Simplicial Approximation of Deforming 3D Spaces for Visualizing Fusion Plasma Simulation Data

Abstract: We introduce a fast and invertible approximation for data simulated as 2D planar meshes with connectivities along the poloidal dimension in deforming 3D toroidal (donut-like) spaces generated by fusion simulations. In fusion simulations, scientific variables (e.g., density and temperature) are interpolated following a complex magnetic-field-line-following scheme in the toroidal space represented by a cylindrical coordinate system. This deformation in 3D space poses challenges for visualization tasks such as volume rendering and isosurfacing. To address these challenges, we propose a novel paradigm for visualizing and analyzing such data based on a newly developed algorithm for constructing a 3D simplicial mesh within the deforming 3D space. Our algorithm introduces no new nodes and operates with reduced time complexity, generating a mesh that connects the 2D meshes using tetrahedra while adhering to the constraints on node connectivities imposed by the magnetic field-line scheme. In the algorithm, we first divide the space into smaller partitions to reduce complexity based on the input geometries and constraints on connectivities. Then we independently search for a feasible tetrahedralization of each partition taking nonconvexity into consideration. We demonstrate use cases of our method for visualizing XGC simulation data on ITER and W7-X.