Novel multiscale finite element methods for deterministic and stochastic time-harmonic wave equations
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Authors
Jagalur Mohan, Jayanth
Issue Date
2014-05
Type
Electronic thesis
Thesis
Thesis
Language
ENG
Keywords
Mechanical engineering
Alternative Title
Abstract
We extend and analyze the VMS method to partial differential equations with stochastic coefficients. For a natural choice of an "optimal" coarse-scale solution and L2-orthogonal stochastic basis functions, we demonstrate that the fine-scale stochastic Green's function is intimately linked to its deterministic counterpart. Further, we prove whenever the deterministic fine-scale function vanishes, the stochastic fine-scale function satisfies a weaker, and discrete notion of vanishing stochastic coefficients. Using the theoretical insights, we argue how approximations to enable a practical implementation of the VMS method can be made. Subsequently, on select model problems we demonstrate how we gain improved statistics of the solution at a much lower computational cost.
Description
May 2014
School of Engineering
School of Engineering
Full Citation
Publisher
Rensselaer shePolytechnic Institute, Troy, NY