Isogeometric high order mesh generation

In this paper, we present a new posteriori method to generate high order curved meshes directly from linear meshes through a recently developed poly-spline isogeometric (IGA) method. Given an input structured or unstructured linear quadrilateral or hexahedral mesh, our method constructs quadratic poly-spline IGA bases for each element and ensures continuity and smoothness across neighboring elements. With these smooth IGA bases, each element can be sampled into a high order element of arbitrary order while maintaining consistently continuous and smooth interfaces between elements. Several fitting algorithms are developed to adjust the IGA control points to ensure the final mesh interpolates or approximates the initial boundary closely. Our method requires no CAD geometry of the initial mesh and guarantee C¹ smoothness in regular regions and C⁰ continuity across interfaces of spline-incompatible elements. The method is compared with an elastic analogy based approach and is shown to be superior in terms of computational performance and overall mesh quality and smoothness. The current method can also be extended for higher order IGA basis construction and smooth refinement of meshes that are important for high order physics simulations.