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Explore a novel approach to immersed finite element analysis that dramatically reduces implementation complexity in this seminar presentation from the FEM@LLNL series. Learn how interpolating finite element basis functions from non-body-fitted background meshes onto Lagrange bases defined over body-fitted integration meshes enables powerful simulation capabilities for physical systems previously out of reach. Discover how this interpolation-based method allows classical finite element codes to be converted into immersed finite element codes with minimal modifications, requiring only Lagrange extraction operators, connectivity arrays, and the ability to evaluate background basis functions. Understand the theoretical foundations including stability and convergence analysis for model problems, and see practical demonstrations across structural mechanics and fluid dynamics applications. Examine how this framework extends naturally to immersed isogeometric analysis and explore the open-source software that generates necessary data structures for implementation within the FEniCS platform. Gain insights into how interpolation onto body-fitted integration meshes can transform classical finite element analysis codes into meshless analysis codes based on the Reproducing Kernel Particle Method, opening new possibilities for shape and topology optimization technologies.
