Remapping Between Meshes with Isoparametric Cells: a Case Study

doi:10.1007/s42967-023-00250-4

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (3): 1551-1574.doi: 10.1007/s42967-023-00250-4

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Remapping Between Meshes with Isoparametric Cells: a Case Study

Mikhail Shashkov², Konstantin Lipnikov¹

1 Applied Mathematics and Plasma Physics Group, Theoretical Division, Los Alamos National Laboratory, Mail Stop B284, Los Alamos, NM 87545, USA;
2 Continuum Models and Numerical Methods Group, X-Computational Physics Division, Los Alamos National Laboratory, Mail Stop F644, Los Alamos, NM 87545, USA

Received:2022-09-08 Revised:2022-11-21 Accepted:2022-12-29 Published:2024-12-20
Contact: Mikhail Shashkov,shashkov@lanl.gov;Konstantin Lipnikov,lipnikov@lanl.gov E-mail:shashkov@lanl.gov;lipnikov@lanl.gov
Supported by:
This work was performed under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No. 89233218CNA000001. The authors gratefully acknowledge the support of the US Department of Energy National Nuclear Security Administration Advanced Simulation and Computing Program. The authors would like to thank M. Kucharik and LANL ASC PORTAGE team members for the multiple useful discussions and suggestions.

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Mikhail Shashkov, Konstantin Lipnikov. Remapping Between Meshes with Isoparametric Cells: a Case Study[J]. Communications on Applied Mathematics and Computation, 2024, 6(3): 1551-1574.

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1. Anderson, R., Dobrev, V., Kolev, T., Rieben, R.:Monotonicity in high-order curvilinear finite element arbitrary Lagrangian-Eulerian remap. Int. J. Numer. Meth. Fluids 77, 249-273 (2015)
2. Anderson, R., Dobrev, V., Kolev, T., Rieben, R., Tomov, V.:High-order multi-material ALE hydrodynamics. SIAM J. Sci. Comput. 40(1), B32-B58 (2018)
3. Arnold, D.N., Awanou, G.:The serendipity family of finite elements. Found. Comput. Math. 11, 337-344 (2011)
4. Barnhill, R., Farin, G., Jordan, M., Piper, B.:Surface/surface intersection. Comput. Aided Geom. Des. 4(1/2), 3-16 (1987)
5. Boutin, B., Deriaz, E., Hoch, P., Navaro, P.:Extension of ALE methodology to unstructured conical meshes. ESAIM:Procs. 22, 31-55 (2011)
6. Dobrev, V., Kolev, T., Rieben, R.:High-order curvilinear finite element methods for Lagrangian hydrodynamics. SIAM J. Sci. Comput. 34(5), 606-641 (2012)
7. Dukowicz, J., Kodis, J.:Accurate conservative remapping (rezoning) for arbitrary Lagrangian-Eulerian computations. SIAM J. Stat. Comput. 8, 305-321 (1987)
8. Ergatoudis, I., Irons, B., Zienkiewicz, O.:Curved, isoparametric, quadrilateral elements for finite element analysis. Int. J. Solids Struct. 4, 31-42 (1968)
9. Gillette, A., Kloefkorn, T.:Trimmed serendipity finite element differential forms. Math. Comput. 88(316), 583-606 (2019)
10. Kenamond, M., Kuzmin, D., Shashkov, M.:Intersection-distribution-based remapping between arbitrary meshes for staggered multi-material arbitrary Lagrangian-Eulerian hydrodynamics. J. Comput. Phys. 429, 110014 (2021)
11. Lieberman, E., Liu, X., Morgan, N., Lusher, D., Burton, D.:A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics. Comput. Methods Appl. Mech. Engrg. 353, 467-490 (2019)
12. Lipnikov, K., Morgan, N.:Conservative high-order discontinuous Galerkin remap scheme on curvilinear polyhedral meshes. J. Comput. Phys. 420, 109712 (2020)
13. Lipnikov, K., Shashkov, M.:Conservative high-order data transfer method on generalized polygonal meshes. Technical Report LA-UR-22-26391, Los Alamos National Laboratory (2022)
14. Loubère, R., Ovadia, J., Abgrall, R.:A Lagrangian discontinuous Galerkin-type method on unstructured meshes to solve hydrodynamics problems. Int. J. Numer. Meth. Fluids 44, 645-663 (2004)
15. Margolin, L., Shashkov, M.:Second-order sign-preserving conservative interpolation (remapping) on general grids. J. Comput. Phys. 184(1), 266-298 (2003)
16. Mosso, S., Burton, D.:A second-order two- and three-dimensional remap method. Technical Report LA-UR-98-5353, Los Alamos National Laboratory (1998)
17. Shashkov, M., Wendroff, B.:The repair paradigm and application to conservation laws. J. Comput. Phys. 198, 265-277 (2004)
18. Vacarro, J., Lipnikov, K.:Applying an oriented divergence theorem to swept face remap. Technical Report LA-UR-22-28731, Los Alamos National Laboratory (2022)
19. Velechovsky, J., Kikinzon, E., Navamita, R., Rakotoarivelo, H., Herring, A., Kenamond, M., Lipnikov, K., Shashkov, M., Garimella, R., Shevitz, D.:Multi-material swept face remapping on polyhedral meshes. J. Comput. Phys. 469, 111553 (2022)
20. Warsaw, S.:Area of intersection of arbitrary polygons. Technical Report UCID-17430, Report of Lawrence Livermore National Laboratory. Available at https://www. osti. gov/servl ets/purl/73099 16 (1977)

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Remapping Between Meshes with Isoparametric Cells: a Case Study

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