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Smoothed Point Interpolation Methods G Space Theory And Weakened Weak Forms
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Book Synopsis Smoothed Point Interpolation Methods: G Space Theory And Weakened Weak Forms by : Gui-rong Liu
Download or read book Smoothed Point Interpolation Methods: G Space Theory And Weakened Weak Forms written by Gui-rong Liu and published by World Scientific. This book was released on 2013-08-16 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the widely used finite element method (FEM) and the latest Meshfree methods, a next generation of numerical method called Smoothed Point Interpolation Method (S-PIM) has been recently developed. The S-PIM is an innovative and effective combination of the FEM and the meshfree methods, and enables automation in computation, modeling and simulations — one of the most important features of the next generation methods. This important book describes the various S-PIM models in a systematic, concise and easy-to-understand manner. The underlying principles for the next generation of computational methods, G space theory, novel weakened weak (W2) formulations, techniques for shape functions, formulation procedures, and implementation strategies are presented in detail. Numerous examples are provided to demonstrate the efficiency and accuracy of the S-PIM solutions in comparison with the FEM and other existing methods. Effective techniques to compute solution bounds employing both S-PIM and FEM are highlighted to obtain certified solutions with both upper and lower bounds.The book also presents a systematically way to conduct adaptive analysis for solutions of desired accuracy using these bound properties, which is another key feature of the next generation of computational methods. This will benefit researchers, engineers and students who are venturing into new areas of research and computer code development.
Book Synopsis Smoothed Point Interpolation Methods by : Gui-Rong Liu
Download or read book Smoothed Point Interpolation Methods written by Gui-Rong Liu and published by World Scientific. This book was released on 2013 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the various Smoothed Point Interpolation Method (S-PIM) models in a systematic, concise and easy-to-understand manner. The underlying principles for the next generation of computational methods, G space theory, novel weakened weak (W2) formulations, techniques for shape functions, formulation procedures, and implementation strategies are presented in detail.
Book Synopsis Gradient Smoothing Methods With Programming: Applications To Fluids And Landslides by : Gui-rong Liu
Download or read book Gradient Smoothing Methods With Programming: Applications To Fluids And Landslides written by Gui-rong Liu and published by World Scientific. This book was released on 2023-12-27 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique compendium presents the Gradient Smoothing Methods (GSMs), as a general solver for linear and nonlinear PDEs (Partial Differential Equations) with a focus on fluids and flowing solids.The volume introduces the basic concepts and theories of the gradient smoothing technique used in the GSMs. Formulations for both Eulerian-GSM and Lagrangian-GSM are presented. The key ingredients of GSMs and its effectiveness in solving challenging fluid/solid flow problems with complex geometries are then discussed.Applications of GSM are highlighted, including compressible and incompressible flows, hydrodynamics with flexible free surface, and flowing solids with material strength and large deformation in geotechnical engineering, in particular, landslide simulations.In-house MATLAB codes are provided for both Eulerian and Lagrangian GSMs, along with detailed descriptions. More efficient FORTRAN source codes for solving complex engineering problems are also available on Github.
Book Synopsis Smoothed Finite Element Methods by : G.R. Liu
Download or read book Smoothed Finite Element Methods written by G.R. Liu and published by CRC Press. This book was released on 2016-04-19 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generating a quality finite element mesh is difficult and often very time-consuming. Mesh-free methods operations can also be complicated and quite costly in terms of computational effort and resources. Developed by the authors and their colleagues, the smoothed finite element method (S-FEM) only requires a triangular/tetrahedral mesh to achieve mo
Book Synopsis Particle Methods for Multi-Scale and Multi-physics by : Moubin E. T. Al LIU
Download or read book Particle Methods for Multi-Scale and Multi-physics written by Moubin E. T. Al LIU and published by World Scientific. This book was released on 2015-12-28 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-scale and multi-physics modeling is useful and important for all areas in engineering and sciences. Particle Methods for Multi-Scale and Multi-Physics systematically addresses some major particle methods for modeling multi-scale and multi-physical problems in engineering and sciences. It contains different particle methods from atomistic scales to continuum scales, with emphasis on molecular dynamics (MD), dissipative particle dynamics (DPD) and smoothed particle hydrodynamics (SPH). This book covers the theoretical background, numerical techniques and many interesting applications of the particle methods discussed in this text, especially in: micro-fluidics and bio-fluidics (e.g., micro drop dynamics, movement and suspension of macro-molecules, cell deformation and migration); environmental and geophysical flows (e.g., saturated and unsaturated flows in porous media and fractures); and free surface flows with possible interacting solid objects (e.g., wave impact, liquid sloshing, water entry and exit, oil spill and boom movement). The presented methodologies, techniques and example applications will benefit students, researchers and professionals in computational engineering and sciences --
Book Synopsis Numerical Methods in Geotechnical Engineering IX by : António S. Cardoso
Download or read book Numerical Methods in Geotechnical Engineering IX written by António S. Cardoso and published by CRC Press. This book was released on 2018-06-19 with total page 2563 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods in Geotechnical Engineering IX contains 204 technical and scientific papers presented at the 9th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE2018, Porto, Portugal, 25—27 June 2018). The papers cover a wide range of topics in the field of computational geotechnics, providing an overview of recent developments on scientific achievements, innovations and engineering applications related to or employing numerical methods. They deal with subjects from emerging research to engineering practice, and are grouped under the following themes: Constitutive modelling and numerical implementation Finite element, discrete element and other numerical methods. Coupling of diverse methods Reliability and probability analysis Large deformation – large strain analysis Artificial intelligence and neural networks Ground flow, thermal and coupled analysis Earthquake engineering, soil dynamics and soil-structure interactions Rock mechanics Application of numerical methods in the context of the Eurocodes Shallow and deep foundations Slopes and cuts Supported excavations and retaining walls Embankments and dams Tunnels and caverns (and pipelines) Ground improvement and reinforcement Offshore geotechnical engineering Propagation of vibrations Following the objectives of previous eight thematic conferences, (1986 Stuttgart, Germany; 1990 Santander, Spain; 1994 Manchester, United Kingdom; 1998 Udine, Italy; 2002 Paris, France; 2006 Graz, Austria; 2010 Trondheim, Norway; 2014 Delft, The Netherlands), Numerical Methods in Geotechnical Engineering IX updates the state-of-the-art regarding the application of numerical methods in geotechnics, both in a scientific perspective and in what concerns its application for solving practical boundary value problems. The book will be much of interest to engineers, academics and professionals involved or interested in Geotechnical Engineering.
Download or read book Meshfree Methods written by G.R. Liu and published by CRC Press. This book was released on 2009-10-06 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understand How to Use and Develop Meshfree TechniquesAn Update of a Groundbreaking WorkReflecting the significant advances made in the field since the publication of its predecessor, Meshfree Methods: Moving Beyond the Finite Element Method, Second Edition systematically covers the most widely used meshfree methods. With 70% new material, this edit
Book Synopsis Numbers And Functions: Theory, Formulation, And Python Codes by : Gui-rong Liu
Download or read book Numbers And Functions: Theory, Formulation, And Python Codes written by Gui-rong Liu and published by World Scientific. This book was released on 2024-06-18 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume covers two fundamental elements of computational methods — numbers and functions. It provides an in-depth discussion of the behaviors of numbers, including both real and complex numbers. The discussion leads to the important closure properties of numbers, ensuring solution consistence and existence, and also possible failure in numerical computations in science and engineering.This text then introduces types of functions that take numbers as independent variables and produce a single number. Approaches for constructing inverse functions are also provided. Frequently used basis functions are introduced, with detailed studies on their properties and behaviors. Techniques are presented for constructing basis functions and their use in function approximation in computational methods.
Book Synopsis Advanced Computational Methods and Geomechanics by : Shenghong Chen
Download or read book Advanced Computational Methods and Geomechanics written by Shenghong Chen and published by Springer Nature. This book was released on 2023-01-01 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is intended, through parallel expounding, to help readers comprehensively grasp the intrinsic features of typical advanced computational methods. These methods are created in recent three decades for the understanding of the post-failure of geo-materials accompanied with discontinuous and finite deformation/dislocation, as well as the violent fluid-structure interaction accompanied with strong distortion of water surface. The strong points and weak points of the formalisms for governing equations, the discretization schemes, the nodal interpolation /approximation of field variables, and their connectivity (via support domains, covers, or enrichments), the basic algorithms, etc., are clarified. Being aware of that the differences in these methods are not so large as at the first glance, this book will help readers to select appropriate methods, to improve the methods for their specific purpose, and to evaluate the reliability/applicability of the outcomes in the hazard evaluation of geotechnical (hydraulic) structures beyond extreme work situation. This book may be looked at as an advanced continuation of “Computational Geomechanics and Hydraulic Structures” by the author (2018) (Springer-Verlag, ISBN 978-981-10-8134-7) which elaborates the fundamental computational methods in geomechanics for the routine design of geotechnical (hydraulic) engineering.
Book Synopsis Machine Learning With Python: Theory And Applications by : Gui-rong Liu
Download or read book Machine Learning With Python: Theory And Applications written by Gui-rong Liu and published by World Scientific. This book was released on 2022-12-05 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine Learning (ML) has become a very important area of research widely used in various industries.This compendium introduces the basic concepts, fundamental theories, essential computational techniques, codes, and applications related to ML models. With a strong foundation, one can comfortably learn related topics, methods, and algorithms. Most importantly, readers with strong fundamentals can even develop innovative and more effective machine models for his/her problems. The book is written to achieve this goal.The useful reference text benefits professionals, academics, researchers, graduate and undergraduate students in AI, ML and neural networks.
Book Synopsis The Finite Element Method by : G.R. Liu
Download or read book The Finite Element Method written by G.R. Liu and published by Butterworth-Heinemann. This book was released on 2013-08-07 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for practicing engineers and students alike, this book emphasizes the role of finite element modeling and simulation in the engineering design process. It provides the necessary theories and techniques of the FEM in a concise and easy-to-understand format and applies the techniques to civil, mechanical, and aerospace problems. Updated throughout for current developments in FEM and FEM software, the book also includes case studies, diagrams, illustrations, and tables to help demonstrate the material. Plentiful diagrams, illustrations and tables demonstrate the material Covers modeling techniques that predict how components will operate and tolerate loads, stresses and strains in reality Full set of PowerPoint presentation slides that illustrate and support the book, available on a companion website
Book Synopsis Numerical Methods in Geotechnical Engineering IX, Volume 1 by : Manuel de Matos Fernandes
Download or read book Numerical Methods in Geotechnical Engineering IX, Volume 1 written by Manuel de Matos Fernandes and published by CRC Press. This book was released on 2018-06-22 with total page 935 pages. Available in PDF, EPUB and Kindle. Book excerpt: NUMGE 2018 is the ninth in a series of conferences on Numerical Methods in Geotechnical Engineering organized by the ERTC7 under the auspices of the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE). The first conference was held in 1986 in Stuttgart, Germany and the series continued every four years (1990 Santander, Spain; 1994 Manchester, United Kingdom; 1998 Udine, Italy; 2002 Paris, France; 2006 Graz, Austria; 2010 Trondheim, Norway; 2014 Delft, The Netherlands). The conference provides a forum for exchange of ideas and discussion on topics related to numerical modelling in geotechnical engineering. Both senior and young researchers, as well as scientists and engineers from Europe and overseas, are invited to attend this conference to share and exchange their knowledge and experiences. This work is the first volume of NUMGE 2018.
Book Synopsis Introduction to Numerical Methods for Variational Problems by : Hans Petter Langtangen
Download or read book Introduction to Numerical Methods for Variational Problems written by Hans Petter Langtangen and published by Springer Nature. This book was released on 2019-09-26 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Finite Element Method: Theory, Implementation, and Applications by : Mats G. Larson
Download or read book The Finite Element Method: Theory, Implementation, and Applications written by Mats G. Larson and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Book Synopsis An Introduction to Meshfree Methods and Their Programming by : G.R. Liu
Download or read book An Introduction to Meshfree Methods and Their Programming written by G.R. Liu and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. The FDM works well for problems of simple geometry and was widely used before the invention of the much more efficient, robust finite element method (FEM). FEM is now widely used in handling problems with complex geometry. Currently, we are using and developing even more powerful numerical techniques aiming to obtain more accurate approximate solutions in a more convenient manner for even more complex systems. The meshfree or meshless method is one such phenomenal development in the past decade, and is the subject of this book. There are many MFree methods proposed so far for different applications. Currently, three monographs on MFree methods have been published. Mesh Free Methods, Moving Beyond the Finite Element Method d by GR Liu (2002) provides a systematic discussion on basic theories, fundamentals for MFree methods, especially on MFree weak-form methods. It provides a comprehensive record of well-known MFree methods and the wide coverage of applications of MFree methods to problems of solids mechanics (solids, beams, plates, shells, etc.) as well as fluid mechanics. The Meshless Local Petrov-Galerkin (MLPG) Method d by Atluri and Shen (2002) provides detailed discussions of the meshfree local Petrov-Galerkin (MLPG) method and itsvariations. Formulations and applications of MLPG are well addressed in their book.
Book Synopsis A Multigrid Tutorial by : William L. Briggs
Download or read book A Multigrid Tutorial written by William L. Briggs and published by SIAM. This book was released on 2000-07-01 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Finite Element Method written by G.R. Liu and published by Elsevier. This book was released on 2003-02-21 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Finite Element Method (FEM) has become an indispensable technology for the modelling and simulation of engineering systems. Written for engineers and students alike, the aim of the book is to provide the necessary theories and techniques of the FEM for readers to be able to use a commercial FEM package to solve primarily linear problems in mechanical and civil engineering with the main focus on structural mechanics and heat transfer. Fundamental theories are introduced in a straightforward way, and state-of-the-art techniques for designing and analyzing engineering systems, including microstructural systems are explained in detail. Case studies are used to demonstrate these theories, methods, techniques and practical applications, and numerous diagrams and tables are used throughout. The case studies and examples use the commercial software package ABAQUS, but the techniques explained are equally applicable for readers using other applications including NASTRAN, ANSYS, MARC, etc. A practical and accessible guide to this complex, yet important subject Covers modeling techniques that predict how components will operate and tolerate loads, stresses and strains in reality
