Treating complex geometries using voxel-based FEM, CDFEM, and fictitious domain method

The integration of complex geometries into numerical simulations remains a significant challenge in computational mechanics, particularly in applications such as additive manufacturing, biomedical imaging, and materials science. To provides practical guidelines for selecting the most suitable method based on problem complexity and desired accuracy, advancing the seamless integration of image-based computations and complex geometric modeling in engineering simulations, we compare different numerical methods. Only methods involving minimal geometrical pre-treatment are considered here: voxel-based FEM, conformal decomposition FEM (CDFEM) and fictitious domain methods. The geometry is represented thanks to level-set functions which can be obtained from a segmentation or recalculated from a meshed surface. To validate and compare these methods, convergence analyses are conducted for 2D and 3D scalar and vector problems of increased complexity. Results show that although voxel-based FEM is easy to implement, it is outperformed by both CDFEM and fictitious domain methods. Our benchmarks show that the CDFEM is effective for low-order approximations, whereas fictitious domain methods are better suited for higher-order approximations.