SoftIGA: Soft isogeometric analysis

We extend the softFEM idea to isogeometric analysis (IGA) reduce stiffness (consequently, condition numbers) of IGA discretized problem. refer resulting approximation technique as softIGA. obtain discretization by first removing spectral outliers system’s stiffness. then add high-order derivative-jump penalization terms (with negative penalty parameters) standard bilinear forms. The parameter seeks minimize spectral/dispersion errors while maintaining coercivity form. establish dispersion for both outlier-free (OF-IGA) and softIGA elements. also derive analytical eigenpairs matrix eigenvalue problems show that numbers systems significantly improve (reduce). prove a superconvergent result order h 2 p + eigenvalues where characterizes mesh size specifies B-spline basis functions. To illustrate main results, we focus on uniform meshes in 1D tensor-product multiple dimensions. For eigenfunctions, delivers same optimal convergence rates approximation. Various numerical examples demonstrate advantages over IGA.