As a result of using a pure polynomial representation due to the feature implemented by this issue https://github.com/dougshidong/PHiLiP/issues/9, we simply cannot use an exact boundary to refine the surface.
As we refine, we would asymptotically have a constant error since the geometry will never be exact. For test cases that depend on having a smoother and smoother geometry, such as the convergence to zero entropy for the Euler cylinder or Gaussian bump, we need the initial surface grid to be fine enough such that this constant error is less than the error improvement we get from refining. This increases the computational cost since the initial grid now needs to be much larger.
A solution to this would be to move/project the surface nodes to the exact geometry every time a surface cell has been refined. The geometry would still be polynomial, but the refinement would then have new nodes on the exact surface.
dougshidong
commented
4 years ago
As a result of using a pure polynomial representation due to the feature implemented by this issue https://github.com/dougshidong/PHiLiP/issues/9, we simply cannot use an exact boundary to refine the surface.
As we refine, we would asymptotically have a constant error since the geometry will never be exact. For test cases that depend on having a smoother and smoother geometry, such as the convergence to zero entropy for the Euler cylinder or Gaussian bump, we need the initial surface grid to be fine enough such that this constant error is less than the error improvement we get from refining. This increases the computational cost since the initial grid now needs to be much larger.
A solution to this would be to move/project the surface nodes to the exact geometry every time a surface cell has been refined. The geometry would still be polynomial, but the refinement would then have new nodes on the exact surface.