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Old   February 21, 2007, 12:37
Default non-confirming grids
  #1
raju
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Does somebody know how to deal with non-conforming meshes for finite element formulation. I have a mesh for a complicated domain, which is divided into subzones, but the problem is that the mesh at the interface is matching. Please let me know if there is a good reference for this.
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Old   February 21, 2007, 13:49
Default Re: non-confirming grids
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Mani
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> but the problem is that the mesh at the interface is matching

I don't see a problem with a matching interface. You mean "not" matching?

In FEM each element has a number of computational nodes. At a non-matching interface, the boundary nodes of neighboring elements do not coincide, so there is some additional work (interpolation) needed to transfer information. Knowing the positions of all nodes (in real space as well as in computational space), it should be relatively straight-forward to do this using the shape functions of the elements which enclose the nodes. If it's a static mesh, this can be done very efficiently by working out the metrics as a pre-processing step. If it's a dynamically deforming mesh it will be more involved.
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Old   February 21, 2007, 14:57
Default Re: non-confirming grids
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rt
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i think mani cure is incomplete or description is unclear,

based on type of system several treatement can be used, care is essential for ellyptic systems.

Interpolation (explicit) is possible for parabolic with explict time integration. but for ellyptic system interpolation (as dirichlet bc) leads to iterative procedure.

My suggestion:

1) if u deal with 2D case, u can simply refine mesh at interface, e.g. when u have 2-nodes of other sub-domain at an edge of a triangle, u can divide this triangle to 3 triangle and do such operation for others, in all sub-domain, in 3d it is more difficult.

2) ur problem is not strange and usually happen in AMR grid refinement, especially Quad/Octree refinement of Quad/Hex element, in literature produced additional nodes are called "Hanging nodes". Usuall treatment is using traditional FEM procedure but add some additional constrain in final system for incorporation of hanging nodes effect. These constrain can be extracted form shape function, consider continuty of solution (C0-space), as mani noted.
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Old   February 22, 2007, 10:20
Default Re: non-confirming grids
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raju
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Thank you for your responses.

>Usuall treatment is using traditional FEM procedure but >add some additional constrain in final system for >incorporation of hanging nodes effect. These constrain >can be extracted form shape function, consider continuty >of solution (C0-space), as mani noted.

I am getting a sense of it but I have no idea about the details of implementing it. Is there any paper or material from which I can get more details about implementing this?

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Old   February 22, 2007, 13:26
Default Re: non-confirming grids
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rt
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i only want to give a guideline, for more detail simply search in web with "hanging node + finite element", keyword, surley you find several usefull material, also in classic book there are some material.

note that hanging node is usually related to AMR FEM but your case is probably more complex.

out of curiosity:

what is your dimension (2d or 3d)? what is your element type (tri/tet or quad/hex)? what is your problem type (ellyptic/ parabolic)? and why you have such non-trivial mesh and why you don't convert it to traditional mesh?

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