ExaStencils – Advanced Multigrid Solver Generation

Lengauer C, Apel S, Bolten M, Chiba S, Rüde U, Teich J, Größlinger A, Hannig F, Köstler H, Claus L, Grebhahn A, Groth S, Kronawitter S, Kuckuk S, Rittich H, Schmitt C, Schmitt J (2020)

Publication Language: English

Publication Type: Book chapter / Article in edited volumes

Publication year: 2020

Publisher: Springer

Edited Volumes: Software for Exascale Computing – SPPEXA 2016-2019

Series: Lecture Notes in Computer Science and Engineering

Book Volume: 136

Pages Range: 405-452

ISBN: 978-3-030-47955-8

URI: https://www12.cs.fau.de/downloads/hannig/publications/ExaStencils_Advanced_Multigrid_Solver_Generation.pdf

DOI: 10.1007/978-3-030-47956-5_14


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. Project ExaStencils pursued a domain-specific approach with a language, called ExaSlang, that is stratified into four layers of abstraction, the most abstract being the formulation in continuous mathematics and the most concrete a full, automatically generated implementation. At every layer, the corresponding language expresses not only computational directives but also domain knowledge of the problem and platform to be leveraged for optimization. We describe the approach, the software technology behind it and several case studies that demonstrate its feasibility and versatility: high-performance stencil codes can be engineered, ported and optimized more easily and effectively.

Authors with CRIS profile

Related research project(s)

Involved external institutions

How to cite


Lengauer, C., Apel, S., Bolten, M., Chiba, S., Rüde, U., Teich, J.,... Schmitt, J. (2020). ExaStencils – Advanced Multigrid Solver Generation. In Hans-Joachim Bungartz, Severin Reiz, Philipp Neumann, Benjamin Uekermann, Wolfgang Nagel (Eds.), Software for Exascale Computing – SPPEXA 2016-2019. (pp. 405-452). Springer.


Lengauer, Christian, et al. "ExaStencils – Advanced Multigrid Solver Generation." Software for Exascale Computing – SPPEXA 2016-2019. Ed. Hans-Joachim Bungartz, Severin Reiz, Philipp Neumann, Benjamin Uekermann, Wolfgang Nagel, Springer, 2020. 405-452.

BibTeX: Download