Triangulations, and more precisely meshes, are at the heart of many problems relating to a wide variety of scientific disciplines, and in particular numerical simulations of all kinds of physical phen
Written in easy to understand language, this self-explanatory guide introduces the fundamentals of finite element methods and its application to differential equations. Beginning with a brief introduction to Sobolev spaces and elliptic scalar problems, the text progresses through an explanation of finite element spaces and estimates for the interpolation error. The concepts of finite element methods for parabolic scalar parabolic problems, object-oriented finite element algorithms, efficient implementation techniques, and high dimensional parabolic problems are presented in different chapters. Recent advances in finite element methods, including non-conforming finite elements for boundary value problems of higher order and approaches for solving differential equations in high dimensional domains are explained for the benefit of the reader. Numerous solved examples and mathematical theorems are interspersed throughout the text for enhanced learning.
This book is the second in a series of volumes that cover the topic of aerospace actuators following a systems-based approach.This second volume brings an original, functional and architectural vision
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a
The third edition of the book introduces the fundamentals of the finite element method through simple examples and an applications-oriented approach using the latest computational tools. Using the tra
Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for sol
A comprehensive treatment of the theory and practice of equilibrium finite element analysis in the context of solid and structural mechanics Equilibrium Finite Element Formulations is an up to date ex
This book is dedicated to the general study of the dynamics of mechanical structures with consideration of uncertainties. In the second part, we present a study of structural optimization. The goal is
Simulation and the Monte Carlo Method, Third Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte
This book presents the latest numerical solutions to initial value problems and boundary value problems described by ODEs and PDEs. The author offers practical methods that can be adapted to solve wide ranges of problems and illustrates them in the increasingly popular open source computer language R, allowing integration with more statistically based methods. The book begins with standard techniques, followed by an overview of 'high resolution' flux limiters and WENO to solve problems with solutions exhibiting high gradient phenomena. Meshless methods using radial basis functions are then discussed in the context of scattered data interpolation and the solution of PDEs on irregular grids. Three detailed case studies demonstrate how numerical methods can be used to tackle very different complex problems. With its focus on practical solutions to real-world problems, this book will be useful to students and practitioners in all areas of science and engineering, especially those using R.
This book is the first of a series of volumes that cover the topic of aerospace actuators following a systems-based approach. This first volume provides general information on actuators and their rel
This textbook is an accessible and concise introduction to numerical analysis for upper undergraduate and beginning graduate students from various backgrounds. It was developed from the lecture notes
This book provides an introduction to programming in SAGE, with an emphasis on how to create SAGE Interacts, for those who are studying numerical analysis. The author does not delve into the mat
This concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis o
This concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis o
Variance-Constrained Multi-Objective Stochastic Control and Filtering establishes a unified framework for filtering and control problems for various discrete-time nonlinear stochastic systems with eng
Charts and graphs help students illustrate their point in research papers, presentations, and other class projects. This book teaches readers how to read, understand, and create charts and graphs. It
This well-respected book introduces readers to the theory and application of modern numerical approximation techniques. Providing an accessible treatment that only requires a calculus prerequisite, th
