Stability calculations, error control and mesh-handling, and some elementary time-integration for the associated parabolic problem are also supported. The continuation, branch-switching, plotting etc are performed via Matlab command-line function calls guided by the AUTO style. The software can be downloaded from www.staff.uni-oldenburg.de/hannes.uecker/pde2path, where also an online documentation of the software is provided such that in this paper we focus more on the mathematics and the example systems.

Advances in Studies and Applications of Centroidal Voronoi Tessellations

Abstract: Centroidal Voronoi tessellations (CVTs) have become a useful tool in many applications ranging from geometric modeling, image and data analysis, and numerical partial differential equations, to problems in physics, astrophysics, chemistry, and biology. In this paper, we briefly review the CVT concept and a few of its generalizations and well-known properties. We then present an overview of recent advances in both mathematical and computational studies and in practical applications of CVTs. Whenever possible, we point out some outstanding issues that still need investigating. AMS subject classifications: 5202, 52B55, 62H30, 6502, 65D30, 65U05, 65Y25, 68U05, 68U10

Fast Texture Segmentation Based on Semi-Local Region Descriptor and Active Contour

Abstract: In this paper, we present an efficient approach for unsupervised segmenta- tion of natural and textural images based on the extraction o fi mage features and a fast active contour segmentation model. We address the problem of textures where neither the gray-level information nor the boundary information is adequate for object extraction. This is often the case of natural images compose do f both homogeneous and textured regions. Because these images cannot be in generaldirectly processed by the gray-level information, we propose a new texture descripto rw hich intrinsically def ines the geometry of textures using semi-local image informatio na nd tools from differen- tial geometry. Then, we use the popular Kullback-Leibler distance to design an active contour model which distinguishes the background and textures of interest. The exis- tence of a minimizing solution to the proposed segmentationmodel is proven. Finally, at exture segmentation algorithm based on the Split-Bregma nm ethod is introduced to extract meaningful objects in a fast way. Promising synthetic and real-world results for gray-scale and color images are presented.

An Adaptive Strategy for the Restoration of Textured Images using Fractional Order Regularization

Abstract: Total variation regularization has good performance in noise removal and edge preservation but lacks in texture restoration. Here we present a texture-preserving strategy to restore images contaminated by blur and noise. According to a texture de- tection strategy, we apply spatially adaptive fractional order diffusion. A fast algorithm based on the half-quadratic technique is used to minimize the resulting objective func- tion. Numerical results show the effectiveness of our strategy.

A review of unified a posteriori finite element error control

Abstract: This paper aims at a general guideline to obtain a posteriori error estimates for the finite element error control in computational partial differential equations. In the abstract setting of mixed formulations, a generalised formulation of the corre- sponding residuals is proposed which then allows for the unified estimation of the re- spective dual norms. Notably, this can be done with an approach which is applicable in the same way to conforming, nonconforming and mixed discretisations. Subsequently, the unified approach is applied to various model problems. In particular, we consider the Laplace, Stokes, Navier-Lame, and the semi-discrete eddy current equations.