TrueGrid® FAQ: Why does an interpolation or smoothing operation appear to have no affect on a solid mesh?

Why does an interpolation or smoothing operation appear to have no affect on a solid mesh?

Answer: There is a consistent way that TrueGrid^® interpolates or smoothes part of the mesh and it is based on the dimension of the selected region. There is one exception, but it has not been implemented in TrueGrid^®, yet.

CASE 1: 1 Dimension

When an interpolation is done along an edge of the mesh, the end nodes are fixed and serve as the boundary condition for the interpolation.

CASE 2: 2 Dimensions

When a face is interpolated or smoothed, the edges of the face are fixed and serve as the boundary conditions for the interior.

CASE 3: 3 Dimensions

When a solid is interpolated or smoothed, the faces of the solid are fixed and serve as the boundary conditions for the interior.

CASE 4: Neumann boundary conditions (not yet implemented)

Some smoothing algorithms, not yet in TrueGrid^®, will move the boundary nodes to produce a near orthogonal mesh near the boundary. This makes it possible to glue several blocks together and get a smooth mesh at their interface. The disadvantage is two fold. First, this limits the shape of the mesh at the interface, which may not be ideal. Secondly, most implementations cause the nodes to wonder off of the surface. In TrueGrid^®, we have resisted this approach. A better solution can be gotten by smoothing the two blocks together. Also, the Neumann boundary condition violates the nodal distribution conditions that TrueGrid^® works hard at preserving. Alternatively, if an near orthogonal mesh is desired at a boundary, one can use the TME command which smoothes the interior nodes to produce orthogonality at the boundary. Having said all of this, it is our intent to also offer a Neumann boundary condition with our smoothing methods. This will probably be available in a year.

As a final note, if you select a solid to be interpolated or smoothed and you what the boundary faces to be smoothed as well, then you should select each of the faces for the same interpolation or smoothing. Sometimes, by interpolating or smoothing the faces, there is no need to interpolate or smooth the interior.

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