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These functions were the old (and slow) way to evaluate the solution at particle positions. They were necessary in the past, because FEPointEvaluation did not support all the mappings we use (in particular MappingCartesian) and prior to deal.II 9.4 there was a bug in FEPointEvaluation if evaluation started not a the first component of an FESystem. Both limitations have been fixed for a while and I couldnt think of (or find) any configuration in which we would still need the old code path. I still left an assert in that ensure we will not use the slow path of FEPointEvaluation (which is even slower than the implementation I am removing here). This will make sure that if someone uses an exotic mapping in the future, or other conditions change we at least learn about it.