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Title: Optimization-based mesh correction with volume and convexity constraints

In this study, we consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. This volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimization problem in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.
 [1] ;  [1] ;  [1] ;  [1] ;  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-15-22070; SAND-2015-1521J
Journal ID: ISSN 0021-9991; PII: S0021999116001224
Grant/Contract Number:
14-017511; AC52-06NA25396; AC04-94AL85000
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 313; Journal Issue: C; Journal ID: ISSN 0021-9991
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; lagrangian motion; incremental remap; semi-lagrangian transport; departure volume correction; volume fraction; passive tracer transport; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1254321; OSTI ID: 1348256