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Hello @kaipengliuHIT, the example nurbs_patch_ex1.cpp currently works only in 3D. The sample runs use the 3D mesh data/beam-hex-nurbs.mesh. There is an error message in DiffusionIntegrator::AssemblePatchMatrix_reducedQuadrature if the dimension is not 3.
This example demonstrates patch-based integration rules, as opposed to the usual element-based integration used in MFEM. There are computational savings with patch-based integration, more so in 3D than 2D. This is why 3D is the main target for this example. With some further implementation, a 2D example could be supported, and it should be straightforward to do so by following the 3D example.
For more background and comments on this example, see the merged PR 3088.
maybe patchRule->Finalize(mesh); in the NURBS example only works on 3D mesh
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