Fault Resilient Domain Decomposition Preconditioner for PDEs

Technical Report · Mon Jun 01 00:00:00 EDT 2015

DOI:https://doi.org/10.2172/1494624· OSTI ID:1494624

Sargsyan, Khachik ^[1]; Rizzi, Francesco ^[1]; Mycek, Paul ^[2]; Safta, Cosmin ^[1]; Morris, Karla Vanessa ^[1]; Najm, Habib N. ^[1]; Maitre, Olivier Le ^[3]; Knio, Omar ^[2]; Debusschere, Bert ^[1]

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1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
2. Duke Univ., Durham, NC (United States)
3. Laboratoire d'Informatique pour la Mecanique et les Sciences de l'Ingénieur (LIMSI), Orsay (France)

The move towards extreme-scale computing platforms challenges scientific simulations in many ways. Given the recent tendencies in computer architecture development, one needs to reformulate legacy codes in order to cope with large amounts of communication, system faults and requirements of low-memory usage per core. In this work, we develop a novel framework for solving partial differential equations (PDEs) via domain decomposition that reformulates the solution as a state-of-knowledge with a probabilistic interpretation. Such reformulation allows resiliency with respect to potential faults without having to apply fault detection, avoids unnecessary communication and is generally well-positioned for rigorous uncertainty quantification studies that target improvements of predictive fidelity of scientific models. We demonstrate our algorithm for one-dimensional PDE examples where artificial faults have been implemented as bit-flips in the binary representation of subdomain solutions.

• Research Organization: Sandia National Lab. (SNL-CA), Livermore, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 1494624
• Report Number(s): SAND-2015-4706; 672345
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING