  The requirements for accurate numerical simulation are increasing constantly.
Modern high precision physics experiments now exceed the achievable numerical
accuracy of standard commercial and scientific simulation tools. One example
are optical resonators for which changes in the optical length are now commonly
measured to 10^{-15} precision. The achievable measurement accuracy for
resonators and cavities is directly influenced by changes in the distances
between the optical components. If deformations in the range of 10^{-15} occur,
those effects cannot be modeled and analysed any more with standard methods
based on double precision data types. New experimental approaches point out
that the achievable experimental accuracies may improve down to the level of
10^{-17} in the near future. For the development and improvement of high
precision resonators and the analysis of experimental data, new methods have to
be developed which enable the needed level of simulation accuracy. Therefore we
plan the development of new high precision algorithms for the simulation and
modeling of thermo-mechanical effects with an achievable accuracy of 10^{-20}.
In this paper we analyse a test case and identify the problems on the way to
this goal.
