Sparse Grids and Applications - Munich 2018

Sparse grids are a powerful tool for solving high-dimensional problems, and this volume showcases recent advances in their application to various fields.

Format: Paperback / softback
Length: 264 pages
Publication date: 16 March 2023
Publisher: Springer Nature Switzerland AG

Sparse grids have emerged as a widely adopted approach for the numerical resolution of complex high-dimensional problems. In cases where traditional numerical discretization methods encounter limitations in more than three or four dimensions, sparse grids offer a viable alternative. This volume of LNCSE showcases a selection of papers from the fifth workshop on sparse grids and applications, highlighting the significance of this numerical discretization technique. The articles presented herein showcase recent advancements in the numerical analysis of sparse grids, encompassing a diverse range of applications such as uncertainty quantification, plasma physics simulations, and computational chemistry, among others.

Sparse grids find widespread application in various fields, including engineering, physics, and mathematics. They offer several advantages over traditional discretization methods, such as reduced memory requirements, improved stability, and enhanced accuracy. One of the key features of sparse grids is their ability to represent complex geometries and structures efficiently. By discretizing the domain using a small number of points or elements, sparse grids can capture the essential features of the problem while reducing the computational complexity. This makes them particularly useful for solving large-scale problems that require extensive computational resources.

In recent years, sparse grids have been extensively used in uncertainty quantification, where they are employed to model and analyze the uncertainties associated with complex systems. By incorporating sparse grids into the numerical solution process, it is possible to account for the effects of randomness, variability, and uncertainty in the model parameters and results. This approach enables scientists and engineers to make more informed decisions based on the available data and reduces the risk of errors and misinterpretations.

Another area where sparse grids have made significant contributions is in plasma physics simulations. Plasma is a highly dynamic and complex medium, characterized by its high electric conductivity, magnetic fields, and charged particles. Traditional numerical methods often struggle to handle the complexity of plasma simulations due to the large number of variables and equations involved. Sparse grids, on the other hand, can effectively represent the plasma domain using a small number of points or elements, allowing for faster and more accurate simulations.

Sparse grids have also found applications in computational chemistry, where they are used to model the behavior of molecules and chemical reactions. By discretizing the molecular structure and properties, sparse grids can simulate the interactions between molecules and predict the properties of complex systems with high accuracy. This has significant implications in drug discovery, materials science, and other areas where understanding the behavior of molecules is crucial.

In conclusion, sparse grids have emerged as a powerful tool for the numerical treatment of high-dimensional problems. Their ability to represent complex geometries and structures efficiently, coupled with their advantages in uncertainty quantification, plasma physics simulations, and computational chemistry, has made them a widely adopted approach in various fields. As research in this area continues to advance, it is expected that sparse grids will play an increasingly important role in solving complex problems and advancing scientific knowledge.

Weight: 421g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030813642
Edition number: 1st ed. 2021