arXiv subjects

Martin Alkämper

Publications and source records attributed to Martin Alkämper.

4 recordsLinked to original sources

arXiv2025

A primal-dual adaptive finite element method for total variation minimization

Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general $L^1$-$L^2$-$TV$ functional over the space of functions of bounded variations by adaptivity in a finite element setting. For automatically generating an adaptive grid we introduce indicators based on a-posteriori error estimates. Further we discuss data interpolation methods on unstructured grids in the context of image processing and present a pixel-based interpolation method. The efficiency of our derived adaptive finite element scheme is demonstrated on image inpainting and the task of computing the optical flow in image sequences. In particular, for optical flow estimation we derive an adaptive finite element coarse-to-fine scheme which allows resolving large displacements and speeds-up the computing time significantly.

math.NA↗

arXiv2017

A Weak Compatibility Condition for Newest Vertex Bisection in any dimension

We define a weak compatibility condition for the Newest Vertex Bisection algorithm on simplex grids of any dimension and show that using this condition the iterative algorithm terminates successfully. Additionally we provide an O(n) algorithm that renumbers any simplex grid to fulfil this condition. Furthermore we conduct experiments to estimate the distance to the standard compatibility and also the geometric quality of the produced meshes.

math.NA↗

arXiv2016

Distributed Newest Vertex Bisection

Distributed adaptive conforming refinement requires multiple iterations of the serial refinement algorithm and global communication as the refinement can be propagated over several processor boundaries. We show bounds on the maximum number of iterations. The algorithm is implemented within the software package DUNE-ALUGrid.

cs.DC↗

arXiv2015

The DUNE-ALUGrid Module

In this paper we present the new DUNE-ALUGrid module. This module contains a major overhaul of the sources from the ALUgrid library and the binding to the DUNE software framework. The main changes include user defined load balancing, parallel grid construction, and an redesign of the 2d grid which can now also be used for parallel computations. In addition many improvements have been introduced into the code to increase the parallel efficiency and to decrease the memory footprint. The original ALUGrid library is widely used within the DUNE community due to its good parallel performance for problems requiring local adaptivity and dynamic load balancing. Therefore, this new model will benefit a number of DUNE users. In addition we have added features to increase the range of problems for which the grid manager can be used, for example, introducing a 3d tetrahedral grid using a parallel newest vertex bisection algorithm for conforming grid refinement. In this paper we will discuss the new features, extensions to the DUNE interface, and explain for various examples how the code is used in parallel environments.

cs.MS↗