Accelerated Finite Element Solvers for Fluid, Solid, and Radiation Problems on a Unfitted Boundary Mesh
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The unfitted boundary method embeds the domain of interest into a larger computational domain that is easier to mesh. It utilises an additional transformation map in addition to the Finite Element reference map. The well-posedness of the method is ensured by a positive Jacobian. A similar structure can be achieved using certain mesh generators, such as ChopMesh and SnappyHexMesh. In this work, we present finite element solvers that leverage an unfitted boundary mesh to accelerate numerical simulations. We also explore the use of graphics card hardware acceleration through the Taichi Language. Modifications have been made to the Cartesian-based solver, encompassing both explicit and implicit finite element implementations, coupled with a multigrid solver. Several numerical examples are provided to illustrate the speed differences compared with the standard unstructured implementation, covering applications in fluid dynamics, solid mechanics, and radiation transport problems.
