model reduction of parametrized systems

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Model Reduction Of Parametrized Systems

Author : Peter Benner
ISBN : 9783319587868
Genre : Mathematics
File Size : 72. 56 MB
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The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems. The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effor t, carried out over the last 12 years, to build a growing research community in this field. Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).

Model Order Reduction Of Parametrized Systems With Sparse Grid Learning Techniques

Author : Benjamin Peherstorfer
ISBN : OCLC:870907874
Genre :
File Size : 81. 69 MB
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Model Reduction And Approximation

Author : Peter Benner
ISBN : 9781611974829
Genre : Science
File Size : 24. 56 MB
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Many 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.

Numerical Methods For Pdes

Author : Daniele Antonio Di Pietro
ISBN : 9783319946764
Genre : Mathematics
File Size : 56. 16 MB
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This 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.

Mathematical Models For The Simulation Of Combined Depth And Cake Filtration Processes

Author : Sebastian Osterroth
ISBN : 9783839612972
Genre : Computers
File Size : 70. 98 MB
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In this work, mathematical models for combined depth and cake filtration are developed. Their formulation is either based on a moving or free boundary description. For the free boundary model existence and uniqueness of the solution is shown. To study the influence of the model parameters, two different tools are introduced, namely model reduction and parameter identification. Model reduction is used to study the sensitivity of the parameters and to accelerate the solution procedure. Multiple ways to construct a projection basis are discussed and reviewed. For parameter identification, an optimization framework for the free boundary problem is derived. Therefore a gradient algorithm in combination with an adjoint formulation is used. The models are compared to several experimental data and different mathematical aspects of the problem are tested, too. The results show that it is possible to reproduce the experimental data. It is further shown that a nonlinear pressure drop, often arising in cake filtration, can be explained by the model without considering compression of the cake.

Mathematical Modelling Of The Human Cardiovascular System

Author : Alfio Quarteroni
ISBN : 9781108480390
Genre : Mathematics
File Size : 62. 90 MB
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Addresses the mathematical and numerical modelling of the human cardiovascular system, from patient data to clinical applications.

Reduced Order Methods For Modeling And Computational Reduction

Author : Alfio Quarteroni
ISBN : 9783319020907
Genre : Mathematics
File Size : 90. 65 MB
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This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics. Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects. This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

Fundamentals Of Dynamical Systems And Bifurcation Theory

Author :
ISBN : 0750301503
Genre : Mathematics
File Size : 76. 11 MB
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This graduate level text explains the fundamentals of the theory of dynamical systems. After reading it you will have a good enough understanding of the area to study the extensive literature on dynamical systems. The book is self contained, as all the essential definitions and proofs are supplied, as are useful references: all the reader needs is a knowledge of basic mathematical analysis, algebra and topology. However, the first chapter contains an explanation of some of the methods of differential topology an understanding of which is essential to the theory of dynamical systems. A clear introduction to the field, which is equally useful for postgraduates in the natural sciences, engineering and economics.

Correct System Design

Author : Ernst-RĂ¼diger Olderog
ISBN : 9783540666240
Genre : Computers
File Size : 65. 80 MB
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Computers are gaining more and more control over systems that we use or rely on in our daily lives, privately as well as professionally. In safety-critical applications, as well as in others, it is of paramount importance that systems controled by a computer or computing systems themselves reliably behave in accordance with the specification and requirements, in other words: here correctness of the system, of its software and hardware is crucial. In order to cope with this callenge, software engineers and computer scientists need to understand the foundations of programming, how different formal theories are linked together, how compilers correctly translate high-level programs into machine code, and why transformations performed are justifiable. This book presents 17 mutually reviewed invited papers organized in sections on methodology, programming, automation, compilation, and application.

Discrete Time Control System Implementation Techniques

Author :
ISBN : 9780080529882
Genre : Technology & Engineering
File Size : 35. 28 MB
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These papers cover the recent advances in the field of control theory and are designed for electrical engineers in digital signal processing.

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