Refined Isogeometric Analysis for fluid mechanics and electromagnetism

Starting from a highly continuous isogeometric analysis discretization, we introduce hyperplanes that partition the domain into subdomains and reduce the continuity of the discretization spaces at these hyperplanes. As the continuity is reduced, the number of degrees of freedom in the system grows. The resulting discretization spaces are finer than standard maximal continuity IGA spaces. Despite the increase in the number of degrees of freedom, these finer spaces deliver simulation results faster with direct solvers than both traditional finite element and isogeometric analysis for meshes with a fixed number of elements. In this work, we analyze the impact of continuity reduction on the number of Floating Point Operations (FLOPs) and computational times required to solve fluid flow and electromagnetic problems with structured meshes and uniform polynomial orders. Theoretical estimates show that for sufficiently large grids, an optimal continuity reduction decreases the computational cost by a factor of . Numerical results confirm these theoretical estimates. In a 2D mesh with one million elements and polynomial order equal to five, the discretization including an optimal continuity pattern allows to solve the vector electric field, the scalar magnetic field, and the fluid flow problems an order of magnitude faster than when using a highly continuous IGA discretization. 3D numerical results exhibit more moderate savings due to the limited mesh sizes considered in this work