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Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems [chapter]

Leonid Oliker, Xiaoye Li, Gerd Heber, Rupak Biswas
2000 Lecture Notes in Computer Science  
Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency.  ...  The bandwidth, or profile, of the matrix, has a significant impact on the efficiency of linear systems and eigensolvers.  ... 
doi:10.1007/3-540-45591-4_66 fatcat:uwd33zzsmfdfhgexzcmbxheoty

Productive Parallel Linear Algebra Programming with Unstructured Topology Adaption

Peter Gottschling, Torsten Hoefler
2012 2012 12th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (ccgrid 2012)  
The discretization of complex geometries in unstructured meshes leads to sparse matrices with irregular patterns.  ...  Contributions: In this work, we propose an abstract library interface for parallel sparse matrix computations and effective mapping schemes.  ...  Acknowledgments We thank Sebastian Aland for the CFD example and Thomas Witkowski and Andreas Naumann for the benchmarks with PMTL4 and PETSc.  ... 
doi:10.1109/ccgrid.2012.51 dblp:conf/ccgrid/GottschlingH12 fatcat:q7xojjtnd5elhkhh37f2rghpge

Accelerating FVM-Based Parallel Fluid Simulations with Better Grid Renumbering Methods

Huajian Zhang, Xiao-Wei Guo, Chao Li, Qiao Liu, Hanwen Xu, Jie Liu
2022 Applied Sciences  
Grid renumbering techniques have been shown to be effective in improving the efficiency of computational fluid dynamics (CFD) numerical simulations based on the finite volume method (FVM).  ...  Thus, our new metric can more accurately evaluate the renumbering method for numerical fluid simulations, which is of great value in selecting a better mesh renumbering method in engineering applications  ...  The structure of sparse matrices determines the order of memory access for parallel computation.  ... 
doi:10.3390/app12157603 fatcat:rjbsrkorl5fzxe6myzd2jpzhby

Data-parallel support for numerical irregular problems

E.L. Zapata, O. Plata, R. Asenjo, G.P. Trabado
1999 Parallel Computing  
Second, irregular data structures, derived from computations involving sparse matrices, grids, trees, graphs, etc.  ...  This paper discusses the eective parallelization of numerical irregular codes, focusing on the de®nition and use of data-parallel extensions to express the parallelism that they exhibit.  ...  Ujald on, at the Department of Computer Architecture, University of M alaga, Spain, and R. Doallo and J.  ... 
doi:10.1016/s0167-8191(99)00090-3 fatcat:ymeizehfevcfvkrivsnce2hfs4

A flexible sparse matrix data format and parallel algorithms for the assembly of sparse matrices in general finite element applications using atomic synchronisation primitives [article]

Adam Sky, César Polindara, Ingo Muench, Carolin Birk
2021 arXiv   pre-print
In this paper we focus on the assembly process of the global stiffness matrix and explore different algorithms and their efficiency on shared memory systems using C++.  ...  The composition process combines the computation of element stiffness matrices and their assembly into the global stiffness matrix, which is commonly sparse.  ...  scheme on our system.  ... 
arXiv:2012.00585v2 fatcat:5ygxdlwitfcjtd5rzwydeyp6ge

High-performance 3D Unstructured Mesh Deformation Using Rank Structured Matrix Computations

Rabab Alomairy, Wael Bader, Hatem Ltaief, Youssef Mesri, David Keyes
2022 ACM Transactions on Parallel Computing  
We report and compare performance results on various parallel systems against existing state-of-the-art matrix solvers.  ...  In this article, we accelerate the computations of 3D unstructured mesh deformation based on RBF interpolations by exploiting the rank structured property of the matrix operator.  ...  ACKNOWLEDGMENTS The authors would like to thank Cray Inc. and Intel Corp. in the context of the Cray Center of Excellence and Intel Parallel Computing Center awarded to the Extreme Computing Research Center  ... 
doi:10.1145/3512756 fatcat:vxfsbtyl4ncgvbi7tfqnv444wu

Computational Strategies Improvement For The Unstructured Inductive PEEC Method

Kouceila Alkama, Gerard Meunier, Olivier Chadebec, Jean-Michel Guichon, Bertrand Bannwarth, Enrico Vialardi, Remy Perrin-Bit
2020 2020 IEEE 19th Biennial Conference on Electromagnetic Field Computation (CEFC)  
Equivalent circuit representation for an unstructured mesh and one self inductance for each face of the mesh element Fig. 2 . 2 Fig. 2.  ...  J • n = 0 (8) Matrix system (6) can be seen as a classical circuit matrix system ZI = U, where each unstructured mesh element is associated to its equivalent circuit representation, as shown in Fig. 1  ... 
doi:10.1109/cefc46938.2020.9451292 fatcat:xxgnvqxghfadlfmkqbvooy2lpy

Two-dimensional frequency-domain visco-elastic full waveform inversion: Parallel algorithms, optimization and performance

R. Brossier
2011 Computers & Geosciences  
The resolution of the elastodynamic equations, as the forward problem of the inversion, is performed in the frequency domain on unstructured triangular meshes, using a low-order finite element discontinuous  ...  Two levels of parallelism are implemented in the algorithm, based on message passing interfaces and multi-threading, for optimal use of computational time and the core-memory resources available on modern  ...  Virieux (LGIT, Université Joseph Fourier) for fruitful and stimulating discussions on full waveform modelling and inversion, on parallel implementation, and for manuscript review.  ... 
doi:10.1016/j.cageo.2010.09.013 fatcat:l6lv25z7tjbq7hlyam33rbmfcq

Sustained Petascale Performance of Seismic Simulations with SeisSol on SuperMUC [chapter]

Alexander Breuer, Alexander Heinecke, Sebastian Rettenberger, Michael Bader, Alice-Agnes Gabriel, Christian Pelties
2014 Lecture Notes in Computer Science  
In this paper, we present optimizations of SeisSol -a seismic wave propagation solver based on the Arbitrary high-order accurate DERivative Discontinuous Galerkin (ADER-DG) method on fully adaptive, unstructured  ...  Improvements cover the entire simulation chain: from an enhanced ADER time integration via highly scalable routines for mesh input up to hardware-aware optimization of the innermost sparse-/densematrix  ...  Acknowledgements We would like to thank Mikhail Smelyanskiy at Intel's Parallel Computing Lab for assisting us in the development of hardware-aware kernels, as well as all colleagues of the Leibniz Supercomputing  ... 
doi:10.1007/978-3-319-07518-1_1 fatcat:h525lzq53zd7nnoqxz7g2nsxim

Global finite element matrix construction based on a CPU-GPU implementation [article]

Francisco Javier Ramírez-Gil, Marcos de Sales Guerra Tsuzuki and Wilfredo Montealegre-Rubio
2015 arXiv   pre-print
This methodology allows generating the global sparse matrix from any unstructured finite element mesh size on GPUs with little memory capacity, only limited by the CPU memory.  ...  However, the finite element matrix construction, which is also time-consuming for unstructured meshes, has been less investigated.  ...  Acknowledgments The first author thanks to Universidad Nacional de Colombia for the financial support to this work with the Estudiantes sobresalientes de posgrado scholarship.  ... 
arXiv:1501.04784v1 fatcat:35c5al4xwjfybmbxv6jziargmi

Parallel implicit unstructured grid Euler solvers

1994 AIAA Journal  
Therefore, for general sparse matrices, the ILU(0) preconditioner is ill-suited for implementation on a distributed-memory parallel computer.  ...  way to compute the matrix vector product on a parallel computer, where locality is of utmost importance.  ... 
doi:10.2514/3.12242 fatcat:hj66mgvxa5awxh4a5dn5vy4u2u

Sparse matrix factorization in the implicit finite element method on petascale architecture

Seid Koric, Anshul Gupta
2016 Computer Methods in Applied Mechanics and Engineering  
The performance of the massively parallel direct multifrontal solver Watson Sparse Matrix Package (WSMP) for solving large sparse systems of linear equations arising in implicit finite element method on  ...  unstructured (free) meshes in solid mechanics was evaluated on one of the most powerful supercomputers currently available to the open science community-the sustained petascale high performance computing  ...  Acknowledgments The authors would like to thank the Private Sector Program and the Blue Waters sustained-petascale computing project at the National Center for Supercomputing Applications (NCSA).  ... 
doi:10.1016/j.cma.2016.01.011 fatcat:7fvypjoinrcmnigv3hldkqfcxe

High Order Finite Element Schemes And Domain Decomposition Solvers For Large-Scale Simulations In Electromagnetics

Stéphane Lanteri
2017 Zenodo  
finite element discretization scheme formulated on an unstructured tetrahedral grid, and scalable sparse linear solvers.  ...  The enabling numerical tool is a domain decomposition solution strategy for the sparse system of linear equations resulting from the spatial discretization of the underlying PDEs (Partial Differential  ...  This HDG method designed on an unstructured possibly non-conforming tetrahedral mesh, leads to the formulation of an unstructured complex coefficients sparse linear system of equations for the DoF of the  ... 
doi:10.5281/zenodo.830354 fatcat:zdaf5nmg3bbntevadby5i737ym

Efficient CUDA Polynomial Preconditioned Conjugate Gradient Solver for Finite Element Computation of Elasticity Problems

Jianfei Zhang, Lei Zhang
2013 Mathematical Problems in Engineering  
This paper discusses the efficient way to implement polynomial preconditioned conjugate gradient solver for the finite element computation of elasticity on NVIDIA GPUs using compute unified device architecture  ...  example meshes.  ...  Because the stiffness matrix arising from finite element discretization of elasticity on unstructured mesh is a general sparse SPD matrix, the CSR format [13] is commonly used to store these matrices  ... 
doi:10.1155/2013/398438 fatcat:xzkngvgn6fh2xl7jm4uh2uayda

10. A Survey of Parallelization Techniques for Multigrid Solvers [chapter]

Edmond Chow, Robert D. Falgout, Jonathan J. Hu, Raymond S. Tuminaro, Ulrike Meier Yang
2006 Parallel Processing for Scientific Computing  
This paper surveys the techniques that are necessary for constructing computationally efficient parallel multigrid solvers. Both geometric and algebraic methods are considered.  ...  We then cover the parallelism issues that must be addressed: parallel smoothing and coarsening, operator complexity, and parallelization of the coarsest grid solve.  ...  To compute a sparse approximate inverse M for the matrix A, this form minimizes the Frobenius norm of the residual matrix (I − M A).  ... 
doi:10.1137/1.9780898718133.ch10 fatcat:q72n4g5jybbtzeawtcyvjjxecy
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