Multiresolution Methods In Scattered Data Modelling

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Multiresolution Methods in Scattered Data Modelling

Armin Iske
Multiresolution Methods in Scattered Data Modelling Book PDF

Author : Armin Iske
Publisher : Springer Science & Business Media
Page : 188 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642187544

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Multiresolution Methods in Scattered Data Modelling by Armin Iske Pdf

This application-oriented work concerns the design of efficient, robust and reliable algorithms for the numerical simulation of multiscale phenomena. To this end, various modern techniques from scattered data modelling, such as splines over triangulations and radial basis functions, are combined with customized adaptive strategies, which are developed individually in this work. The resulting multiresolution methods include thinning algorithms, multi levelapproximation schemes, and meshfree discretizations for transport equa tions. The utility of the proposed computational methods is supported by their wide range of applications, such as image compression, hierarchical sur face visualization, and multiscale flow simulation. Special emphasis is placed on comparisons between the various numerical algorithms developed in this work and comparable state-of-the-art methods. To this end, extensive numerical examples, mainly arising from real-world applications, are provided. This research monograph is arranged in six chapters: 1. Introduction; 2. Algorithms and Data Structures; 3. Radial Basis Functions; 4. Thinning Algorithms; 5. Multilevel Approximation Schemes; 6. Meshfree Methods for Transport Equations. Chapter 1 provides a preliminary discussion on basic concepts, tools and principles of multiresolution methods, scattered data modelling, multilevel methods and adaptive irregular sampling. Relevant algorithms and data structures, such as triangulation methods, heaps, and quadtrees, are then introduced in Chapter 2.

Multiscale Modeling and Simulation in Science

Björn Engquist,Per Lötstedt,Olof Runborg
Multiscale Modeling and Simulation in Science Book PDF

Author : Björn Engquist,Per Lötstedt,Olof Runborg
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 55,6 Mb
Release : 2009-02-11
Category : Computers
ISBN : 9783540888574

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Multiscale Modeling and Simulation in Science by Björn Engquist,Per Lötstedt,Olof Runborg Pdf

Most problems in science involve many scales in time and space. An example is turbulent ?ow where the important large scale quantities of lift and drag of a wing depend on the behavior of the small vortices in the boundarylayer. Another example is chemical reactions with concentrations of the species varying over seconds and hours while the time scale of the oscillations of the chemical bonds is of the order of femtoseconds. A third example from structural mechanics is the stress and strain in a solid beam which is well described by macroscopic equations but at the tip of a crack modeling details on a microscale are needed. A common dif?culty with the simulation of these problems and many others in physics, chemistry and biology is that an attempt to represent all scales will lead to an enormous computational problem with unacceptably long computation times and large memory requirements. On the other hand, if the discretization at a coarse level ignoresthe?nescale informationthenthesolutionwillnotbephysicallymeaningful. The in?uence of the ?ne scales must be incorporated into the model. This volume is the result of a Summer School on Multiscale Modeling and S- ulation in Science held at Boso ¤n, Lidingo ¤ outside Stockholm, Sweden, in June 2007. Sixty PhD students from applied mathematics, the sciences and engineering parti- pated in the summer school.

Tutorials on Multiresolution in Geometric Modelling

Armin Iske,Ewald Quak,Michael S. Floater
Tutorials on Multiresolution in Geometric Modelling Book PDF

Author : Armin Iske,Ewald Quak,Michael S. Floater
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 40,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662043882

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Tutorials on Multiresolution in Geometric Modelling by Armin Iske,Ewald Quak,Michael S. Floater Pdf

This is the only textbook available on multiresolution methods in geometric modeling, a central topic in visualization, which is of great importance for industrial applications. Written in tutorial form, the book is introductory in character, and includes supporting exercises. Other supplementary material and software can be downloaded from the website www.ma.tum.de/primus 2001/.

Meshfree Approximation Methods with MATLAB

Gregory E. Fasshauer
Meshfree Approximation Methods with MATLAB Book PDF

Author : Gregory E. Fasshauer
Publisher : World Scientific
Page : 520 pages
File Size : 40,6 Mb
Release : 2007
Category : Technology & Engineering
ISBN : 9789812706331

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Meshfree Approximation Methods with MATLAB by Gregory E. Fasshauer Pdf

Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. It places emphasis on a hands-on approach that includes MATLAB routines for all basic operations.

Coping with Complexity: Model Reduction and Data Analysis

Alexander N. Gorban,Dirk Roose
Coping with Complexity Model Reduction and Data Analysis Book PDF

Author : Alexander N. Gorban,Dirk Roose
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 48,5 Mb
Release : 2010-10-21
Category : Mathematics
ISBN : 9783642149412

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Coping with Complexity: Model Reduction and Data Analysis by Alexander N. Gorban,Dirk Roose Pdf

This volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 – September 4, 2009. The book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.

Numerical Techniques for Global Atmospheric Models

Peter H. Lauritzen,Christiane Jablonowski,Mark A. Taylor,Ramachandran D. Nair
Numerical Techniques for Global Atmospheric Models Book PDF

Author : Peter H. Lauritzen,Christiane Jablonowski,Mark A. Taylor,Ramachandran D. Nair
Publisher : Springer Science & Business Media
Page : 564 pages
File Size : 49,8 Mb
Release : 2011-03-29
Category : Mathematics
ISBN : 9783642116407

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Numerical Techniques for Global Atmospheric Models by Peter H. Lauritzen,Christiane Jablonowski,Mark A. Taylor,Ramachandran D. Nair Pdf

This book surveys recent developments in numerical techniques for global atmospheric models. It is based upon a collection of lectures prepared by leading experts in the field. The chapters reveal the multitude of steps that determine the global atmospheric model design. They encompass the choice of the equation set, computational grids on the sphere, horizontal and vertical discretizations, time integration methods, filtering and diffusion mechanisms, conservation properties, tracer transport, and considerations for designing models for massively parallel computers. A reader interested in applied numerical methods but also the many facets of atmospheric modeling should find this book of particular relevance.

An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases

Francis X. Giraldo
An Introduction to Element Based Galerkin Methods on Tensor Product Bases Book PDF

Author : Francis X. Giraldo
Publisher : Springer Nature
Page : 559 pages
File Size : 53,5 Mb
Release : 2020-10-30
Category : Mathematics
ISBN : 9783030550691

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An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases by Francis X. Giraldo Pdf

This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations.

Meshfree Approximation Methods with Matlab

Gregory E Fasshauer
Meshfree Approximation Methods with Matlab Book PDF

Author : Gregory E Fasshauer
Publisher : World Scientific Publishing Company
Page : 520 pages
File Size : 41,7 Mb
Release : 2007-04-17
Category : Mathematics
ISBN : 9789813101579

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Meshfree Approximation Methods with Matlab by Gregory E Fasshauer Pdf

Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. Meshfree approximation methods, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view. A good balance is supplied between the necessary theory and implementation in terms of many MATLAB programs, with examples and applications to illustrate key points. Used as class notes for graduate courses at Northwestern University, Illinois Institute of Technology, and Vanderbilt University, this book will appeal to both mathematics and engineering graduate students.

Introduction to Numerical Methods for Variational Problems

Hans Petter Langtangen,Kent-Andre Mardal
Introduction to Numerical Methods for Variational Problems Book PDF

Author : Hans Petter Langtangen,Kent-Andre Mardal
Publisher : Springer Nature
Page : 395 pages
File Size : 51,7 Mb
Release : 2019-09-26
Category : Mathematics
ISBN : 9783030237882

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Introduction to Numerical Methods for Variational Problems by Hans Petter Langtangen,Kent-Andre Mardal Pdf

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

Multiscale Models in Mechano and Tumor Biology

Alf Gerisch,Raimondo Penta,Jens Lang
Multiscale Models in Mechano and Tumor Biology Book PDF

Author : Alf Gerisch,Raimondo Penta,Jens Lang
Publisher : Springer
Page : 195 pages
File Size : 50,9 Mb
Release : 2018-03-16
Category : Mathematics
ISBN : 9783319733715

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Multiscale Models in Mechano and Tumor Biology by Alf Gerisch,Raimondo Penta,Jens Lang Pdf

This book presents and discusses the state of the art and future perspectives in mathematical modeling and homogenization techniques with the focus on addressing key physiological issues in the context of multiphase healthy and malignant biological materials. The highly interdisciplinary content brings together contributions from scientists with complementary areas of expertise, such as pure and applied mathematicians, engineers, and biophysicists. The book also features the lecture notes from a half-day introductory course on asymptotic homogenization. These notes are suitable for undergraduate mathematics or physics students, while the other chapters are aimed at graduate students and researchers.

Modeling, Simulation and Optimization of Fluid Dynamic Applications

Armin Iske,Thomas Rung
Modeling Simulation and Optimization of Fluid Dynamic Applications Book PDF

Author : Armin Iske,Thomas Rung
Publisher : Springer Nature
Page : 165 pages
File Size : 48,9 Mb
Release : 2023-12-13
Category : Computers
ISBN : 9783031451584

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Modeling, Simulation and Optimization of Fluid Dynamic Applications by Armin Iske,Thomas Rung Pdf

This book describes recent collaborations combining the expertise of applied mathematicians, engineers and geophysicists within a research training group (RTG) on "Modeling, Simulation and Optimization of Fluid Dynamic Applications”, funded by the Deutsche Forschungsgemeinschaft (DFG). The focus is on mathematical modeling, adaptive discretization, approximation strategies and shape optimization with PDEs. The balanced research program is based on the guiding principle that mathematics drives applications and is inspired by applications. With this leitmotif the RTG advances research in Modeling, Simulation and Optimization by an interdisciplinary approach, i.e., to stimulate fundamental education and research by highly complex applications and at the simultaneously transfer tailored mathematical methods to applied sciences. The reported research involves nine projects and addresses challenging fluid dynamic problems inspired by applied sciences, such as climate research & meteorology, energy, aerospace & marine engineering, or medicine. More fundamental research concerning analysis, approximation and numerics is also covered. The material represents a successful attempt to exchange research paradigms between different disciplines and thus displays a modern approach to basic research into scientifically and societally relevant contemporary problems.

Principal Manifolds for Data Visualization and Dimension Reduction

Alexander N. Gorban,Balázs Kégl,Donald C. Wunsch,Andrei Zinovyev
Principal Manifolds for Data Visualization and Dimension Reduction Book PDF

Author : Alexander N. Gorban,Balázs Kégl,Donald C. Wunsch,Andrei Zinovyev
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 44,6 Mb
Release : 2007-09-11
Category : Technology & Engineering
ISBN : 9783540737506

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Principal Manifolds for Data Visualization and Dimension Reduction by Alexander N. Gorban,Balázs Kégl,Donald C. Wunsch,Andrei Zinovyev Pdf

The book starts with the quote of the classical Pearson definition of PCA and includes reviews of various methods: NLPCA, ICA, MDS, embedding and clustering algorithms, principal manifolds and SOM. New approaches to NLPCA, principal manifolds, branching principal components and topology preserving mappings are described. Presentation of algorithms is supplemented by case studies. The volume ends with a tutorial PCA deciphers genome.

Meshfree Methods for Partial Differential Equations IV

Michael Griebel,Marc Alexander Schweitzer
Meshfree Methods for Partial Differential Equations IV Book PDF

Author : Michael Griebel,Marc Alexander Schweitzer
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 55,8 Mb
Release : 2008-10-10
Category : Mathematics
ISBN : 9783540799931

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Meshfree Methods for Partial Differential Equations IV by Michael Griebel,Marc Alexander Schweitzer Pdf

The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the proceedings papers of the Fourth International Workshop on Meshfree Methods held in September 2007 in Bonn. The articles address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their application in applied mathematics, physics and engineering. The volume is intended to foster this very active and exciting area of interdisciplinary research and to present recent advances and results in this field.

Kernel-based Approximation Methods using MATLAB

Gregory Fasshauer,Michael McCourt
Kernel based Approximation Methods using MATLAB Book PDF

Author : Gregory Fasshauer,Michael McCourt
Publisher : World Scientific Publishing Company
Page : 536 pages
File Size : 48,6 Mb
Release : 2015-07-30
Category : Mathematics
ISBN : 9789814630153

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Kernel-based Approximation Methods using MATLAB by Gregory Fasshauer,Michael McCourt Pdf

In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.

Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models

Aslak Tveito,Glenn T. Lines
Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models Book PDF

Author : Aslak Tveito,Glenn T. Lines
Publisher : Springer
Page : 261 pages
File Size : 42,8 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9783319300306

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Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models by Aslak Tveito,Glenn T. Lines Pdf

Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various drugs. Examples in the text include stochastic calcium release from internal storage systems in cells, as well as stochastic models of the transmembrane potential. Well known Markov models are studied and a systematic approach to including the effect of mutations is presented. Lastly, the book shows how to derive the optimal properties of a theoretical model of a drug for a given mutation defined in terms of a Markov model.