Custom cover image
Partial Differential Equations for Geometric Design / by Hassan Ugail
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: London : Springer-Verlag London Limited, 2011Description: Online-Ressource (IX, 107p. 53 illus, digital)ISBN:- 9780857297846
- 004.0151
- 515.353 515/.353
- QA76.9.M35
- QA377
Contents:
Summary: The subject of Partial Differential Equations (PDEs) which first emerged in the 18th century holds an exciting and special position in the applications relating to the mathematical modelling of physical phenomena. The subject of PDEs has been developed by major names in Applied Mathematics such as Euler, Legendre, Laplace and Fourier and has applications to each and every physical phenomenon known to us e.g. fluid flow, elasticity, electricity and magnetism, weather forecasting and financial modelling. This book introduces the recent developments of PDEs in the field of Geometric Design particularly for computer based design and analysis involving the geometry of physical objects. Starting from the basic theory through to the discussion of practical applications the book describes how PDEs can be used in the area of Computer Aided Design and Simulation Based Design. Extensive examples with real life applications of PDEs in the area of Geometric Design are discussed in the book.PPN: PPN: 1651018863Package identifier: Produktsigel: ZDB-2-SCS
Partial Differential Equations for Geometric Design; Preface; Contents; Chapter 1: Elementary Mathematics for Geometric Design; 1.1 Vector Algebra; 1.2 Lines and Planes in R3; 1.3 Matrix Algebra and Solving Linear Systems; 1.3.1 Properties of Matrices; Transpose; Trace; Addition; Multiplication; Inverse; Determinant; 1.3.2 Solving Systems of Linear Equations; 1.4 Properties of Surfaces; 1.4.1 Parametric Surface Representation; 1.4.1.1 Properties of Parametric Surfaces; Tangent Plane; Unit Normal; Surface Area; The First Fundamental Form; The Second Fundamental Form
Gaussian and Mean Curvature1.5 Summary; References; Chapter 2: Introduction to Geometric Design; 2.1 Introduction; 2.2 Mathematical Methods for Shape Representation in Geometric Design; 2.2.1 Schemes for Geometry Model Representation; B-Rep Approach; CSG Approach; Feature Based Approach; Variational Approach; 2.3 Enhancing Geometric Design Using Interactive and Parametric Design; 2.3.1 Techniques for Interactive Design; 2.3.2 Parametric Design; 2.4 Use of Optimization Techniques in Geometric Design; 2.5 Summary; References; Chapter 3: Introduction to Partial Differential Equations
3.1 Definition of a PDE3.1.1 Examples of PDEs; 3.2 Classification of PDEs; 3.2.1 Order; 3.2.2 Homogeneity; 3.2.3 Linearity; 3.2.4 Use of a Discriminant as a Classification Method; 3.2.4.1 Elliptic PDEs; 3.2.4.2 Parabolic PDEs; 3.2.4.3 Hyperbolic PDEs; 3.3 Harmonic, Biharmonic and the Triharmonic Equation; 3.3.1 The Biharmonic Equation; 3.3.2 The Triharmonic Equation; 3.4 Solution Methods; 3.4.1 Analytic Methods; 3.4.2 Spectral Methods; 3.4.3 Numerical Methods; 3.5 Conclusions; References; Chapter 4: Elliptic PDEs for Geometric Design; 4.1 Introduction; 4.2 The Laplace Equation
4.2.1 Numerical Solution Using Finite Difference Method4.3 The Biharmonic Equation; 4.3.1 Analytic Solution; 4.3.1.1 Discrete Fourier Analysis; 4.3.2 Geometric Properties of the Biharmonic PDE; 4.4 General Elliptic PDEs; 4.4.1 Analytic Solution; 4.5 Other Variations of the General Elliptic Equation; 4.6 Examples; 4.7 Conclusions; References; Chapter 5: Interactive Design; 5.1 The Approach to Interactive Surface Design; 5.2 Trimming PDE Geometry; 5.2.1 Manipulating Blend Geometry; 5.3 Spine of PDE Geometry; 5.4 Conclusions; References; Chapter 6: Parametric Design
6.1 Design Parameters via the Boundary Curves6.2 Local Parameters on the Boundary Curves; 6.3 The Effect of the Smoothing Parameter a; 6.4 The Effect of v Parametrization; 6.4.1 Time-Dependent Parametrization; 6.5 Summary; References; Chapter 7: Functional Design; 7.1 Introduction; 7.2 Principles of Shape Optimization; 7.3 Simulated Annealing; 7.4 Application of Simulated Annealing to Continuous Optimization Problems; 7.4.1 Simulated Annealing Algorithm; 7.4.2 Constraints; 7.5 Further Examples; 7.5.1 Design Optimization of a Thin-Walled Structure
7.5.2 Prediction of Stable Structures of Vesicles Occurring in Biological Organisms
No physical items for this record