A numerical simulation approach that uses the same spline-based functions (e.g., NURBS, B-splines) for both exact geometry representation and field approximation, thereby integrating CAD geometry and analysis bases.

Principle

Unify geometric representation and solution spaces so that the geometry is represented exactly (or with the CAD parametrization) and approximation properties of splines yield smooth, higher-continuity basis functions for analysis.

Demonstration

In structural analysis of a curved shell described by NURBS, use the same NURBS basis for the mid-surface geometry and for displacement approximation; this avoids geometry approximation error and simplifies mesh refinement by knot insertion.

Misapplication

Treating arbitrary low-regularity polygonal meshes as if spline geometry continuity holds, or using incompatible spline spaces for geometry and solution, breaks the isogeometric premise and introduces geometric or approximation inconsistencies.

Consequence

Proper application yields exact CAD-consistent geometry, higher-order continuity across elements, improved accuracy per degree of freedom for smooth problems, and straightforward h/p/k refinement strategies aligned with CAD operations.

Reversal

The opposite is traditional finite element analysis: geometry is approximated by piecewise polynomials on a mesh independent of CAD, producing geometric error and lower inter-element continuity unless special elements are used.

Boundary

Best suited for problems where CAD geometry is available and spline bases are practical; less advantageous for problems requiring unstructured simplicial meshes, discontinuous solutions, or where CAD parametrizations are unavailable or too complex to integrate.

Semantic Tension

Competes with classical FEM and CAD-to-mesh pipelines: it reduces geometry error and improves continuity but requires spline technology and can complicate local adaptivity compared to simplicial finite elements.

Synthesis

Isogeometric Analysis: an approach that merges CAD parametrizations and analysis by employing spline-based bases for both exact geometry and solution approximation, delivering smoother bases and CAD-consistent discretizations.