Meeting Summaries
Please note that most papers mentioned below can be found here

Fall 2006 (MATH4991: Mathematical Research)
Meeting 13 (11-28-06): Course summary.
Meeting 12 (11-21-06): Group discussion.
Meeting 11 (11-14-06): Presentation by Jace Rowland: Postscript visualization of triangular grids.
Meeting 10 (11-7-06): Presentation by David Cook: The null space method
Meeting 9 (10-31-06): Introduction to preconditioning of saddle point problems.
Meeting 8 (10-24-06): Presentation by Sabine Le Borne.
Meeting 7 (10-10-06): (Geometric) index clustering; matrix row/column permutation.
Meeting 6 (10-3-06): HLib implementation of rank-k addition
Meeting 5 (9-26-06): Lapack in HLib: Matrix-vector multiplication.
Meeting 4 (9-19-06): Lapack in HLib: Vector addition, scaling, norm.
Meeting 3 (9-12-06): Presentation by Stephenie Brown: Implementation of backward step triangulation..
Meeting 2 (9-5-06): Exchange of individual c-code routines (Stephenie: backward step grid; Jace: postscript visualization of grid)
Meeting 1 (8-29-06): ``Informal'' summer reports

Spring 2006 (MATH4991: Mathematical Research)
Meeting 13 (4-23-06): Course summary.
Meeting 12 (4-17-06): Presentation by Stephenie Brown: Backward facing step domains
Meeting 11 (4-10-06): Hierarchical matrices: Implementation in HLIB.
Meeting 10 (4-3-06): Presentation by David Cook: Read/Write routines for sparse matrices, complexity comparisons of HLib and MATLAB iterative and exact solvers.
Meeting 9 (3-27-06): Group discussion.
Meeting 8 (3-20-06): Hierarchical matrices: Definition and construction.
Meeting 7 (3-13-06): Presentation by Jace Rowland: Postscript visualization of triangular grids.
Meeting 6 (2-27-06): Presentation by Jason Taylor: ILU(p)
Meeting 5 (2-20-06): Basic iterative solvers, preconditioning, additive & multiplicative splittings.
Meeting 4 (2-13-06): Basic aspects of discretization.
Meeting 3 (2-6-06): The governing equations of fluid dynamics, boundary conditions.
Meeting 2 (1-30-06): Introduction to the HLIB software package.
Meeting 1 (1-23-06): Computational fluid dynamics: Components of a numerical simulation.

Fall 2005 (MATH4991: Mathematical Research)
Meeting 14 (12-6-05): Course summary.
Meeting 13 (11-29-05): Presentation by Deepti Jakkula: Hierarchical matrix preconditioners for saddle point problems.
Meeting 12 (11-22-05): Hierarchical matrix construction: Admissibility condition, underlying geometry.
Meeting 11 (11-15-05): Hierarchical matrices: Matrix arithmetic and complexity.
Meeting 10 (11-8-05): Hierarchical matrices: Motivation and Definition.
Meeting 9 (11-1-05): Presentation by Jason Taylor: ILU(p)
Meeting 8 (10-25-05): Preconditioning, Krylov acceleration, multigrid.
Meeting 7 (10-11-05): Basic iterative solvers and convergence criterion.
Meeting 6 (10-4-05): Presentation by Jill Santoro: Prolongation and restriction in one and two spatial dimensions.
Meeting 5 (9-27-05): Group discussion.
Meeting 4 (9-20-05): Sparsity of discrete systems of equations, sparse storage format, matrix arithmetic.
Meeting 3 (9-13-05): Presentation by Jace Rowland: Triangulation data structures and construction of a grid hierarchy.
Meeting 2 (9-6-05): Admissible triangulations and FE Discretization by continuous, piecewise linear functions. DoFs and vertices.
Meeting 1 (8-30-05): Computational fluid dynamics: Components of a numerical simulation.

Spring 2005 (MATH4991: Mathematical Research)
Meeting 13 (4-21-05): Presentation by Michael Holloway (LU, ILU and TILU).
Meeting 12 (4-14-05): Presentation by Anna Ablamowicz (Importing a MATLAB-generated triangulation into HLIB).
Meeting 11 (4-7-05): Presentation by Jill Santoro (Grid generation for irregular domains using the MATLAB mesh generator distmesh by Pearson/Strang).
Meeting 10 (3-31-05): Presentation by Deepti Jakkula (Preconditioning for saddle point problems).
Meeting 9 (3-24-05): Presentation by Aparna Sonar (Domain-decomposition based H-Matrices).
Meeting 8 (3-17-05): Iterative solvers, preconditioning, Krylov acceleration.
Meeting 7 (3-3-05): Mixed finite elements for systems of PDEs and resulting system of equations.
Meeting 6 (2-24-05): Sparsity of discrete systems of equations, ordering and bandwidth.
Meeting 5 (2-17-05): Tetrahedral grids in 3D (and finite element spaces).
Meeting 4 (2-10-05): Admissible triangulations and conforming finite element spaces in 2D.
Meeting 3 (2-3-05): Definition of two-dimensional domains using distance functions, contour lines or polygons.
Meeting 2 (1-27-05): Continued the derivation of the Euler- and Navier-Stokes equations, initial and boundary conditions.
Meeting 1 (1-20-05): (Heuristic) derivation of the Euler- and Navier-Stokes equations.

Fall 2004
Meeting 13 (12-10-04): Presentation of numerical test results using HLib library.
Meeting 12 (12-3-04): Presentation of HLib program (compile, run, document test results in Latex tables).
Meeting 11 (11-19-04): Presentation introducing the concept/notion of consistency, stability, and convergence in numerical analysis.
Meeting 10 (11-12-04): Concept of preconditioning; grid data structures and generating software packages
Meeting 9 (11-5-04): Overview of basic linear iterative solvers.
Meeting 8 (10-29-04): Discussion of the paper "An introdution to hierarchical matrices with Applications" by W. Hackbusch, L. Grasedyck, S Borm, Technical Report 18 (2002), Max-Planck-Institute for Mathematics in the Sciences
Meeting 7 (10-22-04): Completed discussion on 2001 paper. Discussed grid data structure and 2D grid generation in HLib.
Meeting 6 (10-15-04): Lecture continued through Discretisation in the 2001 paper (Sec. 2.2-3.2).
Meeting 5 (10-8-04): Began discussion of paper by Hackbusch, Grasedyck, and Borm: " An Introduction to Hierarchical Matrices", Technical Report 105 (2001), Max-Planck-Institute for Mathematics in the Sciences, (Sec. 1.1-2.1), brief overview of HLib package (implementation of H-matrix arithmetic)
Meeting 4 (10-1-04): C Presentations: Loops; Functions
Meeting 3 (9-24-04): C Presentations: Macros and Preprocessors; Data Types and Structures; Pointers and Arrays
Meeting 2 (9-17-04): Lecture on 1999 paper continued.
Meeting 1 (9-10-04): Began discussion of Hackbusch's first paper on H-matrices: "A Sparse Matrix Arithmetic based on H-Matrices. Part I: Introdcuction to H-Matrices", Computing 62, 89-108 (1999)