Kai Diethelm is a software developer for GNS Gesellschaft f¿r Numerische Simulation mbH in Braunschweig, Germany, and an adjunct professor at the Computational Mathematics Institute, Technische Universit¿t Braunschweig. His position at GNS is focused on the development of specialized mathematical software for the highly accurate simulation of sheet metal forming processes, with applications mainly stemming from the automotive industry and their suppliers. This includes work on a finite element package, including the parallelization of the code. Moreover, he is involved in aspects dealing with pre- and post-processing, including the visualization of the results, and the integration of the code into a virtual process chain with an emphasis on the optimization of the forming operation in various ways.

Before joining GNS, he held research and teaching positions in applied and numerical mathematics at the universities of Hildesheim, Gie¿en and Braunschweig, where he has mainly worked in numerical integration and the numerical solution of differential equations. His favorite fields in this area are differential equations of noninteger order that can be used, for example, to model the mechanical behavior of viscoelastic materials like rubber, modern plastics (such as polymers), and even biological tissue, under the influence of external forces. He is a member of the editorial boards of Fractional Calculus and Applied Analysis and Fractional Dynamic Systems.

He received his diploma in mathematics from Technische Universit¿t Braunschweig in 1992, a PhD in computer science from Universit¿t Hildesheim in 1994, and a habilitation degree in mathematics, also from Universit¿t Hildesheim, in 1998. In addition, he has been named an Honorary Research Fellow in the Department of Mathematics at the University of Chester, UK.

Finite elements: theory and algorithms Ganesan S., Tobiska L., Cambridge University Press, New York, NY, 2017. 216 pp. Type: Book (978-1-108415-70-5) The finite-element method is a well-established mathematical tool that allows the use of computing techniques for the solution of problems arising in the sciences and engineering. As such, it is a topic that can be addressed from many different pe...

Feb 1 2018

High-order accurate adaptive kernel compression time-stepping schemes for fractional differential equations Baffet D., Hesthaven J. Journal of Scientific Computing 72(3): 1169-1195, 2017. Type: Article The numerical solution of differential equations of fractional order is a notoriously difficult and complex matter, mainly due to the nonlocality of the operators and the nonsmoothness of the exact solutions. The former leads to a very high arithm...

Jan 30 2018

Advanced finite element simulation with MSC Marc: application of user subroutines Javanbakht Z., Öchsner A., Springer International Publishing, New York, NY, 2017. 347 pp. Type: Book (978-3-319476-67-4) Commercial (and other) finite element packages give their users the option to replace some of the package’s built-in subroutines with user-defined customized versions. This feature provides great flexibility and permits, for example, enhanci...

Jul 13 2017

Mathematical analysis and the mathematics of computation Römisch W., Zeugmann T., Springer International Publishing, New York, NY, 2016. 703 pp. Type: Book (978-3-319427-53-9), Reviews: (1 of 2) Even though there are many deep connections between mathematical analysis and the mathematics of computation, these two fields are usually taught completely separately from each other. This traditional approach has the disadvantage that the concep...

May 24 2017

IsoGeometric analysis: a new paradigm in the numerical approximation of PDEs Buffa A., Sangalli G., Springer International Publishing, New York, NY, 2016. 193 pp. Type: Book (978-3-319423-08-1) For their daily work, computational engineers in many technical disciplines rely heavily on the use of finite element software systems. However, certain features of the traditional mathematical approaches on which these systems are based impose li...

Feb 22 2017

Optimal error estimates of linearized Crank-Nicolson Galerkin method for Landau-Lifshitz equation An R. Journal of Scientific Computing 69(1): 1-27, 2016. Type: Article The Landau–Lifshitz equation is a well-known mathematical model for describing the evolution of magnetization in ferromagnets. It is a partial differential equation that, due to its nonlinear structure, poses a number of challenges when one tries ...

The mathematics of medical imaging: a beginner’s guide (2nd ed.) Feeman T., Springer International Publishing, New York, NY, 2015. 197 pp. Type: Book (978-3-319226-64-4) Medical imaging is a very important application area of advanced computational techniques. Without the use of up-to-date mathematical ideas and the corresponding algorithms, it would not be possible to convert the measurement data coming out of to...

May 2 2016

Computing real roots of real polynomials Sagraloff M., Mehlhorn K. Journal of Symbolic Computation 73(C): 46-86, 2016. Type: Article The computation of roots of a univariate polynomial is the most classical task in computational algebra. Since this problem arises in very many applications, plenty of techniques for its solution have been proposed. In this paper, Sagraloff and Me...

Dec 1 2015

The concept of stability in numerical mathematics Hackbusch W., Springer Publishing Company, Incorporated, New York, NY, 2014. 188 pp. Type: Book (978-3-642393-85-3) Common wisdom demands that unstable algorithms be avoided when numerically solving problems given in a mathematical formulation. But what does “(un)stable” actually mean? The usual answer to this question is that stable algorithms do n...