ESAIM.
Author:
Publisher:
Published: 2008
Total Pages: 620
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Thomas Gerstner
Publisher: World Scientific
Published: 2013
Total Pages: 481
ISBN-13: 9814436429
DOWNLOAD EBOOKComputational finance is an interdisciplinary field which joins financial mathematics, stochastics, numerics and scientific computing. Its task is to estimate as accurately and efficiently as possible the risks that financial instruments generate. This volume consists of a series of cutting-edge surveys of recent developments in the field written by leading international experts. These make the subject accessible to a wide readership in academia and financial businesses. The book consists of 13 chapters divided into 3 parts: foundations, algorithms and applications. Besides surveys of existing results, the book contains many new previously unpublished results.
Author: Ravi P. Agarwal
Publisher: Hindawi Publishing Corporation
Published: 2006
Total Pages: 1266
ISBN-13: 9789775945389
DOWNLOAD EBOOKAuthor: Peter Benner
Publisher: SIAM
Published: 2017-07-06
Total Pages: 421
ISBN-13: 161197481X
DOWNLOAD EBOOKMany physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.
Author: Daniele Antonio Di Pietro
Publisher: Springer
Published: 2018-10-12
Total Pages: 323
ISBN-13: 3319946765
DOWNLOAD EBOOKThis volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields. Numerical analysis applied to the approximate solution of PDEs is a key discipline in applied mathematics, and over the last few years, several new paradigms have appeared, leading to entire new families of discretization methods and solution algorithms. This book is intended for researchers in the field.
Author: Stéphane P. A. Bordas
Publisher: Springer
Published: 2018-03-13
Total Pages: 371
ISBN-13: 3319714317
DOWNLOAD EBOOKThis book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering.
Author: Peter Benner
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2020-12-16
Total Pages: 369
ISBN-13: 3110671506
DOWNLOAD EBOOKAn increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.
Author: Slawomir Koziel
Publisher: Springer
Published: 2016-02-12
Total Pages: 405
ISBN-13: 3319275178
DOWNLOAD EBOOKThis edited volume is devoted to the now-ubiquitous use of computational models across most disciplines of engineering and science, led by a trio of world-renowned researchers in the field. Focused on recent advances of modeling and optimization techniques aimed at handling computationally-expensive engineering problems involving simulation models, this book will be an invaluable resource for specialists (engineers, researchers, graduate students) working in areas as diverse as electrical engineering, mechanical and structural engineering, civil engineering, industrial engineering, hydrodynamics, aerospace engineering, microwave and antenna engineering, ocean science and climate modeling, and the automotive industry, where design processes are heavily based on CPU-heavy computer simulations. Various techniques, such as knowledge-based optimization, adjoint sensitivity techniques, and fast replacement models (to name just a few) are explored in-depth along with an array of the latest techniques to optimize the efficiency of the simulation-driven design process. High-fidelity simulation models allow for accurate evaluations of the devices and systems, which is critical in the design process, especially to avoid costly prototyping stages. Despite this and other advantages, the use of simulation tools in the design process is quite challenging due to associated high computational cost. The steady increase of available computational resources does not always translate into the shortening of the design cycle because of the growing demand for higher accuracy and necessity to simulate larger and more complex systems. For this reason, automated simulation-driven design—while highly desirable—is difficult when using conventional numerical optimization routines which normally require a large number of system simulations, each one already expensive.
Author: Emmanuel Franck
Publisher: Springer Nature
Published: 2023-10-12
Total Pages: 296
ISBN-13: 3031408608
DOWNLOAD EBOOKThis volume comprises the second part of the proceedings of the 10th International Conference on Finite Volumes for Complex Applications, FVCA, held in Strasbourg, France, during October 30 to November 3, 2023. The Finite Volume method, and several of its variants, is a spatial discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods are also built to preserve some properties of the continuous equations, including maximum principles, dissipativity, monotone decay of the free energy, asymptotic stability, or stationary solutions. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. In recent years, the efficient implementation of these methods in numerical software packages, more specifically to be used in supercomputers, has drawn some attention. The first volume contains all invited papers, as well as the contributed papers focusing on finite volume schemes for elliptic and parabolic problems. They include structure-preserving schemes, convergence proofs, and error estimates for problems governed by elliptic and parabolic partial differential equations. This volume is focused on finite volume methods for hyperbolic and related problems, such as methods compatible with the low Mach number limit or able to exactly preserve steady solutions, the development and analysis of high order methods, or the discretization of kinetic equations.
Author: Habib Ammari
Publisher: American Mathematical Soc.
Published: 2016-03-23
Total Pages: 160
ISBN-13: 1470419238
DOWNLOAD EBOOKThis volume contains the proceedings of the Seoul ICM 2014 Satellite Conference on Imaging, Multi-scale and High-Contrast PDEs, held from August 7-9, 2014, in Daejeon, Korea. The mathematical analysis of partial differential equations modelling materials, or tissues, presenting multiple scales has been a very active area of research. The study of the corresponding imaging or reconstruction problem is a more recent area. If the material parameters of the partial differential equation present high contrast ratio, then the solution to the PDE becomes particularly challenging to analyze and compute. On the other hand, imaging in highly heterogeneous media poses significant challenges to the mathematical community. The focus of this volume is on recent progress towards complete understanding of the direct problem with high contrast or high frequencies, and unified approaches to the inverse and imaging problems for both small and large contrast or frequencies. Of particular importance in imaging are shape representation techniques and regularization approaches. Special attention is devoted to new models and problems coming from physics leading to innovative imaging and signal processing methods.