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For a given PDE problem, three main factors affect the accuracy of FEM solutions: basis order, mesh resolution, and mesh element quality. The first two factors are easy to control, while controlling element shape quality is a challenge, with fundamental limitations on what can be achieved. We propose to use p-refinement (increasing element degree) to decouple the approximation error of the finite element method from the domain mesh quality for elliptic PDEs. Our technique produces an accurate solution even on meshes with badly shaped elements, with a slightly higher running time due to the higher cost of high-order elements. We demonstrate that it is able to automatically adapt the basis to badly shaped elements, ensuring an error consistent with high-quality meshing, without any per-mesh parameter tuning. Our construction reduces to traditional fixed-degree FEM methods on high-quality meshes with identical performance. Our construction decreases the burden on meshing algorithms, reducing the need for often expensive mesh optimization and automatically compensates for badly shaped elements, which are present due to boundary con- straints or limitations of current meshing methods. By tackling mesh gen- eration and finite element simulation jointly, we obtain a pipeline that is both more efficient and more robust than combinations of existing state of the art meshing and FEM algorithms.
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This content will become publicly available on June 23, 2026
Automatic Pipeline to Generate Hexahedral Meshes With Layer-Specific Smoothing From Biomedical Images for Finite Element Modeling
In this study, we present an automatic and user-friendly pipeline for generating high-quality hexahedral FEM models directly from voxel-based biomedical images. Our pipeline incorporates advanced boundary smoothing techniques to eliminate staircase artifacts and improve mesh quality, making it particularly well-suited for applications involving 3D images in biomedical research. By addressing common challenges in mesh generation, this pipeline advances the potential for accurate and efficient mesh generation from biomedical images and FEM analysis in biomedical research.
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- Award ID(s):
- 2138719
- PAR ID:
- 10620553
- Publisher / Repository:
- https://event.asme.org/SBC
- Date Published:
- Format(s):
- Medium: X
- Location:
- Santa Ana Pueblo, New Mexico, USA
- Sponsoring Org:
- National Science Foundation
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