Preface 1. Background in linear algebra 2. Discretization of partial differential equations 3. Sparse matrices 4. Basic iterative methods 5. Projection methods 6. Krylov subspace methods Part I 7. Krylov subspace methods Part II 8. Methods related to the normal equations 9. Preconditioned iterations 10. Preconditioning techniques 11. Parallel implementations 12. Parallel preconditioners 13. Multigrid methods 14. Domain decomposition methods Bibliography Index.

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Iterative Methods for Sparse Linear Systems

We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by the gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We give a numerical algorithm using finite differences. Finally, we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.

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Active contours without edges

Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268

Data Mining - Concepts and Techniques.

https://hal.archives-ouvertes.fr/hal-00417283/document

Independent component analysis, a new concept?

Algebraic preconditioning algorithms suitable for computational fluid dynamics (CFD) based on overlapping and non-overlapping domain decomposition (DD) are considered. Specific distinction is given to techniques well-suited for time-dependent and steady-state computations of fluid flow. For time-dependent flow calculations, the overlapping Schwarz algorithm suggested by Wu et al. [28] together with stabilised (upwind) spatial discretisation shows acceptable scalability and parallel performance without requiring a coarse space correction. For steady-state flow computations, a family of non-overlapping Schur complement DD techniques are developed. In the Schur complement DD technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. The permutation of the mesh vertices based on subdomains and interfaces induces a natural 2 × 2 block partitioning of the discretisation matrix. Exact LU factorisation of this block system introduces a Schur complement matrix which couples subdomains and the interface together. A family of simplifying techniques for constructing the Schur complement and applying the 2 × 2 block system as a DD preconditioner are developed Sample fluid flow calculations are presented to demonstrate performance characteristics of the simplified preconditioners.

Parallel domain-decomposition preconditioning for computational fluid dynamics : Invited talk

The alternate-block-factorization (ABF) method is a procedure for partially decoupling systems of elliptic partial differential equations by means of a carefully chosen change of variables. By decoupling we mean that the ABF strategy attempts to reduce intra-equation coupling in the system rather than intra-grid coupling for a single elliptic equation in the system. This has the effect of speeding convergence of commonly used iteration schemes, which use the solution of a sequence of linear elliptic PDEs as their main computational step. Algebraically, the change of variables is equivalent to a postconditioning of the original system. The results of using ABe: postconditioning on some problems arising from semiconductor device simulation are discussed.

Tony F. Chan

Papers

Parallel domain-decomposition preconditioning for computational fluid dynamics : Invited talk

The a lternate-block- factorization p rocedure for s ystems o f p artial d ifferential e quations