Novel multiscale finite element methods for deterministic and stochastic time-harmonic wave equations
Authors
Jagalur Mohan, Jayanth
ORCID
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Other Contributors
Oberai, Assad
Shephard, M. S. (Mark S.)
De, Suvranu
McLaughlin, Joyce
Li, Fengyan
Shephard, M. S. (Mark S.)
De, Suvranu
McLaughlin, Joyce
Li, Fengyan
Issue Date
2014-05
Keywords
Mechanical engineering
Degree
PhD
Terms of Use
This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.
Full Citation
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
Department
Dept. of Mechanical, Aerospace, and Nuclear Engineering
Publisher
Rensselaer shePolytechnic Institute, Troy, NY
Relationships
Rensselaer Theses and Dissertations Online Collection
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