The finite element method (FEM) has become the most widely accepted general-purpose technique for numerical simulations in engineering and applied mathematics. Principal applications arise in continuum mechanics, fluid flow, thermodynamics, and field theory. In these areas, computational methods are essential and benefit strongly from the enormous advances in computer technology. B-splines play an important role in approximation and geometric modeling. They are used in data fitting, computer-aided design (CAD), automated manufacturing (CAM), and computer graphics. Finite Element Methods with B-Splines describes new weighted approximation techniques, combining the computational advantages of B-splines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often time-consuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction, and elasticity.
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Book Description
Describes new weighted approximation techniques, combining the computational advantages of B-splines and standard finite elements. No grid generation is necessary, which eliminates a difficult and often time-consuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters.
About the Author
Klaus Höllig is professor of Mathematics and Computer Sciences and holds a chair for Numerical Analysis and Computer-Aided Geometric Design at the University of Stuttgart, Germany. His current research focuses on numerical solution of partial differential equations, approximation and geometric modeling, and grid generation. He is also involved in the development of interactive teaching tools and is codirecting the Mathematics-Online project.
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