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How important is the node numbering scheme for simple fem problems or is it important at all?

It will be much easier to explain that by example, if I have following linear algebraic equations to solve with direct stiffness method [itex]\ K*\left\{X\right\}=F[/itex] where K global stiffness, X unknowns, F global forces acting on nodes. During the composition of that equation, node numbering scheme affects only the transformation matrix and sequential integration of each inner product into global matrices, since each individual side of equation will be affected by that accordingly then it shouldn't affect the result, am I correct in that reasoning or not ?

For your information I prefer to use Gauss elimination or LU decomposition for equation solution, if it's got anything to do with node numbering scheme?

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# Node numbering scheme for Fem problems

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