Learn More
We study second order nonconforming finite elements as members of a new family of higher order approaches which behave optimally not only on multilevel refined grids, but also on perturbed grids which are still shape regular but which consist no longer of asymptotically affine equivalent mesh cells. We present two approaches to prevent this order reduction:(More)
Many modern programming languages support both imperative and functional idioms. However, state-of-the-art imperative intermediate representations (IRs) cannot natively represent crucial functional concepts (like higher-order functions). On the other hand, functional IRs employ an explicit scope nesting, which is cumbersome to maintain across certain(More)
Partial evaluation allows for specialization of program fragments. This can be realized by staging, where one fragment is executed earlier than its surrounding code. However, taking advantage of these capabilities is often a cumbersome endeavor. In this paper, we present a new metaprogramming concept using staging parameters that are first-class citizen(More)
A straightforward implementation of an algorithm in a general-purpose programming language does usually not deliver peak performance: Compilers often fail to automatically tune the code for certain hardware peculiarities like memory hierarchy or vector execution units. Manually tuning the code is firstly error-prone as well as time-consuming and secondly(More)
A straightforward implementation of an algorithm in a general purpose programming language does usually not deliver peak performance: compilers often fail to automatically tune the code for certain hardware peculiarities like memory hierarchy or vector execution units. Manually tuning the code is firstly error-prone as well as time-consuming and secondly(More)
We present a framework for setting up interactive three-dimensional outer-space simulations for media facades and other display environments. The core of this framework consists of a space simulator that is capable of efficiently rendering large amounts of objects and computing their physical behavior in real time. The extensible framework further allows to(More)
While simulation methods in the field of Computational Fluid Dynamics (CFD) are already quite advanced, efficient and well developed numerical approaches for optimisation and optimal control in CFD are still under development. Particular challenges in this context are optimisation problems with instationary flows, resulting in discrete nonlinear systems of(More)
The Position Based Fluids (PBF) method is a state-of-the-art approach for fluid simulations in the context of real-time applications like games. It uses an iterative solver concept that tries to maintain a constant fluid density (incompressibility) to realize incompressible fluids like water. However, larger fluid volumes that consist of several hundred(More)
In this paper we will give a short introduction to the installation and efficiency of state-of-the-art direct solver packages like CROUT and UMFPACK for linear systems, combined with highly processor optimised BLAS libraries. We will give an overview about the methods that can be used to integrate these libraries into Fortran programs compiled with the(More)