University of Illinois Urbana-Champaign

A stabilized discontinuous Galerkin method for variational embedding of physics-based data

Goraya, Shoaib Ahmad

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GORAYA-THESIS-2019.pdf

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https://hdl.handle.net/2142/105935

Description

Title
A stabilized discontinuous Galerkin method for variational embedding of physics-based data
Author(s)
Goraya, Shoaib Ahmad
Issue Date
2019-07-15
Director of Research (if dissertation) or Advisor (if thesis)
Masud, Arif
Department of Study
Civil & Environmental Eng
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Date of Ingest
2019-11-26T20:59:45Z
Keyword(s)
  • Variational Multiscale
  • Discontinuous Galerkin
  • Interfaces
  • Data
  • Multiple PDEs
  • Multiscale Methods
  • Linear Elasticity
  • Stokes Flow
  • Darcy Flow
  • Stokes-Darcy Flow
  • Mixed Elasticity
  • Stabilized Methods
  • Residual-free Bubbles
  • Posteriori Error Estimation
Abstract
A stabilized variational framework that admits overlapping as well as non overlapping coupling of domains for a variety of Partial Differential Equations (PDEs) is employed in this work. This method accommodates non-matching meshes across the interfaces between the subdomain boundaries and allows for sharp changes in mechanical material properties. Interface coupling operators that emanate via embedding of Discontinuous Galerkin ideas in the continuous Galerkin framework provide a unique avenue to embed physics-based data in the modeling and analysis of the system. Physics-based data, either in discrete or in distributed form can be embedded via the interface operators that are otherwise devised to enforce continuity of the fields across internal discontinuities. The least-squares form of the interface coupling operators is exploited for its inherent linear regression type structure, and it is shown that it helps improve the overall accuracy of the numerical solution. Method is applicable to multi-PDE class of problems wherein different PDEs are operational on adjacent domains across the common interface. The method also comes equipped with a residual based error estimation method which is shown to be applicable to test problems employed. Different test cases are employed to investigate the mathematical attributes of the method.
Graduation Semester
2019-08
Type of Resource
text
Permalink
http://hdl.handle.net/2142/105935
Copyright and License Information
Copyright 2019 Shoaib Ahmad Goraya

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