Optimal mass transport for higher dimensional adaptive grid generation
| Autor: | J. F. Williams, Mohamed H. M. Sulman, Robert D. Russell |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Numerical Analysis
Mathematical optimization Steady state Physics and Astronomy (miscellaneous) Applied Mathematics Coordinate system Grid Parabolic partial differential equation Computer Science Applications Computational Mathematics Transformation (function) Mesh generation Modeling and Simulation Fluid dynamics Applied mathematics Vector field Mathematics |
| Zdroj: | Journal of Computational Physics. 230:3302-3330 |
| ISSN: | 0021-9991 |
| Popis: | In this work, we describe an approach for higher dimensional adaptive grid generation based on solving the L^2 Monge-Kantorovich problem (MKP) which is a special case of the classical optimal mass transportation problem. Two methods are developed for computing the coordinate transformation used to define the grid adaptation. For the first method, the transformation is determined by solving a parabolic Monge-Ampere equation for a steady state solution. For the second method, the grid movement is determined from the velocity field obtained by solving a fluid dynamics formulation of the L^2 MKP. Several numerical experiments are presented to demonstrate the performance of the MKP methods and to compare them with some related adaptive grid methods. The experimental results demonstrate that the MKP methods show promise as effective and reliable methods for higher dimensional adaptive grid generation. |
| Databáze: | OpenAIRE |
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