Ulrich Ruede

Modeling Multigrid Algorithms for Variational Imaging

UML-based modeling is becoming increasingly popular in many software development projects. One of the key aspects is the possibility to support automatic code generation from UML models while keeping the easy to use modeling abstraction for the software developer. The framework Syntony has been developed to generate discrete-event simulations from standard-compliant UML models in order to support simulation based performance evaluation of systems. In this work, we discuss the extension of Syntony to include automatic code generation in the context of large scale continuous simulations that require the numerical solution of partial differential equations (PDE). We choose variational imaging as an example field, and multigrid as numerical solver. Multigrid algorithms exhibit a fixed sequential structure, where the single steps are problem dependent. Typically, they are implemented in C++, and may depend on special hardware since most of their applications require the solution of large numerical systems and therefore high computational performance. Using Syntony, we provide a modeling framework that can be extended to cover new applications by providing the basic modules and data structures in C++ and modeling the high-level algorithms and classes in UML class and activity diagrams. We evaluate the applicability of our approach in a case study for image denoising. The generated code is a fully working application that computes a denoised output image from a given input image using the methods specified in the UML model. The key benefit lies in the abstraction from low level programming for building complex denoising algorithms. In addition, we show that the code generation and compilation process runs significantly faster than the compilation of the entire framework. We also show that the run-time overhead introduced by the generated code is neglible.

Special Issue on Computational Science and Engineering

Leading-edge science and engineering depend on advanced computing for understanding, prediction, and control. In response to these needs, the field of computational science and engineering (CS&E) is evolving rapidly, to the point that it is now widely considered to be a new discipline by itself and a third pillar of the scientific enterprise, a peer alongside theory and physical experiment. CS&E is unique in that it enables progress in virtually all other disciplines by providing windows of discovery when traditional means of research reach their limits. Because of its flexibility, computer simulation has become a universal tool. A simulation may serve as a virtual microscope that lets scientists observe the world of quantum physics much smaller than an atom, or it may be employed as a virtual telescope that allows us to explore how galaxies are forming in the universe. In this way, CS&E helps scientists to reach beyond our physical limitations in space and time. When physical experiments are too dangerou...