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Figure 1: Three frames from a simulation of smoke flowing past a sphere on a 256 × 512 × 256 grid. AbstractWe present a novel multigrid scheme based on a cut-cell formulation on regular staggered grids which generates compatible systems of linear equations on all levels of the multigrid hierarchy. This geometrically motivated formulation is derived from a finite volume approach and exhibits an improved rate of convergence compared to previous methods. Existing fluid solvers with voxelized domains can directly benefit from this approach by only modifying the representation of the non-fluid domain. The necessary building blocks are fully parallelizable and can therefore benefit from multi-and many-core architectures.

In this paper, we present a novel volumetric mesh representation suited for parallel computing on modern GPU architectures. The data structure is based on a compact, ternary sparse matrix storage of boundary operators. Boundary operators correspond to the first‐order top‐down relations of k‐faces to their (k − 1)‐face facets. The compact, ternary matrix storage format is based on compressed sparse row matrices with signed indices and allows for efficient parallel computation of indirect and bottom‐up relations. This representation is then used in the implementation of several parallel volumetric mesh algorithms including Laplacian smoothing and volumetric Catmull‐Clark subdivision. We compare these algorithms with their counterparts based on OpenVolumeMesh and achieve speedups from 3× to 531×, for sufficiently large meshes, while reducing memory consumption by up to 36%.

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We present a novel bounding volume hierarchy for GPU-accelerated direct volume rendering (DVR) as well as volumetric mesh slicing and inside-outside intersection testing. Our novel octree-based data structure is laid out linearly in memory using space filling Morton curves. As our new data structure results in tightly fitting bounding volumes, boundary markers can be associated with nodes in the hierarchy. These markers can be used to speed up all three use cases that we examine. In addition, our data structure is memory-efficient, reducing memory consumption by up to 75%. Tree depth and memory consumption can be controlled using a parameterized heuristic during construction. This allows for significantly shorter construction times compared to the state of the art. For GPU-accelerated DVR, we achieve performance gain of 8.4$$\times $$ × –13$$\times $$ × . For 3D printing, we present an efficient conservative slicing method that results in a 3$$\times $$ × –25$$\times $$ × speedup when using our data structure. Furthermore, we improve volumetric mesh intersection testing speed by 5$$\times $$ × –52$$\times $$ × .

Figure 1: Left: outer surface of the high-resolution mesh with 1.7 million tetrahedra used in the evaluation of our method. Right: cut through a lower-resolution model to show its inner structure. The models are based on the Airbus flight crew rest compartment (FCRC) bracket, a titanium 3D-printed part developed using simulation and topological optimization (see, e.g., [Kra17]).

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