Interpolation-based immersed finite element and isogeometric analysis

We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange defined foreground that captures the domain geometry but is otherwise subject to minimal constraints quality or connectivity. This generalization of concept extraction analysis literature also related certain variants cell material point methods. Crucially, interpolation may be approximate without sacrificing high-order convergence rates, which distinguishes present method existing cell, CutFEM, immersogeometric approaches. The permits non-invasive reuse software analysis. analyze properties interpolation-based model problem implement it top open-source FEniCS software, apply variety problems in fluid, solid, structural mechanics where we demonstrate accuracy applicability practical geometries like trimmed spline patches.