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Algebraic description and automatic generation of multigrid methods in SPIRAL

Matthias Bolten, Franz Franchetti, Paul H. J. Kelly, Christian Lengauer, Marcus Mohr
2017 Concurrency and Computation  
SPIRAL is an autotuning, program generation and code synthesis system that offers a fully automatic generation of highly optimized target codes, customized for the specific execution platform at hand.  ...  We open SPIRAL up to a new, practically relevant and challenging domain: multigrid solvers. SPIRAL is driven by algebraic transformation rules.  ...  SPPEXA also partially supported the attendance of Franchetti and Kelly at this seminar. Mohr is an unfunded member of SPPEXA project TerraNeo [34] .  ... 
doi:10.1002/cpe.4105 fatcat:yf7wzyevvvfflcln5tpoykwhtq

Advanced Stencil-Code Engineering (Dagstuhl Seminar 15161)

Christian Lengauer, Matthias Bolten, Robert D. Falgout, Olaf Schenk, Marc Herbstritt
2015 Dagstuhl Reports  
It brought together experts from mathematics, computer science and applications to explore the challenges of very high performance and massive parallelism in solving partial differential equations.  ...  This report documents the program and the outcomes of Dagstuhl Seminar 15161 "Advanced Stencil-Code Engineering".  ...  Several issues for DSLs in this context are discussed including the automatic generation of a geometric multigrid for the coupled equations of the linearized system of equations.  ... 
doi:10.4230/dagrep.5.4.56 dblp:journals/dagstuhl-reports/LengauerBFS15 fatcat:suk5zayvlnb63ozlamrw2vk2w4

ExaStencils: Advanced Multigrid Solver Generation [chapter]

Christian Lengauer, Sven Apel, Matthias Bolten, Shigeru Chiba, Ulrich Rüde, Jürgen Teich, Armin Größlinger, Frank Hannig, Harald Köstler, Lisa Claus, Alexander Grebhahn, Stefan Groth (+5 others)
2020 Lecture Notes in Computational Science and Engineering  
and the most concrete a full, automatically generated implementation.  ...  Present-day stencil codes are implemented in general-purpose programming languages, such as Fortran, C, or Java, Python or derivates thereof, and harnesses for parallelism, such as OpenMP, OpenCL or MPI  ...  Acknowledgments Project ExaStencils received generous funding from the Deutsche Forschungsgemeinschaft (DFG) in its priority programme SPP 1648 "Software for Exascale Computing" under grant numbers AP  ... 
doi:10.1007/978-3-030-47956-5_14 fatcat:xhbxnt45ynhilgh6vv2ui2n76i

A Scala Prototype to Generate Multigrid Solver Implementations for Different Problems and Target Multi-Core Platforms [article]

Harald Koestler, Christian Schmitt, Sebastian Kuckuk, Frank Hannig, Juergen Teich, Ulrich Ruede
2014 arXiv   pre-print
Two different test problems showcase our proposed automatic generation of multigrid solvers for both CPU and GPU target platforms.  ...  In this article we provide a prototype implementation in Scala for a framework that allows abstract descriptions of PDEs, their discretization, and their numerical solution via multigrid algorithms.  ...  Acknowledgments EXASTENCILSis funded by the German Research Foundation (DFG) as part of the Priority Programme 1648 (Software for Exascale Computing).  ... 
arXiv:1406.5369v1 fatcat:m644lfexcnhrxmpgxi4ab2pouy

ECP Math Libraries: Capabilities and Application Engagement [article]

Sherry Li, Lois Curfman McInnes, ECP Math Libraries Community
2021 figshare.com  
, and (3) how to pursue application-specific customization, so that together we can more effectively work toward next-generation science goals.  ...  In the second half, we will conduct breakout sessions for in-depth discussion of each topical area.  ...  Automated invocation of Spiral to generate code and header file. -CPU, cuda code generation. Examples include forward / inverse FFTs (c-to-c and r-to-c); periodic and free-space convolutions.  ... 
doi:10.6084/m9.figshare.14346254.v1 fatcat:5j6utwsevrehhif2gytsraob7m

Code generation approaches for parallel geometric multigrid solvers

Harald Köstler, Marco Heisig, Nils Kohl, Sebastian Kuckuk, Martin Bauer, Ulrich Rüde
2020 Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica  
As an example the numerical solution of an elliptic partial differential equation via generated geometric multigrid solvers is considered.  ...  In contrast to manual implementations in a general-purpose computing language, they allow to integrate automatic code transforms to produce efficient code for different models and platforms.  ...  This research has been funded partly by the Federal Ministry of Education and Research of Germany (BMBF) through the HPC2SE project and partly by the Deutsche Forschungsgemeinschaft (DFG) in its priority  ... 
doi:10.2478/auom-2020-0038 fatcat:rr63bsabc5cbbbcw7eljtr3gzy

Object oriented design philosophy for scientific computing

Philippe R.B. Devloo, Gustavo C. Longhin
2002 Mathematical Modelling and Numerical Analysis  
, multigrid methods applied to adaptively refined finite element solution spaces and parallel computing.  ...  The following areas are current topics of research and documented within the paper: hp-adaptive finite elements in one-, two-and three dimensions with the development of automatic refinement strategies  ...  The financial support of FAPESP, CAPES, CNPq and of the companies Petrobras and Commodity is also gratefully acknowledged.  ... 
doi:10.1051/m2an:2002041 fatcat:46f2zq35xfaphi745kg3ltnbli

Book Review: Lectures on finite precision computations

Hans J. Stetter, Charles Van Loan, Michael Holst, Frank Stenger, Chi-Wang Shu, R. Mattheij, Stephen J. Wright, Thomas F. Coleman, Lars B. Wahlbin
1997 Mathematics of Computation  
The survey then moves to iterative methods, such as classical relaxation and multigrid methods.  ...  It starts with a careful examination of Hilbert and related transforms, and then leads to methods of approximation of solutions of CSIE, including Fourier series and multigrid methods.  ... 
doi:10.1090/s0025-5718-97-00910-1 fatcat:kiiohmhwnrh5rkjl672eqoqnre

A second-order virtual node algorithm for nearly incompressible linear elasticity in irregular domains

Yongning Zhu, Yuting Wang, Jeffrey Hellrung, Alejandro Cantarero, Eftychios Sifakis, Joseph M. Teran
2012 Journal of Computational Physics  
We target high-resolution problems and present a class of geometric multigrid methods for solving the discrete equations for displacements and pressures that achieves nearly optimal convergence rates independent  ...  We present a cut cell method in R 2 for enforcing Dirichlet and Neumann boundary conditions with nearly incompressible linear elastic materials in irregular domains.  ...  Without loss of generality, we assume the variables to be reordered such that P = I. We will make use of this property in the smoother for our geometric multigrid method.  ... 
doi:10.1016/j.jcp.2012.05.015 fatcat:mjo4cf2fbvdqlbqhw22nggifae

PetaBricks

Jason Ansel, Cy Chan, Yee Lok Wong, Marek Olszewski, Qin Zhao, Alan Edelman, Saman Amarasinghe
2009 SIGPLAN notices  
When choosing between various direct and iterative methods, the PetaBricks compiler is able to tune a program in such a way that delivers near-optimal efficiency for any desired level of accuracy.  ...  Choices also include different automatic parallelization techniques, data distributions, algorithmic parameters, transformations, and blocking.  ...  Acknowledgments This work is partially supported by NSF Award CCF-0832997 and an award from the Gigascale Systems Research Center.  ... 
doi:10.1145/1543135.1542481 fatcat:vsheaa64enefxer2agyrgtor4q

PetaBricks

Jason Ansel, Cy Chan, Yee Lok Wong, Marek Olszewski, Qin Zhao, Alan Edelman, Saman Amarasinghe
2009 Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation - PLDI '09  
When choosing between various direct and iterative methods, the PetaBricks compiler is able to tune a program in such a way that delivers near-optimal efficiency for any desired level of accuracy.  ...  Choices also include different automatic parallelization techniques, data distributions, algorithmic parameters, transformations, and blocking.  ...  Acknowledgments This work is partially supported by NSF Award CCF-0832997 and an award from the Gigascale Systems Research Center.  ... 
doi:10.1145/1542476.1542481 dblp:conf/pldi/AnselCWOZEA09 fatcat:ngwno3ifavddno4qjbsj2jjlli

Matrix Renumbering ILU: An Effective Algebraic Multilevel ILU Preconditioner for Sparse Matrices

E. F. F. Botta, F. W. Wubs
1999 SIAM Journal on Matrix Analysis and Applications  
The first roots of the approach lie in the 1960s [13, 42, 43] and since then the method has become applicable to a wide class of problems.  ...  The results illustrate the efficiency of the method and show in several cases near grid independent convergence. Introduction.  ...  Henk van der Vorst for providing the code for the discretization of the aquifer problem.  ... 
doi:10.1137/s0895479897319301 fatcat:4a3plxwsirap3ioey6asnlmlkq

The DUNE Framework: Basic Concepts and Recent Developments [article]

Peter Bastian, Markus Blatt, Andreas Dedner, Nils-Arne Dreier, Christian Engwer, René Fritze, Carsten Gräser, Christoph Grüninger, Dominic Kempf, Robert Klöfkorn, Mario Ohlberger, Oliver Sander
2020 arXiv   pre-print
and node level performance, non-smooth multigrid methods, and multiscale methods.  ...  of the first Dune version in 2007 and the main papers describing that state [1, 2].  ...  Acknowledgements We thank the Dune users and contributors for their continuous support, as only a vivid community unfolds the power of open source.  ... 
arXiv:1909.13672v3 fatcat:hc5a7al4xvhahdp7fs7f55cwg4

The Dune framework: Basic concepts and recent developments

Peter Bastian, Markus Blatt, Andreas Dedner, Nils-Arne Dreier, Christian Engwer, René Fritze, Carsten Gräser, Christoph Grüninger, Dominic Kempf, Robert Klöfkorn, Mario Ohlberger, Oliver Sander
2020 Computers and Mathematics with Applications  
and node level performance, non-smooth multigrid methods, and multiscale methods.  ...  This discussion is accompanied with a description of various advanced features, such as coupling of domains and cut cells, grid modifications such as adaptation and moving domains, high order discretizations  ...  Such so-called hybrid preconditioners are commonly used in parallel (algebraic) multigrid methods, see [42] . A list of preconditioners provided by Dune-ISTL is in Table 3 .  ... 
doi:10.1016/j.camwa.2020.06.007 fatcat:37m6di54rbgo3m2y5y5m2hd234

3D PIC model of the helical current filament

Petr Kulhanek
2001 AIP Conference Proceedings  
In multigrid methods the number of the grid points in arbitrary dimension must have shape . 1 2 * 1 + = − n k N The method works most efficiently if k is small prime (2 or 3) and n is much greater than  ...  This method was named Fast LIC [38] . In the implemented LIC method the algorithm of generating the RGB colors was modified. The details are described in [56] .  ...  It is observed in many laboratory experiments, in space plasma as well as in numerical simulations. Even spiral arms of some galaxies have structures typical for the diocotron instability.  ... 
doi:10.1063/1.1386854 fatcat:bepu3sccafdajot2z7lgpregqu
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