Finite Element Methods with B-Splines:
Sample MATLAB Programs
The small collection of MATLAB programs illustrates the methods described in the book. Our examples show that the elegance and efficiency of B-spline algorithms, familiar from numerous applications, also prevail for the numerical solution of partial differential equations. This is due to the exceptionally simple data structure of uniform B-splines with its obvious advantages. Most importantly, regardless of the degree, the finite element subspace is spanned by translates of a single basis function, and the coefficients are associated with a regular grid; no mesh generation and connectivity data structures are necessary as for conventional finite element codes.
The goal of our sample programs is not to cover a broad range of partial differential equations or to provide B-spline software ready to serve potential applications. Instead, our MATLAB routines for basic model problems are intended as examples which show how to exploit standard B-spline features. In particular, the m-files provide illustrations for teaching purposes. Moreover, experimenting with our sample codes can facilitate the development of b-spline-based finite element software.
For programs and demos illustrating the geometric properties of B-splines see the supplementary material for the book Approximation and Modeling with B-Splines (OT132).
The programs of the package FEMB (Version 1.0) are test versions, intended only for educational use, and for illustrating the methods described in the SIAM book Finite Element Methods with B-Splines. No permission is granted for any other application, in particular for any commercial use or applications of the programs which can result in material or physical damage. A possible lack of reliability of the numerical algorithms, which to some extent are based on heuristic strategies, has been emphasized. As a consequence, no guarantees for the correctness of the computed results can be given. In addition to the above restrictions, the general terms of MathWorks for using MATLAB programs apply.
Included in download:
Demo: Approximation of Poisson's Problem |
The slides facilitate teaching courses on finite element methods based on the SIAM book. For each subsection, a pdf-file with a beamer presention of the main topics is provided (see the sample index for the slides corresponding to the first two chapters). Moreover, a template explains how to generate additional presentations in the same style. This allows professors to adapt the material according to the content of their course.
The problem collection contains 75 theoretical as well as programming exercises pertaining to the topics of books. For most problems hints are given. Morever, an extended pdf-document with solutions is available for professors.
*Professors may contact Klaus Höllig at [email protected] for the full slideshow and solutions to problems.