Non-intrusive method imposes boundary conditions in unfitted meshes
A Non-intrusive Approach for the Imposition of Strong Dirichlet Boundary Conditions in Unfitted Boundary Meshes
Computational Engineering, Finance, and ScienceSoftware Engineering
Summary
Often when simulating physical systems with computers, accurately setting boundary conditions can be tough, especially if the mesh does not fit the shape exactly. The authors present a method that lets users impose these essential boundary conditions without needing to change the solver software itself, which is helpful when using commercial codes. Their approach works by leveraging scripting features to modify boundary conditions and ignore mesh parts outside the area of interest. They demonstrate this method works well for standard finite element and isogeometric analysis techniques.
What this means in practice
- •For simulation engineers: Use commercial solvers to run simulations with complex domains without modifying solver code by enforcing boundary conditions through scripting.
- •For computer-aided engineering teams: Implement boundary condition imposition on unfitted meshes within existing commercial finite element or isogeometric analysis software to handle complicated geometries.
Authors
J. I. Camarotti, R. Aristio, R. Rossi, R. Zorrilla, R. Wüchner
Abstract
The enforcement of essential boundary conditions is a fundamental challenge in unfitted boundary methods. This paper presents a non-intrusive, black-box strategy for imposing such conditions in unfitted meshes. The approach is intended for situations where the user does not have access to the solver's source code or its mathematical formulation, which is often the case when using commercial software. The proposed algorithm allows solvers originally designed for body-fitted meshes to be used in unfitted cases, provided that four conditions are satisfied: (i) the solver must support user customization by means of scripting, (ii) allow the imposition of Dirichlet boundary conditions at the node level through scripting, (iii) permit the deactivation of elements outside the physical domain, and (iv) provide access to the solution gradient within active elements. The last condition can also be satisfied by externally reconstructing the gradient from nodal values and connectivity information, provided the element formulation is known, making it optional in practice. These requirements are very fair demands and are satisfied by the vast majority of production-ready, possibly commercial, codes. In the current work, we show the application of this non-intrusive algorithm in the context of the Finite Element Method (FEM) and Isogeometric Analysis (IGA) discretizations, demonstrating optimal $L^2$-norm error convergence. This is demonstrated using the Kratos Multiphysics code (release \texttt{v10.1}) \emph{from the user API, simply leveraging the capabilities mentioned above.}