Calculating non-equidistant discretizations generated by Blaschke products

The argument functions of Blaschke products provide a very elegant way of handling non-uniformity of discretizations. In this paper we analyse the efficiency of numerical methods as the bisection method and Newton's method in the case of calculating non-equidistant discretizations generated by Blaschke products. By taking advantage of the strictly increasing property of argument functions we may calculate the discrete points in an enhanced order — to be introduced here. The efficiency of the discrete points' sequential calculation in this order is significantly increased compared to the naive implementation. In our research we are primarily motivated by ECG curves which usually have alternating regions of high or low variability, and therefore different degree of discretization is needed at different regions of the signals

Computational Methods in Science and Engineering : Proceedings of the Workshop SimLabs@KIT, November 29 - 30, 2010, Karlsruhe, Germany

In this proceedings volume we provide a compilation of article contributions equally covering applications from different research fields and ranging from capacity up to capability computing. Besides classical computing aspects such as parallelization, the focus of these proceedings is on multi-scale approaches and methods for tackling algorithm and data complexity. Also practical aspects regarding the usage of the HPC infrastructure and available tools and software at the SCC are presented

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282