th This volume contains a selection of 41 refereed papers presented at the 18 International Conference of Domain Decomposition Methods hosted by the School of ComputerScience and Engineering(CSE) of the Hebrew Universityof Jerusalem, Israel, January 12-17, 2008. 1 Background of the Conference Series The International Conference on Domain Decomposition Methods has been held in twelve countries throughout Asia, Europe, the Middle East, and North America, beginning in Paris in 1987. Originally held annually, it is now spaced at roughly 18-month intervals. A complete list of past meetings appears below. The principal technical content of the conference has always been mathematical, but the principal motivation has been to make ef cient use of distributed memory computers for complex applications arising in science and engineering. The leading 15 such computers, at the "petascale" characterized by 10 oating point operations per second of processing power and as many Bytes of application-addressablem- ory, now marshal more than 200,000 independentprocessor cores, and systems with many millions of cores are expected soon. There is essentially no alternative to - main decomposition as a stratagem for parallelization at such scales. Contributions from mathematicians, computerscientists, engineers,and scientists are together n- essary in addressing the challenge of scale, and all are important to this conference.

"These are the proceedings of the 18th international conference on domain decomposition methods in science and engineering, held in Jerusalem, January 12-17, 2008. Domain decomposition methods are iterative methods for solving the often very large linear or nonlinear systems of algebraic equations that arise when various problems in continuum mechanics are discretized using finite elements. They are designed for massively parallel computers and take the memory hierarchy of such systems into account. This is essential for approaching peak floating point performance. There is an increasingly well developed theory which is having a direct impact on the development and improvements of these algorithms."

Plenary Presentations.- A Domain Decomposition Approach for Calculating the Graph Corresponding to a Fibrous Geometry.- Adaptive Multilevel Interior-Point Methods in PDE Constrained Optimization.- Numerical Homogeneisation Technique with Domain Decomposition Based a-posteriori Error Estimates.- Multiscale Methods for Multiphase Flow in Porous Media.- Mixed Plane Wave Discontinuous Galerkin Methods.- Numerical Zoom and the Schwarz Algorithm.- BDDC for Nonsymmetric Positive Definite and Symmetric Indefinite Problems.- Accomodating Irregular Subdomains in Domain Decomposition Theory.- Auxiliary Space Preconditioners for Mixed Finite Element Methods.- Minisymposia.- A Multilevel Domain Decomposition Solver Suited to Nonsmooth Mechanical Problems.- A FETI-2LM Method for Non-Matching Grids.- Truncated Nonsmooth Newton Multigrid Methods for Convex Minimization Problems.- A Recursive Trust-Region Method for Non-Convex Constrained Minimization.- A Robin Domain Decomposition Algorithm for Contact Problems: Convergence Results.- Patch Smoothers for Saddle Point Problems with Applications to PDE-Constrained Optimization Problems.- A Domain Decomposition Preconditioner of Neumann-Neumann Type for the Stokes Equations.- Non-overlapping Domain Decomposition for the Richards Equation via Superposition Operators.- Convergence Behavior of a Two-Level Optimized Schwarz Preconditioner.- An Algorithm for Non-Matching Grid Projections with Linear Complexity.- A Maximum Principle for L 2-Trace Norms with an Application to Optimized Schwarz Methods.- An Extended Mathematical Framework for Barrier Methods in Function Space.- Optimized Schwarz Preconditioning for SEM Based Magnetohydrodynamics.- Nonlinear Overlapping Domain Decomposition Methods.- Optimized Schwarz Waveform Relaxation: Roots, Blossoms and Fruits.- Optimized Schwarz Methods.- The Development of Coarse Spaces for Domain Decomposition Algorithms.- Contributed Presentations.- Distributed Decomposition Over Hyperspherical Domains.- Domain Decomposition Preconditioning for Discontinuous Galerkin Approximations of Convection-Diffusion Problems.- Linearly Implicit Domain Decomposition Methods for Nonlinear Time-Dependent Reaction-Diffusion Problems.- NKS for Fully Coupled Fluid-Structure Interaction with Application.- Weak Information Transfer between Non-Matching Warped Interfaces.- Computational Tool for a Mini-Windmill Study with SOFT.- On Preconditioners for Generalized Saddle Point Problems with an Indefinite Block.- Lower Bounds for Eigenvalues of Elliptic Operators by Overlapping Domain Decomposition.- From the Boundary Element Domain Decomposition Methods to Local Trefftz Finite Element Methods on Polyhedral Meshes.- An Additive Neumann-Neumann Method for Mortar Finite Element for 4th Order Problems.- A Numerically Efficient Scheme for Elastic Immersed Boundaries.- A Domain Decomposition Method Based on Augmented Lagrangian with a Penalty Term.- Parallelization of a Constrained Three-Dimensional Maxwell Solver.- A Discovery Algorithm for the Algebraic Construction of Optimized Schwarz Preconditioners.- On the Convergence of Optimized Schwarz Methods by way of Matrix Analysis.