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Title: Scalable Nonlinear Compact Schemes

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.
Authors:
 [1] ;  [2] ;  [3]
  1. Argonne National Lab. (ANL), Argonne, IL (United States)
  2. Univ. of Chicago, IL (United States)
  3. Univ. of Colorado, Boulder, CO (United States)
Publication Date:
OSTI Identifier:
1171189
Report Number(s):
ANL/MCS-TM-340
104241
DOE Contract Number:
AC02-06CH11357
Resource Type:
Technical Report
Research Org:
Argonne National Laboratory (ANL), Argonne, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English