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Construction and Application of an AMR Algorithm for Distributed Memory Computers
 PROC. OF CHICAGO WORKSHOP ON ADAPTIVE MESH REFINEMENT METHODS
, 2003
"... ... In this paper, a localitypreserving domain decomposition is proposed that partitions the entire AMR hierarchy from the base level on. It is shown that the approach reduces the communication costs and simplifies the implementation. Emphasis is put on the effective parallelization of the flux cor ..."
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Cited by 32 (14 self)
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... In this paper, a localitypreserving domain decomposition is proposed that partitions the entire AMR hierarchy from the base level on. It is shown that the approach reduces the communication costs and simplifies the implementation. Emphasis is put on the effective parallelization of the flux correction procedure at coarsefine boundaries, which is indispensable for conservative finite volume schemes. An easily reproducible standard benchmark and a highly resolved parallel AMR simulation of a diffrracting hydrogenoxygen detonation demonstrate the proposed strategy in practice.
Chombo software package for AMR applications design document
, 2003
"... Disclaimer This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor The Regents of the University of California, nor any of their employ ..."
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Cited by 22 (6 self)
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Disclaimer This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor The Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States
Parallel computation of threedimensional flows using overlapping grids with adaptive mesh refinement
 J. Comput. Phys
, 2008
"... This paper describes an approach for the numerical solution of timedependent partial dierential equations in complex threedimensional domains. The domains are represented by overlapping structured grids, and blockstructured adaptive mesh renement (AMR) is employed to locally increase the grid re ..."
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Cited by 17 (6 self)
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This paper describes an approach for the numerical solution of timedependent partial dierential equations in complex threedimensional domains. The domains are represented by overlapping structured grids, and blockstructured adaptive mesh renement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributedmemory computers using a domaindecomposition approach. The implementation is
exible so that each base grid within the overlapping grid structure and its associated renement grids can be independently partitioned over a chosen set of processors. A modied binpacking algorithm is used to specify the partition for each grid so that the computational work is evenly distributed amongst the processors. All components of the AMR algorithm such as error estimation, regridding, and interpolation are performed in parallel. The parallel timestepping algorithm is illustrated for initialboundaryvalue problems involving a linear advectiondiusion equation and the (nonlinear) reactive Euler equations. Numerical results are presented for both equations to demonstrate the accuracy and correctness of the parallel approach. Exact solutions of the advectiondiusion equation are constructed, and these are used to check the corresponding numerical solutions for a variety of tests involving dierent overlapping grids, dierent numbers of renement levels and renement ratios, and dierent numbers of processors. The problem of planar shock diraction by a sphere is considered as an illustration of the
Adaptive Mesh Refinement in Titanium
 In: Proceedings of the 19th International Parallel and Distributed Processing Symposium (IPDPS
, 2005
"... In this paper, we evaluate Titanium’s usability as a highlevel parallel programming language through a case study, where we implement a subset of Chombo’s functionality in Titanium. Chombo is a software package applying the Adaptive Mesh Refinement methodology to numerical Partial Differential Equa ..."
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Cited by 14 (3 self)
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In this paper, we evaluate Titanium’s usability as a highlevel parallel programming language through a case study, where we implement a subset of Chombo’s functionality in Titanium. Chombo is a software package applying the Adaptive Mesh Refinement methodology to numerical Partial Differential Equations at the production level. In Chombo, the library approach is used to parallel programming (C++ and Fortran, with MPI), whereas Titanium is a Java dialect designed for highperformance scientific computing. The performance of our implementation is studied and compared with that of Chombo in solving Poisson’s equation based on two grid configurations from a real application. Also provided are the counts of lines of code from both sides.
D.: The numerical simulation of ship waves using cartesian grid methods
 Proc. 23rd ONR Symposium on Naval Hydrodynamics
, 2000
"... Two different cartesiangrid methods are used to simulate the flow around the DDG 5415. The first technique uses a “coupled levelset and volumeoffluid ” (CLS) technique to model the freesurface interface. The noflux boundary condition on the hull is imposed using a finitevolume technique. The ..."
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Cited by 13 (8 self)
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Two different cartesiangrid methods are used to simulate the flow around the DDG 5415. The first technique uses a “coupled levelset and volumeoffluid ” (CLS) technique to model the freesurface interface. The noflux boundary condition on the hull is imposed using a finitevolume technique. The second technique uses a levelset technique (LS) to model the freesurface interface. A bodyforce technique is used to impose the hull boundary condition. The predictions of both numerical techniques are compared to whiskerprobe measurements of the DDG 5415. The levelset technique is also used to investigate the breakup of a twodimensional spray sheet. 1
A parallel secondorder adaptive mesh algorithm for incompressible flow in porous media. Philosophical Transactions of the Royal Society A 367: 4633–4654
, 2009
"... Abstract In this paper we present a secondorder accurate adaptive algorithm for solving multiphase, incompressible flows in porous media. We assume a multiphase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conser ..."
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Cited by 12 (4 self)
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Abstract In this paper we present a secondorder accurate adaptive algorithm for solving multiphase, incompressible flows in porous media. We assume a multiphase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting the total velocity, defined to be the sum of the phase velocities, is divergencefree. The basic integration method is based on a totalvelocity splitting approach in which we solve a secondorder elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single grid algorithm is described briefly, but the emphasis here is on the timestepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behavior of the method.
Reconfigurable Hybrid Interconnection for Static and Dynamic Scientific Applications
 ACM International Conference on Computing Frontiers
, 2007
"... As we enter the era of petascale computing, system architects must plan for machines composed of tens or even hundreds of thousands of processors. Although fully connected networks such as fattree configurations currently dominate HPC interconnect designs, such approaches are inadequate for such ult ..."
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Cited by 12 (5 self)
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As we enter the era of petascale computing, system architects must plan for machines composed of tens or even hundreds of thousands of processors. Although fully connected networks such as fattree configurations currently dominate HPC interconnect designs, such approaches are inadequate for such ultrascale concurriencies due to the superlinear growth of component costs. Traditional lowdegree interconnect topologies, such as 3D tori, have reemerged as a competitive solution due to the linear scaling of system components relative to the node count; however, such networks are poorly suited for the requirements of many scientific applications at extreme concurrencies. To address these limitations, we propose HFAST, a hybrid switch architecture that uses circuit switches to dynamically reconfigure lowerdegree interconnects to suit the topological requirements of a given scientific application. This work presents several new research contributions. We develop an optimization strategy for HFAST mappings and demonstrate that efficiency gains can be attained across a broad range of static numerical computations. Additionally, we conduct an extensive analysis of the communication characteristics of a dynamically adapting mesh calculation and show that the HFAST approach can achieve significant performance advantages, even when compared with traditional fattree configurations. Overall results point to the promising potential of utilizing hybrid reconfigurable networks to interconnect future petascale architectures, for both static and dynamically adapting applications. 1
Adaptive solution techniques for simulating underwater explosions and implosions
 Journal of Computational Physics
"... Adaptive solution techniques are presented for simulating underwater explosions and implosions. The liquid is assumed to be an adiabatic fluid and the solution in the gas is assumed to be uniform in space. The solution in the water is integrated in time using a semiimplicit time discretization of ..."
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Cited by 11 (2 self)
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Adaptive solution techniques are presented for simulating underwater explosions and implosions. The liquid is assumed to be an adiabatic fluid and the solution in the gas is assumed to be uniform in space. The solution in the water is integrated in time using a semiimplicit time discretization of the adiabatic Euler equations. Results are presented either using a nonconservative semiimplicit algorithm or a conservative semiimplicit algorithm. A semiimplicit algorithm allows one to compute with relatively large time steps compared to an explicit method. The interface solver is based on the coupled level set and volumeoffluid method (CLSVOF) [19, 20]. Several underwater explosion and implosion test cases are presented to show the performances of our proposed techniques. Key Words: AMR; Semiimplicit; CLSVOF; Multiphase; Underwater explosions and implosions
Adaptive low Mach number simulations of nuclear flame microphysics
 J. Comput. Phys
"... We introduce a numerical model for the simulation of nuclear flames in Type Ia supernovae. This model is based on a low Mach number formulation that analytically removes acoustic wave propagation while retaining the compressibility effects resulting from nuclear burning. The formulation presented he ..."
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Cited by 10 (8 self)
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We introduce a numerical model for the simulation of nuclear flames in Type Ia supernovae. This model is based on a low Mach number formulation that analytically removes acoustic wave propagation while retaining the compressibility effects resulting from nuclear burning. The formulation presented here generalizes low Mach number models used in combustion that are based on an ideal gas approximation to the arbitrary equations of state such as those describing the degenerate matter found in stellar material. The low Mach number formulation permits time steps that are controlled by the advective time scales resulting in a substantial improvement in computational efficiency compared to a compressible formulation. We briefly discuss the basic discretization methodology for the low Mach number equations and their implementation in an adaptive projection framework. We present validation computations in which the computational results from the low Mach number model are compared to a compressible code and present an application of the methodology to the LandauDarrieus instability of a carbon flame. 1