its mechanical state (upward bent or downward bent). Discretizing the beam into elements with one translational degree of motion, the nature of the Worldline numerics algorithm makes it easy to *simultaneously* calculate the Casimir forces on all elements with a computational effort less than one order of magnitude above the effort required to get a reliable estimate for the Casimir energy of the given configuration – *independent of the number of elements*. This is not easily achieved with a number of alternative methods to calculate Casimir forces.]{}

Computational Methods
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In contradistinction to other approaches, Worldline Numerics is remarkably simple to implement in a computer program, requiring almost no advanced software library infrastructure to deal with issues such as parallel sparse matrix linear algebra, multipole moments, or large matrix eigenvalues. Still, there are a number of useful improvements of the basic method that help to ensure making effective use of computational resources. As these are often linked to one another, it makes sense to address them in a coherent fashion.

Monte Carlo integration over Loops
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The Casimir energy for a static geometry that can be modeled by a position-dependent potential $V(x)$ is given as the quantum effective action per 