The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a wide range of geometrical models can be performed. Application of the finite cell method, and other immersed methods, to large real-life and industrial problems is often limited due to the conditioning problems associated with these methods. These conditioning problems have caused researchers to resort to direct solution methods, which significantly limit the maximum size of solvable systems. Iterative solvers are better suited for large-scale computations than their direct counterparts due to their lower memory requirements and suitability for parallel computing. These benefits can, however, only be exploited when systems are properly conditioned. In this contribution we present an Additive-Schwarz type preconditioner that enables efficient and parallel scalable iterative solutions of large-scale multi-level hp-refined finite cell analyses.

Significant developments in the field of additive manufacturing (AM) allowed the fabrication of complex microarchitectured components with varying porosity across different scales. However, due to the high complexity of this process, the final parts can exhibit significant variations in the nominal geometry. Computer tomographic images of 3D printed components provide extensive information about these microstructural variations, such as process-induced porosity, surface roughness, and other undesired morphological discrepancies. Yet, techniques to incorporate these imperfect AM geometries into the numerical material characterization analysis are computationally demanding. In this contribution, an efficient image-to-material-characterization framework using the high-order parallel Finite Cell Method is proposed. In this way, a flexible non-geometry-conforming discretization facilitates mesh generation for very complex microstructures at hand and allows a direct analysis of the images stemming from CT-scans. Numerical examples including a comparison to the experiments illustrate the potential of the proposed framework in the field of additive manufacturing product simulation.

The capability of correctly predicting part deections after support removal is important to asses the quality of a nal artifact produced by laser powder bed fusion (LPBF) technology. The nite element method is usually employed to perform part-scale thermo-mechanical analysis to estimate the nal distortion of 3D printed parts. Due to the high exibility of LPBF additive manufactur

The multi-level hp-refinement scheme is a powerful extension of the finite element method that allows local mesh adaptation without the trouble of constraining hanging nodes. This is achieved through hierarchical high-order overlay meshes, a hp-scheme based on spatial refinement by superposition. An efficient parallelization of this method using standard domain decomposition approaches in combination with ghost elements faces the challenge of a large basis function support resulting from the overlay structure and is in many cases not feasible. In this contribution, a parallelization strategy for the multi-level hp-scheme is presented that is adapted to the scheme's simple hierarchical structure. By distributing the computational domain among processes on the granularity of the active leaf elements and utilizing shared mesh data structures, good parallel performance is achieved, as redundant computations on ghost elements are avoided. We show the scheme's parallel scalability for problems with a few hundred elements per process. Furthermore, the scheme is used in conjunction with the finite cell method to perform numerical simulations on domains of complex shape.

This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This application demands for the solution of a coupled thermo-elasto-plastic problem on transient meshes within which history variables need to be managed dynamically on non-boundary conforming discretizations. To this end, we propose to combine the multi-level hp-method and the finite cell method. The former was specifically designed to treat high-order finite element discretizations on transient meshes, while the latter offers a remedy to retain high-order convergence rates also in cases where the physical boundary does not coincide with the boundary of the discretization. We investigate the performance of the method at two analytical and one experimental benchmark.

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