Interpolation-based immersogeometric analysis methods for multi-material and multi-physics problems
CoRR(2024)
摘要
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.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要