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Title: Formulation and computation of dynamic, interface-compatible Whitney complexes in three dimensions

Journal Article · · Journal of Computational Physics
 [1];  [1];  [1];  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
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A discrete De Rham complex enables compatible, structure-preserving discretizations for a broad range of partial differential equations problems. Such discretizations can correctly reproduce the physics of interface problems, provided the grid conforms to the interface. However, large deformations, complex geometries, and evolving interfaces makes generation of such grids difficult. We develop and demonstrate two formally equivalent approaches that, for a given background mesh, dynamically construct an interface-conforming discrete De Rham complex. Both approaches start by dividing cut elements into interface-conforming subelements but differ in how they build the finite element basis on these subelements. The first approach discards the existing non-conforming basis of the parent element and replaces it by a dynamic set of degrees of freedom of the same kind. The second approach defines the interface-conforming degrees of freedom on the subelements as superpositions of the basis functions of the parent element. These approaches generalize the Conformal Decomposition Finite Element Method (CDFEM) and the extended finite element method with algebraic constraints (XFEM-AC), respectively, across the De Rham complex.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1469640
Report Number(s):
SAND2018-9818J; 667673
Journal Information:
Journal of Computational Physics, Vol. 359, Issue C; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

Figures / Tables (12)

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Figure 11.(p. 43)figure Figure 11.

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS