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  "body": "\n## Summary\n\nIsogeometric analysis is a [[Galerkin method|Y5B0PEBKE8]] built on spline functions, such as [[B-splines|62AFX32JGT]] and [[NURBS|Y8B2N9ERPE]].\nThe same functions describe the geometry and approximate the solution.\nIt was proposed by Thomas Hughes and coworkers to connect computer-aided design directly with simulation.\nGeometries given by NURBS, such as circles and cylinders, are represented exactly, with no meshing error.\nThe basis functions can be smoother than standard finite elements, which helps for higher-order equations.\nSee the [[definition|VF17XWCK8Z]].\n\n## Explanations\n\n### L1 human\n\nEngineers design shapes on computers with smooth spline curves and surfaces.\nClassical finite element methods first replace the shape by a mesh of flat triangles or boxes, which loses the exact geometry.\nIsogeometric analysis skips this step and computes directly with the spline functions of the design.\nFor example, a quarter of a circle is exactly a quadratic NURBS curve, so a ring-shaped part is described without error.\n",
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