Febrianto, Eky and Šístek, Jakub and Kůs, Pavel and Kecman, Matija and Cirak, Fehmi (2024) A three-grid high-order immersed finite element method for the analysis of CAD models. Computer-Aided Design, 173: 103730. ISSN 0010-4485
AI Summary:
The proposed approach introduces an efficient, robust, high-order immersed finite element method for complex CAD models. The approach relies on three adaptive structured grids and iteratively solves the discrete systems of equations in parallel using domain decomposition.AI Topics:
The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an efficient, robust, high-order immersed finite element method for complex CAD models. Our approach relies on three adaptive structured grids: a geometry grid for representing the implicit geometry, a finite element grid for discretising physical fields and a quadrature grid for evaluating the finite element integrals. The geometry grid is a sparse VDB (Volumetric Dynamic B+ tree) grid that is highly refined close to physical domain boundaries. The finite element grid consists of a forest of octree grids distributed over several processors, and the quadrature grid in each finite element cell is an octree grid constructed in a bottom-up fashion. The resolution of the quadrature grid ensures that finite element integrals are evaluated with sufficient accuracy and that any sub-grid geometric features, like small holes or corners, are resolved up to a desired resolution. The conceptual simplicity and modularity of our approach make it possible to reuse open-source libraries, i.e. openVDB and p4est for implementing the geometry and finite element grids, respectively, and BDDCML for iteratively solving the discrete systems of equations in parallel using domain decomposition. We demonstrate the efficiency and robustness of the proposed approach by solving the Poisson equation on domains described by complex CAD models and discretised with tens of millions of degrees of freedom. The solution field is discretised using linear and quadratic Lagrange basis functions.
Febrianto, Eky
Author
Wiragunarsa, I.M. and Zuhal, L.R. and Dirgantara, T. and Putra, I.S. and Febrianto, E. (2024) Total Lagrangian smoothed particle hydrodynamics with an improved bond-based deformation gradient for large strain solid dynamics. Journal of Computational Physics, 518: 113309. ISSN 0021-9991
Alfarisy, Dewangga and Zuhal, Lavi and Ortiz, Michael and Cirak, Fehmi and Febrianto, Eky (2024) Point collocation with mollified piecewise polynomial approximants for high-order partial differential equations. International Journal for Numerical Methods in Engineering, 125 (18): e7548. ISSN 0029-5981
Febrianto, Eky and Šístek, Jakub and Kůs, Pavel and Kecman, Matija and Cirak, Fehmi (2024) A three-grid high-order immersed finite element method for the analysis of CAD models. Computer-Aided Design, 173: 103730. ISSN 0010-4485
See full publications listŠístek, Jakub
Author
Febrianto, Eky and Šístek, Jakub and Kůs, Pavel and Kecman, Matija and Cirak, Fehmi (2024) A three-grid high-order immersed finite element method for the analysis of CAD models. Computer-Aided Design, 173: 103730. ISSN 0010-4485
See full publications listKůs, Pavel
Author
Febrianto, Eky and Šístek, Jakub and Kůs, Pavel and Kecman, Matija and Cirak, Fehmi (2024) A three-grid high-order immersed finite element method for the analysis of CAD models. Computer-Aided Design, 173: 103730. ISSN 0010-4485
See full publications listKecman, Matija
Author
Febrianto, Eky and Šístek, Jakub and Kůs, Pavel and Kecman, Matija and Cirak, Fehmi (2024) A three-grid high-order immersed finite element method for the analysis of CAD models. Computer-Aided Design, 173: 103730. ISSN 0010-4485
See full publications listCirak, Fehmi
Author
Alfarisy, Dewangga and Zuhal, Lavi and Ortiz, Michael and Cirak, Fehmi and Febrianto, Eky (2024) Point collocation with mollified piecewise polynomial approximants for high-order partial differential equations. International Journal for Numerical Methods in Engineering, 125 (18): e7548. ISSN 0029-5981
Febrianto, Eky and Šístek, Jakub and Kůs, Pavel and Kecman, Matija and Cirak, Fehmi (2024) A three-grid high-order immersed finite element method for the analysis of CAD models. Computer-Aided Design, 173: 103730. ISSN 0010-4485
Sun, Fuzheng and Febrianto, Eky and Fernando, Heshan and Butler, Liam J. and Cirak, Fehmi and Hoult, Neil A. (2023) Data-informed statistical finite element analysis of rail buckling. Computers and Structures, 289: 107163. ISSN 0045-7949
See full publications listAvailable under License Creative Commons Attribution.
Download (2MB) | Preview
 |