Paper Info
Title
Optimization-based mesh correction with volume and convexity constraints
Abstract
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.
Year
DOI
Venue
2016
10.1016/j.jcp.2016.02.050
Journal of Computational Physics
Keywords
Field
DocType
Lagrangian motion,Incremental remap,Semi-Lagrangian transport,Departure volume correction,Volume fraction,Passive tracer transport
Mathematical optimization,Convexity,Preconditioner,Robustness (computer science),Constrained optimization problem,Sequential quadratic programming,Multigrid method,Mathematics,Conservation law,Scalability
Journal
Volume
Issue
ISSN
313
C
0021-9991
Citations 
PageRank 
References 
0
0.34
11
Authors
5
Name
Order
Citations
PageRank
marta delia100.34
Denis Ridzal2759.99
Kara Peterson3164.78
Pavel Bochev4143.75
Mikhail Shashkov554254.19