Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 20 of 69 for “"Galerkin Finite Element"”.
-
A Spacetime Discontinuous Galerkin Finite-Element Method for Elastodynamic Analysis
We use the new spacetime discontinuous Galerkin finite element model to investigate a series of elastodynamic problems in both one and two spatial dimensions. The first study focuses on the problems that exhibit discontinuities or shocks. The new method delivers high accurate results. The second …
-
Adaptive unstructured spacetime meshing for four-dimensional spacetime discontinuous Galerkin finite element methods
We describe the spacetime discontinuous Galerkin method, a new type of finite-element method which promises dramatic improvement in solution speed for hyperbolic problems. These methods require the generation of spacetime meshes that satisfy a special causality constraint. This work focuses on the …
-
Efficient matrix-free implementation and automated verification of hybridizable discontinuous Galerkin finite element methods
… methods for hybridizable discontinuous Galerkin (HDG) schemes for fluid and ocean dynamics. In the first part, we compare choices in weak formulations and their numerical consequences. We address details in making the leap from the mathematical formulation to the implementation, …
-
Hypersonic heat transfer and anisotropic visualization with a higher order discontinuous Galerkin finite element method
… methods. In particular, the discontinuous Galerkin (DG) finite element method has O(hP+l) design accuracy and allows for subcell resolution of shocks. This work furthers the DG finite element method in two ways. First, it demonstrates the results of DG when used to predict heat transfer to …
-
Stable algorithms for generalized thermoelasticity based on operator-splitting and time-discontinuous Galerkin finite element methods
… on operator-splitting and the time-discontinuous Galerkin finite element method for the non-classical, linear thermoelastic model. The coupled problem is split into two contractive sub-problems, namely, the mechanical phase and thermal phase, on the basis of an entropy controlling mechanism. In …
-
A high-order, adaptive, discontinuous Galerkin finite element method for the Reynolds-Averaged Navier-Stokes equations
This thesis presents high-order, discontinuous Galerkin (DG) discretizations of the Reynolds-Averaged Navier-Stokes (RANS) equations and an output-based error estimation and mesh adaptation algorithm for these discretizations. In particular, DG discretizations of the RANS equations with the …
-
An a posteriori error control framework for adaptive precision optimization using discontinuous Galerkin finite element method
Introduction: Aerodynamic design optimization has seen significant development over the past decade. Adjoint-based shape design for elliptic systems was first proposed by Pironneau and applied to transonic flow by Jameson . A review of the aerodynamic shape optimization literature and a large list …
-
Shock capturing with PDE-based artificial viscosity for an adaptive, higher-order discontinuous Galerkin finite element method
… be combined with a higher-order discontinuous Galerkin finite element discretization to resolve a shock layer within a single cell. However, when a nonsmooth artificial viscosity model is employed with an otherwise higher-order approximation, element-to-element variations induce oscillations in …
-
On the Formulation of a Hybrid Discontinuous Galerkin Finite Element Method (DG-FEM) for Multi-layered Shell Structures
A high-order hybrid discontinuous Galerkin finite element method (DG-FEM) is developed for multi-layered curved panels having large deformation and finite strain. The kinematics of the multi-layered shells is presented at first. The Jacobian matrix and its determinant are also calculated. The weak …
-
A Flexible Galerkin Finite Element Method with an A Posteriori Discontinuous Finite Element Error Estimation for Hyperbolic Problems
A Flexible Galerkin Finite Element Method (FGM) is a hybrid class of finite element methods that combine the usual continuous Galerkin method with the now popular discontinuous Galerkin method (DGM). A detailed description of the formulation of the FGM on a hyperbolic partial differential equation, …
-
Pressure Poisson Method for the Incompressible Navier-Stokes Equations Using Galerkin Finite Elements
… of the NSE with PPE is derived and used in the Galerkin Finite Element discretization. The Galerkin finite element method is then used to solve the NSE with PPE. Moderate accuracy is shown.</p>
-
Immersed Discontinuous Galerkin Methods for Acoustic Wave Propagation in Inhomogeneous Media
We present immersed discontinuous Galerkin finite element methods for one and two dimensional acoustic wave propagation problems in inhomogeneous media where elements are allowed to be cut by the material interface. The proposed methods use the standard discontinuous Galerkin finite element …
-
A priori analysis of global and local output error estimates for CG, DG and HDG finite element discretizations
… and localizations of output error estimates for Galerkin finite element methods. Specifically, Continuous Galerkin (CG), Discontinuous Galerkin (DG), and Hybridized DG (HDG) methods are analyzed for the Poisson problem. A mixed formulation for DG output error estimation is proposed with improved …
-
A dynamic multiscale viscosity algorithm for shock capturing in Runge Kutta Discontinuous Galerkin methods
… the performance of higher-order Discontinuous Galerkin finite element solvers, a shock capturing procedure has been developed for hyperbolic equations. The Dynamic Multiscale Viscosity method, originally presented by Oberai and Wanderer [8, 9] in a Fourier Galerkin context, is adapted to the …
-
Statistical Inverse Modelling of Aerosol Size Distributions
… distribution is modelled by applying a combined finite element method to the aerosol general dynamic equation. We apply the discontinuous-Galerkin finite element method to the condensation, deposition, and source terms, and the collocation finite element method to the coagulation term in the …
-
An output-based adaptive and high-order method for a rotor in hover
A high-order discontinuous Galerkin finite element discretization and output-based adaptation scheme for the compressible Euler equations are presented and applied to an isolated rotor in hover. A simplex cut-cell mesh generation technique is used to support robust and autonomous creation of …
-
Optimization and validation of discontinuous Galerkin Code for the 3D Navier-Stokes equations
… the components of a high-order, Discontinuous Galerkin Finite Element Method (DGFEM) for the Navier-Stokes equations in 3D are presented. Emphasis is given to residual and Jacobian assembly, since these are rarely discussed in the literature; in particular, this thesis focuses on code …
-
Modeling of Charge Carrier Transport in Photoetching of Gallium Arsenide
… etching process were studied. The model used the Galerkin Finite Element Method to solve the Poisson equation for the potential and the species balance equations for holes and electrons in two dimensions. Each species balance equation included terms for generation, recombination, diffusion and …
-
Galerkin Projections Between Finite Element Spaces
… spaces when solving elliptic PDEs with Galerkin finite element methods. For nonlinear PDEs, solving the nonlinear problem with Newton's method requires an initial guess of the solution on a refined space, which can be found by interpolating the solution from a previous refinement. …
-
Computational design for electromagnetic simulations
… higher-order accurate Streamline Upwind/Petrov-Galerkin finite-element method that numerically solves Maxwell’s equations in the time domain using implicit time stepping. The software for computing sensitivity derivatives employs a reverse-mode time-accurate discrete adjoint methodology that is …
Page 1 of 4