#### DMCA

## Parallelization of structured, hierarchical adaptive mesh refinement algorithms (2000)

Venue: | Computing and Visualization in Science |

Citations: | 39 - 10 self |

### Citations

1362 |
Using MPI: Portable Parallel Programming with the Message Passing Interface
- Gropp, Lusk, et al.
- 1994
(Show Context)
Citation Context ...hese are nearly completely hidden from the application programmer because they are implemented either within BoxLib or AMRLib or one of their auxiliary libraries. Finally we note that we used the MPI =-=[21, 14]-=- message-passing library. We used only core functionality within the MPI library to ensure portability. Furthermore, we encapsulated the MPI specific library calls within a class, ParallelDescriptor, ... |

560 |
Adaptive mesh refinement for hyperbolic partial differential equations
- Berger, Oliger
- 1984
(Show Context)
Citation Context ...ion, multiple-data (MIMD) architectures. The particular form of adaptivity we consider is a blockstructured style of refinement, referred to as AMR, that was originally developed by Berger and Oliger =-=[5]-=-. The development of the methodology here uses the approach developed by Berger and Colella [4] for general systems of conservation laws and the extension of that methodology to three dimensions by Be... |

519 |
Local adaptive mesh refinement for shock hydrodynamics
- Berger, Colella
- 1989
(Show Context)
Citation Context ...ckstructured style of refinement, referred to as AMR, that was originally developed by Berger and Oliger [5]. The development of the methodology here uses the approach developed by Berger and Colella =-=[4]-=- for general systems of conservation laws and the extension of that methodology to three dimensions by Bell et ∗ Support for this work was provided by the Applied Mathematical Sciences Program of the ... |

516 |
Algorithms in C
- Sedgewick
- 1990
(Show Context)
Citation Context ...ted to the standard measure of parallel efficiency. This problem is an application of the knapsack dynamic programming algorithm, a description of which may be found in Sedgewick’s book on algorithms =-=[19]-=-. In general, the knapsack problem is NP complete and finding the best assignment of grids to processors will require O(N!) possible operations, which is not practical. Below is a heuristic algorithm ... |

433 |
On the construction and comparison of difference schemes
- Strang
- 1968
(Show Context)
Citation Context ...y = 4.45 cm, z = 4.45 cm) and the shock is initialized at 13.5 cm in the x direction moving in the direction of increasing x. We use the operator-split second-order Godunov method of [8], with Strang =-=[23]-=- splitting. Reflecting boundary conditions are set on the constant z and constant y planes. To minimize the x extent of the problem, the inflow and outflow velocities on the constant x planes, as well... |

131 | A conservative adaptive projection method for the variable density incompressible Navier-Stokes equation",
- Almgren, Bell, et al.
- 1998
(Show Context)
Citation Context ...hreat Reduction Agency IACRO98-3017, through the U. S. Department of Energy under Contract No. DE-AC03-76SF00098. 1al. [2]. This type of adaptive refinement has been extended to incompressible flows =-=[1]-=- and to low Mach number models for atmospheric flow [22] and combustion [18]. AMR is based on a sequence of nested grids with finer and finer mesh spacing in space, each level being advanced in time w... |

113 |
An algorithm for point clustering and grid generation.
- Berger, Rigoutsos
- 1991
(Show Context)
Citation Context ...scribed in Berger and Colella [4], or it may use some other user-supplied criterion. The tagged cells are grouped into rectangular patches using the clustering algorithm given in Berger and Rigoutsos =-=[6]-=-. The generated patches will in general contain cells that were not tagged for refinement. The grid efficiency is the fraction of the cells in a new grid that are tagged by the error estimation proces... |

96 |
Three-dimensional adaptive mesh refinement for hyperbolic conservation laws
- Bell, Berger, et al.
- 1994
(Show Context)
Citation Context ...ice of Mathematics, Information, and Computational Sciences and by the Defense Threat Reduction Agency IACRO98-3017, through the U. S. Department of Energy under Contract No. DE-AC03-76SF00098. 1al. =-=[2]-=-. This type of adaptive refinement has been extended to incompressible flows [1] and to low Mach number models for atmospheric flow [22] and combustion [18]. AMR is based on a sequence of nested grids... |

57 |
Interactions of weak shock waves with cylindrical and spherical gas inhomogeneities
- Hass, Sturtevant
- 1987
(Show Context)
Citation Context ...port for that model provided by the underlying software. We illustrate the methodology for three-dimensional gas dynamics on computation of a shock-bubble laboratory experiment of Sturtevant and Haas =-=[15]-=-. We discuss overall performance and parallel efficiency in the context of this case study. 2 The Adaptive Mesh Refinement Algorithm AMR solves partial differential equations using a hierarchy of grid... |

44 | On the construction and comparison of di#erence schemes - Strang |

41 |
MPI: The Complete Reference. Scientific and engineering computation series (The
- Snir, Otto, et al.
- 1997
(Show Context)
Citation Context ...hese are nearly completely hidden from the application programmer because they are implemented either within BoxLib or AMRLib or one of their auxiliary libraries. Finally we note that we used the MPI =-=[21, 14]-=- message-passing library. We used only core functionality within the MPI library to ensure portability. Furthermore, we encapsulated the MPI specific library calls within a class, ParallelDescriptor, ... |

30 |
FIDIL: A Language for Scientific Programming
- Hilfinger, Colella
- 1988
(Show Context)
Citation Context ... implement a large portion of the code in a space-dimension independent manner by defining the dimension as a compile time parameter. BoxLib owes many of its concepts to Hilfinger and Colella’s FIDIL =-=[16]-=- language for defining algorithms for solving partial differential equations. However, FIDIL is much more general and expressive, allowing the user to express directly mathematical operations on data ... |

28 | Adaptive mesh re for hyperbolic partial dierential equations - Berger, Oliger - 1984 |

24 |
An adaptive projection method for unsteady, low-mach number combustion
- Pember, Howell, et al.
- 1998
(Show Context)
Citation Context ... under Contract No. DE-AC03-76SF00098. 1al. [2]. This type of adaptive refinement has been extended to incompressible flows [1] and to low Mach number models for atmospheric flow [22] and combustion =-=[18]-=-. AMR is based on a sequence of nested grids with finer and finer mesh spacing in space, each level being advanced in time with time step intervals determined by the Courant-Friedrich-Level (CFL) cond... |

20 | Local Adaptive Mesh Re for Shock Hydrodynamics - Berger, Colella - 1987 |

20 |
Object-oriented implementation of adaptive mesh refinement algorithms
- Crutchfield, Welcome
- 1993
(Show Context)
Citation Context ...a between levels and the coarse-fine interface synchronization routines. The foundation library, BoxLib, and a previous framework library, called libamr, has been described by Crutchfield and Welcome =-=[11]-=-. BoxLib has been modified and improved from the version described in that paper, but has kept its core functionality and data structures intact. The improvements were made incrementally, so that exis... |

18 | Irregular coarse-grain data parallelism under lparx
- Kohn, Baden
- 1996
(Show Context)
Citation Context ... non-rectangular domains of index space, including domains not defined as a union of non-intersecting rectangles. Unfortunately, FIDIL has not become widely available. LPARX, described by Kohn et al. =-=[17]-=-, and KeLP, described by Fink [12], are other libraries that owe much of their conceptual foundation to FIDIL. These libraries have similar purposes to the parallel implementation of BoxLib described ... |

14 | A Programming Model for Block-Structured Scientific Calculations on SMP Clusters
- Fink
- 1998
(Show Context)
Citation Context ...space, including domains not defined as a union of non-intersecting rectangles. Unfortunately, FIDIL has not become widely available. LPARX, described by Kohn et al. [17], and KeLP, described by Fink =-=[12]-=-, are other libraries that owe much of their conceptual foundation to FIDIL. These libraries have similar purposes to the parallel implementation of BoxLib described in this paper. The framework libra... |

12 |
Load balancing irregular algorithms.
- Crutchfield
- 1991
(Show Context)
Citation Context ...interface between coarse and fine grids to insure conservation. Several approaches to parallelization of AMR applied to hyperbolic conservation laws have been addressed in the literature. Crutchfield =-=[9, 10]-=- developed a prototype parallel implementation of a twodimensional, adaptive gas dynamics algorithm using a coarse-grained MIMD model. Berger and Saltzman [3] used a data-parallel model to implement a... |

8 | MPI: The Complete Reference. Scienti and Engineering Computation Series - Snir, Otto, et al. - 1996 |

4 |
A Parallel Adaptive Mesh Refinement Algorithm on the C-90
- Colella, Crutchfield
- 1994
(Show Context)
Citation Context ...cs algorithm using a coarse-grained MIMD model. Berger and Saltzman [3] used a data-parallel model to implement an adaptive gas dynamics algorithm on a Thinking Machines CM-2. Colella and Crutchfield =-=[7]-=- implemented a task-queue parallel model for a multifluid algorithm on a Cray C-90 which was used by Greenough et al. [13] to study a mixing layer. A major departure of the work presented here is the ... |

3 | Three-dimensional adaptive mesh re for hyperbolic conservation laws - Bell, Berger, et al. - 1994 |

3 | Numerical simulation of a wave guide mixing layer on a Cray C-90 - Greenough, Bell, et al. - 1995 |

3 |
Adaptive simulations of trade cumulus convection submitted for publication
- Stevens, Almgren, et al.
- 1998
(Show Context)
Citation Context ...Department of Energy under Contract No. DE-AC03-76SF00098. 1al. [2]. This type of adaptive refinement has been extended to incompressible flows [1] and to low Mach number models for atmospheric flow =-=[22]-=- and combustion [18]. AMR is based on a sequence of nested grids with finer and finer mesh spacing in space, each level being advanced in time with time step intervals determined by the Courant-Friedr... |

3 |
Parallel adaptive mesh refinement: An example of parallel data encapsulation
- Crutchfield
- 1991
(Show Context)
Citation Context ...interface between coarse and fine grids to insure conservation. Several approaches to parallelization of AMR applied to hyperbolic conservation laws have been addressed in the literature. Crutchfield =-=[9, 10]-=- developed a prototype parallel implementation of a twodimensional, adaptive gas dynamics algorithm using a coarse-grained MIMD model. Berger and Saltzman [3] used a data-parallel model to implement a... |

1 | A parallel adaptive mesh re algorithm on the C-90 - Colella, Crutch - 1994 |

1 |
Efficient solution algorithms for the Reimann problem for real gases
- Colella, Glaz
- 1985
(Show Context)
Citation Context ...oint (x = 16 cm, y = 4.45 cm, z = 4.45 cm) and the shock is initialized at 13.5 cm in the x direction moving in the direction of increasing x. We use the operator-split second-order Godunov method of =-=[8]-=-, with Strang [23] splitting. Reflecting boundary conditions are set on the constant z and constant y planes. To minimize the x extent of the problem, the inflow and outflow velocities on the constant... |

1 | Load balancing irregular algorithms - Crutch - 1991 |

1 | Parallel adaptive mesh re An example of parallel data encapsulation - Crutch - 1991 |

1 | Object-oriented implementation of adaptive mesh re algorithms - Crutch, Welcome - 1993 |

1 | FIDIL: A language for scienti computing - Hil, Colella - 1989 |

1 |
The Cray T3E-900 scalable parallel processing system
- Graphics, Inc
- 1999
(Show Context)
Citation Context ...f the two fluids at the same pressure does not result in a pressure and internal energy change of the composite fluid. Two sets of experiments are presented. We used the SGI/Cray T3E-900 (T3E, below) =-=[20]-=- at the NERSC facility at Lawrence Berkeley National Laboratory to perform these experiments. The T3E compute nodes are 450 MHz Digital Alpha 21164 processors, capable of up to 900 MFlops. The communi... |