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Treatment of polar grid singularities in the bi-cubic Hermite-Bézier approximations: Isoparametric finite element framework by Ashish Bhole; Boniface Nkonga; Stanislas Pamela; Guido Huijsmans; Matthias Hoelzl is a Engineering article available to read on EtoBox.
What is Treatment of polar grid singularities in the bi-cubic Hermite-Bézier approximations: Isoparametric finite element framework about?
We propose a numerical treatment for the geometric singularity at the polar grid center encountered in the application of the isoparametric bi-cubic Hermite Bézier finite element method. The treatment applies a set of new basis functions at the polar grid center in the numerical algorithm where the new basis functions are simply the linear transformations of the original basis functions. The linear transformation comes out naturally by analyzing the interpolation formula at the polar grid center. The proposed polar treatment enforces the C 1 regularity in the physical space and preserves the order of the accuracy of the interpolation. The treatment is applied in the nonlinear MHD code JOREK. With the help of a range of numerical tests, it is demonstrated that the polar treatment improves the stability and accuracy of the numerical approximation near the polar grid center. The polar treatment presented can be applied to the grid center of circular or non-circular polar grids and is also applicable for the bi-cubic Hermite finite element method.
Who reads Treatment of polar grid singularities in the bi-cubic Hermite-Bézier approximations: Isoparametric finite element framework?
It is typically read by researchers, students, and practitioners in Engineering.
- Author
- Ashish Bhole; Boniface Nkonga; Stanislas Pamela; Guido Huijsmans; Matthias Hoelzl
- Publisher
- Elsevier BV
- Published
- 2022
- Language
- EN
- Field
- Engineering (Physical Sciences)