Interpolation-based immersogeometric analysis methods for multi-material and multi-physics problems
<|reference_start|>Interpolation-based immersogeometric analysis methods for multi-material and multi-physics problems: Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted meshes, immersed boundary methods instead embed the computational domain in a background grid. Interpolation-based immersed boundary methods augment existing finite element software to non-invasively implement immersed boundary capabilities through extraction. Extraction interpolates the background basis as a linear combination of Lagrange polynomials defined on a foreground mesh, creating an interpolated basis that can be easily integrated by existing methods. This work extends the interpolation-based immersed boundary method to multi-material and multi-physics problems. Beginning from level-set descriptions of domain geometries, Heaviside enrichment is implemented to accommodate discontinuities in state variable fields across material interfaces. Adaptive refinement with truncated hierarchical B-splines is used to both improve interface geometry representations and resolve large solution gradients near interfaces. Multi-physics problems typically involve coupled fields where each field has unique discretization requirements. This work presents a novel discretization method for coupled problems through the application of extraction, using a single foreground mesh for all fields. Numerical examples illustrate optimal convergence rates for this method in both 2D and 3D, for heat conduction, linear elasticity, and a coupled thermo-mechanical problem. The utility of this method is demonstrated through image-based analysis of a composite sample, where in addition to circumventing typical meshing difficulties, this method reduces the required degrees of freedom compared to classical boundary-fitted finite element methods.<|reference_end|>
@article{fromm2024interpolation-based,
    title={Interpolation-based immersogeometric analysis methods for multi-material
  and multi-physics problems},
    author={Jennifer E. Fromm, Nils Wunsch, Kurt Maute, John A. Evans, Jiun-Shyan
  Chen},
    journal={arXiv preprint arXiv:2402.15937},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.15937},
    primaryClass={math.NA cs.NA}
}