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Showing 1 to 14 of 14 for “"Galerkin discretization"”.
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A linear multigrid preconditioner for the solution of the Navier-Stokes equations using a discontinuous Galerkin discretization
… Navier-Stokes equations using a Discontinuous Galerkin (DG) discretization on unstructured meshes. An element Line-Jacobi preconditioner is presented which solves a block tridiagonal system along lines of maximum coupling in the flow. An incomplete block-LU factorization (Block-ILU(O)) is also …
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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 …
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Investigation of a space-time adaptive method for bluff body flows
… Navier-Stokes equations. A fully-unstructured discretization of space and time is used: for d-dimensional spatial problems, (d + 1)-dimensional meshes are generated, where time is treated as an additional dimension. A high-order discontinuous Galerkin discretization is combined with an …
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A Theoretical and Experimental investigation of Nonlinear Vibrations of Buckled Beams
… it has been proved that finite-degree-of-freedom Galerkin-type discretization procedures applied to some distributed-parameter systems may fail to predict the correct dynamics. By contrast, direct procedures yield reliable approximate solutions. Starting from these results and extending some of …
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A finite element analysis of high kappa, high field Ginzburg-Landau type model of superconductivity
… High kappa model are introduced using standard Galerkin discretization in space and Backward-Euler and Crank-Nicolson discretization schemes in time. We establish existence and uniqueness results for the fully-discrete equations as well as optimal L2 and HI error estimates for the …
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The mode-dependent dynamics of nonlinear nanomechanical resonators
… extensively explore simplifications in using a Galerkin discretization of the continuous system, where a single mode's dynamics are described as a damped, Duffing oscillator. We examine limitations of current approaches and find that using a tensioned and doubly-clamped mode shape for the trial …
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Periodic Solutions of Chaotic Partial Differential Equations With Symmetries
… equations, obtained after applying a spectral-Galerkin discretization in space and time to the CGLE. The discretization is designed to include the group element (that defines a relative time-periodic solution) as an unknown. We found a large collection of distinct relative time-periodic …
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Experimental and numerical study of the bleed effect on the propagation of strong plane and converging cylindrical shock waves
… scheme used was implicit time-marching with the Galerkin discretization for spatial coordinate derivatives and multi-step finite difference formulation for time derivatives. Initial trials with 1-D radial flow have shown good agreement with the analytical power law of shock propagation derived by …
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Nonlinear Vibrations of Cantilever Beams and Plates
… internal resonance. Reduced-order models using Galerkin discretization are also developed to predict experimentally observed motions. A good qualitative agreement is obtained between the experimental and numerical results. Experimentally the energy transfer between widely spaced modes is found …
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A Posteriori Error Analysis of the Discontinuous Galerkin Method for Linear Hyperbolic Systems of Conservation Laws
… we present an analysis for the discontinuous Galerkin discretization error of multi-dimensional first-order linear symmetric and symmetrizable hyperbolic systems of conservation laws. We explicitly write the leading term of the local DG error, which is spanned by Legendre polynomials of degree …
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An optimization framework for adaptive higher-order discretizations of partial differential equations on anisotropic simplex meshes
… with any localizable error estimate, handles any discretization order, permits arbitrarily oriented anisotropic elements, robustly treats irregular features, and inherits the versatility of the underlying discretization and error estimate. Given a discretization and any localizable error estimate, …
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A Theoretical and Experimental Study of Nonlinear Dynamics of Buckled Beams
… neighborhood of an equilibrium configuration. A Galerkin approximation is used to discretize the nonlinear partial-differential equation governing the beam's response and obtain a set of nonlinearly coupled ordinary-differential equations governing the time evolution of the response. We based our …
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Nonlinear Vibrations of Doubly Curved Cross-PLy Shallow Shells
… a primary resonance: a $direct$ approach and a $discretization$ approach. In the discretization approach, the nonlinear partial-differential equations are discretized using the Galerkin procedure to reduce them to an infinite system of nonlinearly coupled second-order ordinary-differential …
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Modeling, Simulation, and Analysis of Micromechanical Filters Coupled with Capacitive Transducers
… by writing the Lagrangian and applying the Galerkin procedure using its analytically calculated linear global mode shapes as basis functions. The resulting model accounts for the geometric and electric nonlinearities and the coupling between them. Using the method of multiple scales, we …