Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.17708 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917221331107840 |
|---|---|
| author | Mittal, Ketan Dobrev, Veselin Kolev, Tzanio Tomov, Vladimir |
| author_facet | Mittal, Ketan Dobrev, Veselin Kolev, Tzanio Tomov, Vladimir |
| contents | High-order meshes are crucial for achieving optimal convergence rates in curvilinear domains, preserving symmetry, and aligning with key flow features in moving mesh simulations, but their quality is challenging to control. In prior work, we have developed techniques based on Target-Matrix Optimization Paradigm (TMOP) to adapt a given high-order mesh to the geometry and solution of the partial differential equation (PDE). Here, we extend this framework to address two key gaps in the literature for high-order mesh r-adaptivity. First, we introduce tangential relaxation on curved surfaces using solely the discrete mesh representation, eliminating the need for access to underlying geometry (e.g., CAD model). Second, we ensure a continuously positive Jacobian determinant throughout the domain. This determinant positivity is essential for using the high-order mesh resulting from r-adaptivity with arbitrary quadrature schemes in simulations. The proposed approach is demonstrated to be robust using a variety of numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17708 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | High-Order Mesh r-Adaptivity with Tangential Relaxation and Guaranteed Mesh Validity Mittal, Ketan Dobrev, Veselin Kolev, Tzanio Tomov, Vladimir Numerical Analysis Mathematical Software High-order meshes are crucial for achieving optimal convergence rates in curvilinear domains, preserving symmetry, and aligning with key flow features in moving mesh simulations, but their quality is challenging to control. In prior work, we have developed techniques based on Target-Matrix Optimization Paradigm (TMOP) to adapt a given high-order mesh to the geometry and solution of the partial differential equation (PDE). Here, we extend this framework to address two key gaps in the literature for high-order mesh r-adaptivity. First, we introduce tangential relaxation on curved surfaces using solely the discrete mesh representation, eliminating the need for access to underlying geometry (e.g., CAD model). Second, we ensure a continuously positive Jacobian determinant throughout the domain. This determinant positivity is essential for using the high-order mesh resulting from r-adaptivity with arbitrary quadrature schemes in simulations. The proposed approach is demonstrated to be robust using a variety of numerical experiments. |
| title | High-Order Mesh r-Adaptivity with Tangential Relaxation and Guaranteed Mesh Validity |
| topic | Numerical Analysis Mathematical Software |
| url | https://arxiv.org/abs/2601.17708 |