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A space-time parallel solver for the three-dimensional heat equation [article]

Robert Speck, Daniel Ruprecht, Matthew Emmett, Matthias Bolten, Rolf Krause
2013 arXiv   pre-print
the three-dimensional heat equation with a uniquely high degree of efficient concurrency.  ...  The paper presents a combination of the time-parallel "parallel full approximation scheme in space and time" (PFASST) with a parallel multigrid method (PMG) in space, resulting in a mesh-based solver for  ...  Winkel from JSC for compiling a modern version of GCC on the IBM Blue Gene/Q.  ... 
arXiv:1307.7867v1 fatcat:lfisi42fpfdnxipikqmvik6iju

Parallelizing Alternating Direction Implicit Solver on GPUs

Zhangping Wei, Byunghyun Jang, Yaoxin Zhang, Yafei Jia
2013 Procedia Computer Science  
These memory optimizations further make already parallelized ADI solver twice faster, achieving overall more than 100 times speedup over a highly optimized CPU version.  ...  We also present the analysis of numerical accuracy of the proposed parallel ADI solver.  ...  and The University of Mississippi, and the National Science Foundation under award number EPS-0903787.  ... 
doi:10.1016/j.procs.2013.05.202 fatcat:6r737lx3rzagdpmdw663qdbr6u

A parallel solver for a preconditioned space-time boundary element method for the heat equation [article]

Stefan Dohr, Michal Merta, Günther Of, Olaf Steinbach, Jan Zapletal
2018 arXiv   pre-print
We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation.  ...  The global space-time nature of the system matrices leads to improved parallel scalability in distributed memory systems in contrast to time-stepping methods where the parallelization is usually limited  ...  Conclusion In this note we have described a parallel space-time boundary element solver for the two-dimensional heat equation. The solver is parallelized using MPI in the distributed memory.  ... 
arXiv:1811.05224v1 fatcat:rbez4lgkofdvpdcw2nmq6bjjdq

Recent Progress on Supercomputer Modelling of High-Speed Rarefied Gas Flows Using Kinetic Equations

2018 Supercomputing Frontiers and Innovations  
Numerical solution of the Boltzmann equation for stationary high-speed flows around complex three-dimensional bodies is an extremely difficult computational problem.  ...  Our recent comparison of the DSMC and S-model solutions for monatomic gases with a soft interaction potential shows good agreement of surface coefficients of the pressure, heat transfer and friction, which  ...  Acknowledgments The work was supported by the Russian Foundation for Basic Research, projects 18-08-00501, 18-07-01500. The research is carried out using the equipment of the shared research A.A.  ... 
doi:10.14529/jsfi180322 fatcat:3cxrz74olzbi3ih5rnoyjvalhe

Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling

Huai Zhang, Lili Ju
2011 Numerical Mathematics: Theory, Methods and Applications  
The governing equations for the thermo-mechanical ice-sheet modeling were formulated as a three-dimensional nonlinear full-Stokes system for momentum, an advective-diffusive energy equation for temperature  ...  evolution, and a mass-conservation equation for ice thickness change.  ...  The CPU running times of our parallel, three-dimensional full-Stokes solver for the case L = 160km are given in Table 2 .  ... 
doi:10.4208/nmtma.2011.m1031 fatcat:gojbl3eaqjbf7iigj5lhzaglcy

A Parallel Low-Rank Solver for the Six-Dimensional Vlasov-Maxwell Equations [article]

Florian Allmann-Rahn, Rainer Grauer, Katharina Kormann
2022 arXiv   pre-print
In this paper we present a new parallel low-rank solver for the full six-dimensional electromagnetic Vlasov-Maxwell equations with a compression of the particle distribution function in velocity space.  ...  The so far available low-rank solvers are restricted to either electrostatic systems or low dimensionality and can therefore not be applied to most space, astrophysical and fusion plasmas.  ...  ( for funding this project by providing computing time through the John von Neumann Institute for Computing (NIC) on the GCS Supercomputer JUWELS at Jülich Supercomputing Centre (JSC  ... 
arXiv:2201.03471v1 fatcat:s2bzhcjslrfq5nb3fc523uxyvq

A Direct Solver for the Heat Equation with Domain Decomposition in Space and Time [chapter]

Marc Garbey
2008 Lecture Notes in Computational Science and Engineering  
In this paper we generalize the Aitken-like acceleration method of the additive Schwarz algorithm for elliptic problems to the additive Schwarz waveform relaxation for the heat equation.  ...  The domain decomposition is in space and time. The standard Schwarz waveform relaxation algorithm has a linear rate of convergence and low numerical efficiency.  ...  We have verified also that the accuracy of our AASWR solver is satisfactory for three dimensional problem with singular source terms. Remark 2.  ... 
doi:10.1007/978-3-540-75199-1_63 fatcat:wqa6ksh5rzgjzew6eis2k2djzy

Study on Parallel Computation of CFD Problems

2001 Seisan Kenkyu  
Filtered N-S equations for an uncompressible three dimensional and unsteady flow are expressed in tensor form. ≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥ (1) ≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥ (2) Furthermore in the filtering  ...  A preconditioner in the solver is desired in order to reduce time of computation of this equation. Incomplete LU decompositions [3] can be a feasible option.  ... 
doi:10.11188/seisankenkyu.53.57 fatcat:n4q6eb6hhzdsbg7eq652o6ls6e

Element-by-Element Parallel Computation of Incompressible Navier--Stokes Equations in Three Dimensions

Tony W. H. Sheu, Morten M. T. Wang, S. F. Tsai
1999 SIAM Journal on Scientific Computing  
of our hardware to solve for three-dimensional problems.  ...  Development of a stable finite element model for solving steady incompressible viscous fluid flows in three dimensions is the main theme of the present study.  ...  Parallel calculation of coupled algebraic equations will be proposed as a likely approach to reducing the elapsed time requirements for three-dimensional simulations.  ... 
doi:10.1137/s1064827598335416 fatcat:ueolrouh2nhx3pevufi7jrzi4e

Parallel three-dimensional simulation of the injection molding process

B. J. Araújo, J. C. F. Teixeira, A. M. Cunha, C. P. T. Groth
2009 International Journal for Numerical Methods in Fluids  
This paper describes the development of a parallel three-dimensional unstructured non-isothermal flow solver for the simulation of the injection molding process.  ...  This aspect avoids the complex reconstruction of the interface. A collocated finite volume method is employed, which can switch between first-and second-order accuracy in both space and time.  ...  ACKNOWLEDGEMENTS The author acknowledges the financial support from the Fundação para a Ciência e a Tecnologia (FCT) and the computer resources made available by the University of Toronto Institute for  ... 
doi:10.1002/fld.1852 fatcat:u5zvlfjulbcqvkshpdvltol5zi

Solving Fluid Flow Problems on Moving and Adaptive Overlapping Grids [chapter]

William D. Henshaw
2006 Parallel Computational Fluid Dynamics 2005  
Topics to be addressed include the reactive Euler equations, the incompressible Navier-Stokes equations and elliptic equations solved with a multigrid algorithm.  ...  Overlapping grids provide an effective approach for developing efficient and accurate approximations for complex, possibly moving geometry.  ...  The annular grids are moved at each time step. A Poisson equation for the pressure is solved using the overlapping grid multigrid solver Ogmg.  ... 
doi:10.1016/b978-044452206-1/50004-5 fatcat:6qdz32wx2vcmpf4zgb7xwi6oae

A Conjugate-heat-transfer Immersed-boundary Method for Turbine Cooling

D. De Marinis, M.D. de Tullio, M. Napolitano, G. Pascazio
2015 Energy Procedia  
The aim of this work is to extend the two-dimensional IB solver to three-dimensions, using a new IB least-squares reconstruction, an advanced data structure and a parallel solver, so as to obtain a computational  ...  Due to the very high geometrical complexity of the cooling channels within the blades, generating a body fitted mesh for the three domains-air, gas and blade-is extremely difficult and time consuming.  ...  equipped with: a new IB least-squares reconstruction; an advanced data structure; and a parallel solver.  ... 
doi:10.1016/j.egypro.2015.12.025 fatcat:4hzg2vh7czgqrfaqun4hd7yfue

Toward five-dimensional core-collapse supernova simulations

C Y Cardall, A O Razoumov, E Endeve, E J Lentz, A Mezzacappa
2005 Journal of Physics, Conference Series  
The computational difficulty of six-dimensional neutrino radiation hydrodynamics has spawned a variety of approximations, provoking a long history of uncertainty in the core-collapse supernova explosion  ...  mesh refinement code for self-gravitating, six-dimensional neutrino radiation magnetohydrodynamics.  ...  Bruenn's contribution of subroutines for the computation of neutrino interaction kernels. We thank R. D. Budiardja and M. W. Guidry for discussions on the Poisson solver, and R. D.  ... 
doi:10.1088/1742-6596/16/1/053 fatcat:5m373bwwsragjayivxa6vya7ga

The Two-Dimensional Swept Rule Applied on Heterogeneous Architectures [article]

Anthony S. Walker, Kyle E. Niemeyer
2021 arXiv   pre-print
Our solver showed a speedup range of 0.22-2.71 for the heat diffusion equation and 0.52-1.46 for the compressible Euler equations.  ...  The swept rule is a technique designed to minimize these costs by obtaining a solution to unsteady equations at as many possible spatial locations and times prior to communicating.  ...  Acknowledgments: We gratefully acknowledge the support of NVIDIA Corporation, who donated a Tesla K40c GPU used in developing this research.  ... 
arXiv:2105.10332v1 fatcat:thr7fgyvavaujoyg3fbp4q6b2m

Simulation of thermal flows by lattice Boltzmann method on the CUDA computational platform

D. B. Zhakebayev, National Engineering Academy, Almaty, Kazakhstan, K. K. Karzhaubayev, E. S. Moisseyeva, N. V. Tsoy, National Engineering Academy, Almaty, Kazakhstan, National Engineering Academy, Almaty, Kazakhstan, al-Farabi Kazakh national university
2018 International Journal of Mathematics and Physics  
The main advantage of the solvers based on GPU is their ability to perform significantly more floating point operations per unit time (FLOPS) than a Central Processing Unit (CPU) and a good scalability  ...  of explicit parallel algorithms.  ...  Acknowledgements This work was supported by the MES Republic of Kazakhstan (grant number AP05132121).  ... 
doi:10.26577/ijmph.2018.v9i2.253 fatcat:o5hjg3a62bfilo7yrwz6zxwyze
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