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Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scienti?c?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model’s complexity and the number of data points used for the computations. Therefore, computational scientists tend to?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.
This book investigates the challenges and methodologies for efficiently solving Partial Differential Equations (PDEs) on parallel computing architectures. The authors, drawing on the historical progression of scientific computing from basic tools to supercomputers, explain how PDEs are fundamental to describing natural phenomena and how their numerical solution is crucial for simulation. The text addresses the increasing demand for computational power driven by the complexity of models and the need for higher data resolution, which necessitates parallel processing.
This book is positioned as a technical exploration of a specialized area within scientific computing. The subject matter suggests a dense, detailed treatment aimed at researchers and advanced students in fields that rely on numerical simulations of PDEs. The focus on parallel computing indicates a contemporary approach to tackling computationally intensive problems, likely appealing to those involved in high-performance computing.
Page Count:
482
Publication Date:
2006-03-05
Publisher:
Springer Nature
ISBN-10:
3540316191
ISBN-13:
9783540316190
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