Books and Conference Proceedings

6 publications

Geometric Partial Differential Equations: Surface and Bulk Processes

Oberwolfach Reports 12(4), Titelseite

Klaus Deckelnick, Charles M. Elliott, Ralf Kornhuber and James A. Sethian

Zürich, Switzerland: European Mathematical Society - Publishing House | 2015

Appeared In: Oberwolfach Reports, 12 (4), pp. 3101-3178

https://dx.doi.org/10.4171/OWR/2015/55

The workshop brought together experts representing a wide range of topics in geometric partial differential equations ranging from analyis over numerical simulation to real-life applications. The main themes of the conference were the analysis of curvature energies, new developments in pdes on surfaces and the treatment of coupled bulk/surface problems.

Geometric Partial Differential Equations: Theory, Numerics and Applications

Oberwolfach Reports 8(4), Titelseite

Gerhard Dziuk, Charles M. Elliott, Gerhard Huisken and Ralf Kornhuber

Zürich, Switzerland: European Mathematical Society - Publishing House | 2011

Appeared In: Oberwolfach Reports, 8 (4), 3077-3144

https://dx.doi.org/10.4171/OWR/2011/54

This workshop concentrated on partial differential equations involving stationary and evolving surfaces in which geometric quantities play a major role. Mutual interest in this emerging field stimulated the interaction between analysis, numerical solution, and applications.

Domain Decomposition Methods in Science and Engineering XIX

Domain Decomposition Methods in Science and Engineering XIX, Titelseite

Yunqing Huang, Ralf Kornhuber, Olof Widlund, Jinchao Xu

Springer Berlin Heidelberg | 2011

Appeared In: Lecture Notes in Computational Science and Engineering, 78

http://www.ddm.org/DD19/proceedings/nume ...

These are the proceedings of the 19th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linear or nonlinear systems of algebraic equations that arise in various problems in mathematics, computational science, engineering and industry. They are designed for massively parallel computers and take the memory hierarchy of such systems into account. This is essential for approaching peak floating point performance. There is an increasingly well-developed theory which is having a direct impact on the development and improvement of these algorithms.

Domain Decomposition Methods in Science and Engineering XVIII

Domain Decomposition Methods in Science and Engineering XVIII, Titelseite

Michel Bercovier, Martin J. Gander, Ralf Kornhuber, Olof Widlund

Springer Berlin Heidelberg | 2009

Appeared In: Lecture Notes in Computational Science and Engineering, 70

http://www.ddm.org/DD18/proceedings/nume ...

This volume contains a selection of 41 refereed papers presented at the 18th International Conference of Domain Decomposition Methods hosted by the School of Computer Science and Engineering (CSE) of the Hebrew University of Jerusalem, Israel, January 12–17, 2008.

Domain Decomposition Methods in Science and Engineering

Domain Decomposition Methods in Science and Engineering, Titelseite

Timothy J. Barth, Michael Griebel, David E. Keyes, Risto M. Nieminen, Dirk Roose, Tamar Schlick, Ralf Kornhuber, Ronald Hoppe, Jacques Périaux, Olivier Pironneau, Olof Widlund, Jinchao Xu

Springer Berlin Heidelberg | 2005

Appeared In: Lecture Notes in Computational Science and Engineering, 40

http://www.ddm.org/DD15/proceedings-dd15 ...

Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.

Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems

Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems, Titelseite

Kornhuber, R.

Stuttgart: Vieweg+Teubner Verlag | 1997

http://publications.mi.fu-berlin.de/2000 ...

A wide range of problems occurring in engineering and industry is characterized by the presence of a free (i.e. a priori unknown) boundary where the underlying physical situation is changing in a discontinuous way. Mathematically, such phenomena can be often reformulated as variational inequalities or related non–smooth minimization problems. In these research notes, we will describe a new and promising way of constructing fast solvers for the corresponding discretized problems providing globally convergent iterative schemes with (asymptotic) multigrid convergence speed. The presentation covers physical modelling, existence and uniqueness results, finite element approximation and adaptive mesh–refinement based on a posteriori error estimation. The numerical properties of the resulting adaptive multilevel algorithm are illustrated by typical applications, such as semiconductor device simulation or continuous casting.