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| Partial differential equations (PDEs) are frequently used to model important phenomena. In many application scenarios, such as the top-layer thermal excitation of the earth's atmosphere or ground-motion excitation of multi-storey buildings, PDEs are perturbed by random influences acting on the boundaries of the geometrical domain. The underlying random effects are often modeled as filtered white noise processes (coloured noise) or power law noises, resulting in the mathematical study of random partial differential equations (RPDEs).
In this contribution, we focus on the theoretical and numerical properties of an approach tailored to boundary-excited problems: We apply a method of lines that reduces RPDEs with boundary noise to a finite-dimensional system of random ordinary differential equations (RODEs). The resulting RODEs can be solved efficiently by recent numerical schemes. Hence, this reduction provides a very useful alternative to traditional numerical schemes for boundary-excited RPDEs. We apply our RPDE-RODE reduction method to earthquake-induced oscillations of solid structures. |
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