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 12 of 12 for “"Galerkin approximation"”.
-
Parameter Estimation for Delay Differential Equations: A New Galerkin Approximation Framework
… for these equations from training data through a Galerkin approximation approach proposed by citet{CGLW16}. The adopted Galerkin approximation is based on a particular type of polynomials due to T. H. Koornwinder, which are orthogonal under an inner product with a point mass cite{Koo84}. Within …
-
Modeling, Discontinuous Galerkin Approximation and Simulation of the 1-D Compressible Navier Stokes Equations
… all residual terms resulting from the 1D flow approximations. The final model assumes that all the residual terms are negligible which is a standard assumption in industry. Steady state equations are obtained by assuming the temporal derivatives are zero. We develop a semi-discrete model by …
-
Approximation and Control of the Boussinesq Equations with Application to Control of Energy Efficient Building Systems
… In addition, we present a finite element Galerkin approximation. Finally, we provide numerical results based on standard Taylor-Hood elements to illustrate the theory.
-
Nonlinear vibration analysis of inflatable dams
… dam is derived, then solved using the Galerkin approximation method. The solution is performed for a one-term approximation and a two-term approximation, where both solutions use a sine function to approximate the deflected shape of the dam. Frequencies and amplitudes are calculated and …
-
Superconvergence of Iterated Solutions for Linear and Nonlinear Integral Equations: Wavelet Applications
<p>In this dissertation, we develop the Petrov-Galerkin method and the iterated Petrov-Galerkin method for a class of nonlinear Hammerstein equation. We also investigate the superconvergence phenomenon of the iterated Petrov-Galerkin and degenerate kernel numerical solutions of linear and nonlinear …
-
Nonlinear Dynamics of Tapping Mode Atomic Force Microscopy
… and made of an identical material. A multimode Galerkin approximation is utilized to discretize the nonlinear partial-differential equation of motion and associated boundary conditions governing the cantilever response and obtain a set of nonlinearly coupled ordinary-differential equations (ODE) …
-
A Theoretical and Experimental Study of Nonlinear Dynamics of Buckled Beams
… theory and small strains and moderate rotation approximations are assumed. We derive the equation of motion governing the nonlinear transverse planar vibrations and associated boundary conditions using the extended Hamilton's principle. The governing equation is a nonlinear …
-
Finite Element Analysis of Thermoviscoplastic Deformations of an Impact-Loaded Prenotched Plate
… differential equations (ODEs) by using the Galerkin approximation. The ODEs are integrated by using the stiff solver, LSODE, which adaptively adjusts the time step size and computes the solution within the prescribed accuracy. Results computed with the four constitutive relations are found …
-
Numerical Simulation of 4th Order Total Variation Flow Problem by using C^0 IPDG Method
… in space by C$^0$ Interior Penalty Discontinuous Galerkin (C$^0$IPDG) method. In particular, it is showed that at each time instant the C$^0$IPDG approximation represents the necessary and sufficient optimality condition for the minimization of an associated proper convex, coercive, and lower …
-
Recycling Krylov Subspaces and Preconditioners
… case of generalized bi-Lanczos. The Petrov-Galerkin approximation that includes recycling in the iteration leads to modified two-term recurrences for the solution and residual updates. We generalize and extend the framework of our recycling BiCG to CGS, BiCGSTAB and BiCGSTAB2. We perform …
-
Backward stochastic Navier-Stokes equations in two dimensions
… is shown by the use of suitable truncations and approximations. The continuity of the adapted solutions with respect to the terminal data is also established. The backward stochastic Navier-Stokes equations (BSNSEs, for short) corresponding to incompressible fluid flow in a bounded domain $G$ are …
-
Noncooperative static and dynamic games: addressing shared constraints and phase transitions
… PDE model for the game. In an offline setting, a Galerkin procedure is introduced to choose the optimal parameters. In an online setting, a steepest descent algorithm is proposed. We provide detailed analysis of the optimal parameter values as well as the Bellman error with both the Galerkin …