Householder Symposium XV

Application example: remeshing the Isis statue
 

Fast Solution Methods and Preconditioners for Symmetric and Nonsymmetric Indefinite Systems, Eric de Sturler and Jörg Liesen, plenary presentation at the 15th Householder symposium in Numerical Linear Algebra, June 17-21, Peebles, Scotland.

For more information on this work, applications, and background, please see the following papers and technical reports. The main preconditioning paper is Block-Diagonal Preconditioners for Indefinite Linear Algebraic Systems. Part I: Theory, Eric de Sturler and Jörg Liesen, Technical Report UIUCDCS-R-20022279, also UILU-ENG-2002-1723, June 2002, submitted to SIAM Journal on Scientific Computing. A follow-up paper on applications is in preparation. An earlier paper on preconditioning for the optimization problems arising in mesh flattening for surface parameterization was published in the proceedings of the 10th International Meshing Roundtable, Preconditioners for Indefinite Linear Systems Arising in Surface Parameterization, Jörg Liesen, Eric de Sturler, Alla Sheffer, Yelda Aydin, and Chris Siefert, Proceedings of the 10th International Meshing Round Table, Newport Beach, CA, October 7-10, 2001, Sandia National Laboratories. This paper also has further details on the splitting used in this particular application.

The algorithm for surface parameterization was introduced in Surface Parameterization for Meshing by Triangulation Flattening, Alla Sheffer and Eric de Sturler, Proceedings of the 9^th International Meshing Round Table Conference 2000, New Orleans, October, 2000, and a more elaborate description can be found in Parameterization of Faceted Surfaces for Meshing Using Angle Based Flattening, A. Sheffer and E. de Sturler, Engineering with Computers 17(3) (2001), pp. 326-337 (a special issue featuring revised versions of the best papers of IMR9). An application of the algorithm to texture mapping is described in Smoothing an Overlay Grid to Minimize Linear Distortion in Texture Mapping, A. Sheffer and E. de Sturler, to appear (accepted) in ACM Transaction on Graphics.