Scientific Computing -- Computational Science “Same Old Silence, Same Old Mistakes” “Something More Is Needed … ” -- Massively Parallel Simulations with DOE?s ASCI Supercomputers: An Overview of the Los Alamos Crestone Project -- Methods -- Adaptive Mesh Refinement on Overlapping Grids -- A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics -- Front Tracking Algorithm Using Adaptively Refined Meshes -- An accuracy study of mesh refinement on mapped grids -- Efficiency Gains from Time Refinement on AMR Meshes and Explicit Timestepping -- Using Krylov-Schwarz methods in an adaptive mesh refinement environment -- Dimensional Split Divergence-Free Reconstruction and Prolongation for Adaptive Mesh Refinement -- Multiresolution-based adaptive schemes for Hyperbolic Conservation Laws -- Multiresolution adaptive space refinement in geophysical fluid dynamics simulation -- Anisotropic mesh adaptivity in CFD -- A Posteriori Error Estimation and Mesh Adaptivity for Finite Volume and Finite Element Methods -- AMR for low Mach number reacting flow -- Simulations of Relativistic Astrophysical Flows -- AMR applied to non-linear Elastodynamics -- A Parallel AMR Implementation of The Discrete Ordinates Method for Radiation Transport -- Radiation Transport in AMR -- Software -- HERA: A Hydrodynamic AMR Platform for Multi-Physics Simulations -- Parallel Multi-dimensional and Multi-material Eulerian Staggered Mesh Schemes using Localised Patched Based Adaptive Mesh Refinement (AMR) for Strong Shock Wave Phenomena. -- A general adaptive multi-resolution approach to ocean modelling: experiments in a primitive equation model of the north Atlantic -- An Overview of the PARAMESH AMR Software Package and Some of Its Applications -- AstroBEAR: AMR for Astrophysical Applications - I: Methods -- Introducing Enzo, an AMR Cosmology Application -- Toward Optimizing Enzo, an AMR Cosmology Application -- Construction and Application of an AMR Algorithm for Distributed Memory Computers -- Adaptive Mesh Refinement in a Grid Computing Environment -- Performance of Vector/Parallel Orientated Hydrodynamic Code -- On the efficiency of AMR in NIRVANA3 -- Dynamic Load Balancing of SAMR Applications -- Applications -- The Impact of AMR in Numerical Astrophysics and Cosmology -- Recent Advances in the Collapse and Fragmentation of Turbulent Molecular Cloud Cores: The Formation of Low Mass Stars -- 3D AMR Simulations of Point-Symmetric Nebulae -- Mesh Refinement Calculations of Gravitational Waves and Black Holes in 3-Dimensions -- AstroBEAR: AMR for Astrophysical Applications - II: Tests and Applications -- Parallel, AMR MHD for Global Space Weather Simulations -- Adaptive Mesh Refinement for MHD Fusion Applications -- AMR for global atmospheric modelling -- Simulation of Vortex-Dominated Flows Using the FLASH Code.

Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.