The predominant engineering analysis techniques are the finite element, finite difference and boundary element methods. These techniques are global in that they attempt to solve field problems over an entire domain. Global techniques are, however, an ‘over-kill’ in the early stages of engineering design, when design parameters are fuzzy, and the functional viability of options can be determined through quick check-point analysis.

In this paper, we revisit two ‘discarded’ Monte Carlo (MC) analysis techniques: MC boundary sampling, and MC domain sampling, which can be employed for solving field problems at discrete points. These techniques can be (potentially) more effective than global techniques, especially in the early stages of engineering design, but are ignored in practice because they are computationally expensive if implemented conventionally. In this paper, we argue that an appropriate geometric representation (of the underlying domain) — specifically, ray-representations for boundary sampling, and Voronoi graphs for domain sampling — is critical for efficient implementation of each technique. Exemplary numerical results are also presented.

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