Optimization-based mesh correction with volume and convexity constraints

详细信息    查看全文

• 作者：Marta D'Elia^a ; ^{mdelia@sandia.gov" class="auth_mail" title="E-mail the corresponding author} ; Denis Ridzal^a ; ^{dridzal@sandia.gov" class="auth_mail" title="E-mail the corresponding author} ; Kara J. Peterson^a ; ^{kjpeter@sandia.gov" class="auth_mail" title="E-mail the corresponding author} ; Pavel Bochev^a ; ^{pbbochev@sandia.gov" class="auth_mail" title="E-mail the corresponding author} ; Mikhail Shashkov^b ; ^{shashkov@lanl.gov" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Lagrangian motion ; Incremental remap ; Semi-Lagrangian transport ; Departure volume correction ; Volume fraction ; Passive tracer transport
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：313
• 期：Complete
• 页码：455-477
• 全文大小：2337 K

文摘

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.