Scalable Nonlinear Compact Schemes

Technical Report · Tue Apr 01 04:00:00 EDT 2014

DOI:https://doi.org/10.2172/1171189· OSTI ID:1171189

Ghosh, Debojyoti ^[1]; Constantinescu, Emil M. ^[2]; Brown, Jed ^[3]

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1. Argonne National Lab. (ANL), Argonne, IL (United States)
2. Univ. of Chicago, IL (United States)
3. Univ. of Colorado, Boulder, CO (United States)

In this work, we focus on compact schemes resulting in tridiagonal systems of equations, specifically the fifth-order CRWENO scheme. We propose a scalable implementation of the nonlinear compact schemes by implementing a parallel tridiagonal solver based on the partitioning/substructuring approach. We use an iterative solver for the reduced system of equations; however, we solve this system to machine zero accuracy to ensure that no parallelization errors are introduced. It is possible to achieve machine-zero convergence with few iterations because of the diagonal dominance of the system. The number of iterations is specified a priori instead of a norm-based exit criterion, and collective communications are avoided. The overall algorithm thus involves only point-to-point communication between neighboring processors. Our implementation of the tridiagonal solver differs from and avoids the drawbacks of past efforts in the following ways: it introduces no parallelization-related approximations (multiprocessor solutions are exactly identical to uniprocessor ones), it involves minimal communication, the mathematical complexity is similar to that of the Thomas algorithm on a single processor, and it does not require any communication and computation scheduling.

• Research Organization: Argonne National Laboratory (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: AC02-06CH11357
• OSTI ID: 1171189
• Report Number(s): ANL/MCS-TM-340; 104241
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING