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Numerical simulation is a powerful tool used in various fields of science and engineering to model complex systems and predict their behavior. It involves developing mathematical models that describe the behavior of a system and using computer algorithms to solve these models numerically. By doing so, researchers and engineers can study the behavior of a system in detail, which may only be possible with analytical methods. Numerical simulation has many advantages over traditional analytical methods. It allows researchers and engineers to study complex systems’ behavior in detail and predict their behavior in different scenarios. It also allows for the optimization of systems and the identification of design flaws before they are built. However, numerical simulation has its limitations. It requires significant computational resources, and the accuracy of the results depends on the quality of the mathematical models and the discretization methods used. Nevertheless, numerical simulation remains a valuable tool in many fields and its importance is likely to grow as computational resources become more powerful and widely available. Numerical simulation is widely used in physics, engineering, computer science, and mathematics. In physics, for example, numerical simulation is used to study the behavior of complex systems such as weather patterns, fluid dynamics, and particle interactions. In engineering, it is used to design and optimize systems such as aircraft, cars, and buildings. In computer science, numerical simulation models and optimization algorithms and data structures. In mathematics, it is used to study complex mathematical models and to solve complex equations. This book familiarizes readers with the practical application of the numerical simulation technique to solve complex analytical problems in different industries and sciences.
This entertaining introduction to advanced numerical modeling aims to lead the reader on a journey towards theholy grail of numerical simulation, i.e. one without the requirement of mesh generation, that takes data directly from CAD programs. This hands-on book emphasizes implementation and examples of programming in a higher level language are given. Written for users of simulation software, so they can understand the benefits of this new technology and demand progress from a somewhat conservative industry. Written for software developers, so they can see that this is a technology with a big future and written for researchers, in the hope that it will attract more people to work in this field.
This book presents and discusses mathematical models, numerical methods and computational techniques used for solving coupled problems in science and engineering. It takes a step forward in the formulation and solution of real-life problems with a multidisciplinary vision, accounting for all of the complex couplings involved in the physical description. Simulation of multifaceted physics problems is a common task in applied research and industry. Often a suitable solver is built by connecting together several single-aspect solvers into a network. In this book, research in various fields was selected for consideration: adaptive methodology for multi-physics solvers, multi-physics phenomena and coupled-field solutions, leading to computationally intensive structural analysis. The strategies which are used to keep these problems computationally affordable are of special interest, and make this an essential book.
This book presents lecture notes from the XVI ‘Jacques-Louis Lions’ Spanish-French School on Numerical Simulation in Physics and Engineering, held in Pamplona (Navarra, Spain) in September 2014. The subjects covered include: numerical analysis of isogeometric methods, convolution quadrature for wave simulations, mathematical methods in image processing and computer vision, modeling and optimization techniques in food processes, bio-processes and bio-systems, and GPU computing for numerical simulation. The book is highly recommended to graduate students in Engineering or Science who want to focus on numerical simulation, either as a research topic or in the field of industrial applications. It can also benefit senior researchers and technicians working in industry who are interested in the use of state-of-the-art numerical techniques in the fields addressed here. Moreover, the book can be used as a textbook for master courses in Mathematics, Physics, or Engineering.
This book focuses on numerical simulation-based design theory and methods in mechanical engineering. The simulation-based design of mechanical equipmentinvolves considerable scientific challenges including extremely complex systems,extreme working conditions, multi-source uncertainties, multi-physics coupling, andlarge-scale computation. In order to overcome these technical difficulties, this booksystematically elaborates upon the advanced design methods, covering high-fidelitysimulation modeling, rapid structural analysis, multi-objective design optimization,uncertainty analysis and optimization, which can effectively improve the designaccuracy, efficiency, multi-functionality and reliability of complicated mechanicalstructures. This book is primarily intended for researchers, engineers and postgraduate studentsin mechanical engineering, especially in mechanical design, numerical simulation andengineering optimization.
This book gathers selected contributions presented at the INdAM Workshop “DREAMS”, held in Rome, Italy on January 22−26, 2018. Addressing cutting-edge research topics and advances in computer aided geometric design and isogeometric analysis, it covers distinguishing curve/surface constructions and spline models, with a special focus on emerging adaptive spline constructions, fundamental spline theory and related algorithms, as well as various aspects of isogeometric methods, e.g. efficient quadrature rules and spectral analysis for isogeometric B-spline discretizations. Applications in finite element and boundary element methods are also discussed. Given its scope, the book will be of interest to both researchers and graduate students working in these areas.
Numerical Modelling of Failure in Advanced Composite Materials comprehensively examines the most recent analysis techniques for advanced composite materials. Advanced composite materials are becoming increasingly important for lightweight design in aerospace, wind energy, and mechanical and civil engineering. Essential for exploiting their potential is the ability to reliably predict their mechanical behaviour, particularly the onset and propagation of failure. Part One investigates numerical modeling approaches to interlaminar failure in advanced composite materials. Part Two considers numerical modelling approaches to intralaminar failure. Part Three presents new and emerging advanced numerical algorithms for modeling and simulation of failure. Part Four closes by examining the various engineering and scientific applications of numerical modeling for analysis of failure in advanced composite materials, such as prediction of impact damage, failure in textile composites, and fracture behavior in through-thickness reinforced laminates. - Examines the most recent analysis models for advanced composite materials in a coherent and comprehensive manner - Investigates numerical modelling approaches to interlaminar failure and intralaminar failure in advanced composite materials - Reviews advanced numerical algorithms for modeling and simulation of failure - Examines various engineering and scientific applications of numerical modelling for analysis of failure in advanced composite materials
Many problems in scientific computing are intractable with classical numerical techniques. These fail, for example, in the solution of high-dimensional models due to the exponential increase of the number of degrees of freedom. Recently, the authors of this book and their collaborators have developed a novel technique, called Proper Generalized Decomposition (PGD) that has proven to be a significant step forward. The PGD builds by means of a successive enrichment strategy a numerical approximation of the unknown fields in a separated form. Although first introduced and successfully demonstrated in the context of high-dimensional problems, the PGD allows for a completely new approach for addressing more standard problems in science and engineering. Indeed, many challenging problems can be efficiently cast into a multi-dimensional framework, thus opening entirely new solution strategies in the PGD framework. For instance, the material parameters and boundary conditions appearing in a particular mathematical model can be regarded as extra-coordinates of the problem in addition to the usual coordinates such as space and time. In the PGD framework, this enriched model is solved only once to yield a parametric solution that includes all particular solutions for specific values of the parameters. The PGD has now attracted the attention of a large number of research groups worldwide. The present text is the first available book describing the PGD. It provides a very readable and practical introduction that allows the reader to quickly grasp the main features of the method. Throughout the book, the PGD is applied to problems of increasing complexity, and the methodology is illustrated by means of carefully selected numerical examples. Moreover, the reader has free access to the Matlab© software used to generate these examples.
Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes covers new and exciting modeling methods to help bioengineers tackle problems for which the Finite Element Method is not appropriate. The book covers a wide range of important subjects in the field of numerical methods applied to biomechanics, including bone biomechanics, tissue and cell mechanics, 3D printing, computer assisted surgery and fluid dynamics. Modeling strategies, technology and approaches are continuously evolving as the knowledge of biological processes increases. Both theory and applications are covered, making this an ideal book for researchers, students and R&D professionals. - Provides non-conventional analysis methods for modeling - Covers the Discrete Element Method (DEM), Particle Methods (PM), MessLess and MeshFree Methods (MLMF), Agent-Based Methods (ABM), Lattice-Boltzmann Methods (LBM) and Boundary Integral Methods (BIM) - Includes contributions from several world renowned experts in their fields - Compares pros and cons of each method to help you decide which method is most applicable to solving specific problems
Computing application to materials science is one of the fastest-growing research areas. This book introduces the concepts and methodologies related to the modeling of the complex phenomena occurring in materials processing. It is intended for undergraduate and graduate students in materials science and engineering, mechanical engineering and physics, and for engineering professionals or researchers.