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This content will become publicly available on February 24, 2017

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

Here, 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. Also, 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.
Authors:
 [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:
OSTI Identifier:
1240603
Report Number(s):
LA-UR--15-22070
Journal ID: ISSN 0021-9991; PII: S0021999116001224
Grant/Contract Number:
14-017511; AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 313; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Research Org:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING lagrangian motion; incremental remap; semi-lagrangian transport; departure volume correction; volume fraction; passive tracer transport