Immersed b-spline (i-spline) finite element method for geometrically complex domains

A novel b-spline based immersed finite element method is introduced for the computation of geometrically and topologically complex problems. The geometry description and the finite element analysis rely on a block structured logically Cartesian mesh which encloses the domain of interest. A signed distance function is used for representing the domain on the Cartesian mesh, whereby the domain boundary is the zeroth level set of the signed distance function. Away from the domain boundaries, the standard b-spline basis functions are used for the finite element interpolation. Close to domain boundaries, a new approach has been developed for modifying the b-spline basis functions so that they locally interpolate the Dirichlet boundary conditions. The efficiency and robustness of the proposed approach is demonstrated with a number of one-, two- and three-dimensional linear boundary value problems.