scholarly journals Reciprocal-Log Approximation and Planar PDE Solvers

2021 ◽  
Vol 59 (6) ◽  
pp. 2801-2822
Author(s):  
Yuji Nakatsukasa ◽  
Lloyd N. Trefethen
Keyword(s):  
Pde Solvers

OpenMP versus MPI for PDE solvers based on regular sparse numerical operators

2006 ◽  
Vol 22 (1-2) ◽  
pp. 194-203 ◽  
Author(s):  
Markus Nordén ◽  
Sverker Holmgren ◽  
Michael Thuné
Keyword(s):  
Pde Solvers

scholarly journals Exa-Dune—Flexible PDE Solvers, Numerical Methods and Applications

2020 ◽  
pp. 225-269
Author(s):  
Peter Bastian ◽  
Mirco Altenbernd ◽  
Nils-Arne Dreier ◽  
Christian Engwer ◽  
Jorrit Fahlke ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Pde Solvers

Performance Modeling of PDE Solvers

2003 ◽  
pp. 361-399 ◽  
Author(s):  
X. Cai ◽  
A. M. Bruaset ◽  
H. P. Langtangen ◽  
G. T. Lines ◽  
K. Samuelsson ◽  
...  
Keyword(s):  
Performance Modeling ◽  
Pde Solvers

scholarly journals Compression Challenges in Large Scale Partial Differential Equation Solvers

Algorithms ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 197 ◽  
Author(s):  
Sebastian Götschel ◽  
Martin Weiser
Keyword(s):  
Data Compression ◽  
Large Scale ◽  
Memory Hierarchy ◽  
Main Memory ◽  
Computational Science ◽  
Limiting Factor ◽  
Mass Storage ◽  
Partial Differential ◽  
Computing Power ◽  
Pde Solvers

Solvers for partial differential equations (PDEs) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that need to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth is the limiting factor due to the relatively small arithmetic intensity, and increasingly due to the growing disparity between computing power and bandwidth. Consequently, data compression techniques have been investigated and tailored towards the specific requirements of PDE solvers over the recent decades. This paper surveys data compression challenges and discusses examples of corresponding solution approaches for PDE problems, covering all levels of the memory hierarchy from mass storage up to the main memory. We illustrate concepts for particular methods, with examples, and give references to alternatives.

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