by Ulrich Trottenberg and Han La Poutré

Many phenomena and processes in nature, science, technology and economy are today modeled mathematically, and these models are used for control, prediction and optimization. Virtual models substitute real systems and simulation replaces costly, long lasting and dangerous experiments. Today problems can be treated on computers that seemed utopian to be solved twenty years ago.

Mathematics and Computer Science play a fundamental role in forming these simulated realities. In some sense the mathematical models are horizontally arranged in a landscape of vertically oriented disciplines and applications. Computer Science techniques then play a similar role, using or extending such models.

The articles in this special theme all deal with scientific and high performance computing, with computational science, with numerical and discrete simulation, and with large-scale computation and software – and they reflect a large variety of applications. The range of applications is indeed highly impressive.

The articles do not so much reflect the progress that has been and is being made by the hardware and computer development. We can all observe this progress in our everyday work and life, indeed. Much less, it is known that an even more dramatic progress has been made in mathematical modelling and algorithmic developments. An example: The computing times for a typical large-scale problem in scientific computing (a convection-diffusion type partial differential equation, discretisized in a grid with approx. one million grid points) can today be solved a million times faster than twenty years ago. Here a factor of less than 1000 is due to the hardware development and a factor of more than 1000 is due to the algorithmic progress. And this will continue. We need new algorithms and new algorithmic ideas in order to solve, for example, the global weather forecast problem. In 2012, the weather models, then discretized on a grid with 400 million grid points (to be solved several thousand times every day), are known and used and the 100 teraflops computers will be available – but the algorithms are missing. Therefore – much has to be done within the next two years.

Within Computational Science, the area of scientific computing is the oldest. This typically deals with physical problems, to be tackled with large-scale simulation. More recently, other scientific areas have arisen, from social and economic sciences, to the design of (computer) systems themselves, like in the engineering disciplines. Especially, large scale agent-based simulations systems more and more allow for more recent developments in the field: the simulation of socio-economics systems. Here prediction and emergence play an important role. Similarly, intelligent techniques can deal with more complex optimization problems, like in supply chains or health care, due to large scale computation. In the engineering discplines, large-scale simulation is used to investigate eg the behaviour of the designed systems, like software (agent) systems.

At the same time, additional techniques from computer science are developed in order to deal with computational platforms, like advance visualisation techniques and data rendering and processing techniques.

And much could be done on the software side. The articles of the special theme show how much is being done and achieved in many fields of numerical simulation and computer science. Still – the output with respect to commercial and marketable software is small. Most of the developments remain prototypes; very few of these developments have the ambition to become real and successful software products for technical computing.

In this special issue, a wide variety of articles is included that give an impression of the area of computational science. This area goes from mathematics and scientific computing to advanced computer science techniques, like infrastructures, agent-based simulation, and visualisation. We hope the reader will get an impression of today’s state of Computational Science / Scientific Computing (CS/SC) as multidisciplinary approaches in which advanced computing capabilities are used to understand and solve a wide variety of complex problems. As a methodology, CS/SC can rapidly be seen as the "third way" in science and engineering, allowing researchers to address questions that are largely inaccessible to experimental or theoretical investigations, and allowing practitioners to solve complex engineering and optimization problems.

For a strategic view on computational science, we like to recommend the PITAC 2005 report (PITAC: President’s Information Technology Advisory Committee, USA): Computational Science: Ensuring America's Competitiveness. The report is available for download at: computational.pdf

Please contact:
Ulrich Trottenberg
Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Germany
E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Han La Poutré
CWI, The Netherlands
E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Next issue: July 2023
Special theme:
"Eplainable AI"
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