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This volume introduces recent developments of Partial Differential Equations (PDEs) in the field of Geometric Design. The text is written with a particular emphasis on computer based design and analysis involving the geometry of physical objects.
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.
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.
From the reviews:
"The book is devoted to the application of partial differential equations (PDEs) in geometric design. The main idea of the book is to describe how elliptic PDEs can be used as an intuitive surface generation and manipulation tool. ... The book should equally serve as a reference for the mathematical foundamentals and modern applications using PDEs and as a tool for geometric design. It is suitable both as a textbook and a professional reference for students, researchers and engineers." (Agnieszka Lisowska, Zentralblatt MATH, Vol. 1230, 2012)
"The book is devoted to the application of partial differential equations (PDEs) in geometric design. The main idea of the book is to describe how elliptic PDEs can be used as an intuitive surface generation and manipulation tool. ... The book should equally serve as a reference for the mathematical foundamentals and modern applications using PDEs and as a tool for geometric design. It is suitable both as a textbook and a professional reference for students, researchers and engineers." (Agnieszka Lisowska, Zentralblatt MATH, Vol. 1230, 2012)