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Showing 1 to 20 of 38 for “"Galerkin methods"”.
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Spacetime Meshing for Discontinuous Galerkin Methods
… and efficient solution procedure using SDG methods and to exploit the flexibility of these methods, we give a meshing algorithm to construct an unstructured simplicial spacetime mesh over an arbitrary simplicial space domain. Our algorithm is the first adaptive spacetime meshing algorithm …
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Inertial Manifolds and Nonlinear Galerkin Methods
Nonlinear Galerkin methods utilize approximate inertial manifolds to reduce the spatial error of the standard Galerkin method. For certain scenarios, where a rough forcing term is used, a simple postprocessing step yields the same improvements that can be observed with nonlinear Galerkin. We show …
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Higher-order Petrov-Galerkin methods for analysis of antennas
… and spatially high-order accurate Petrov-Galerkin finite-element method is applied to the analysis of several antenna configurations. The method obtains numerical solutions of Maxwell's equations in the time domain using implicit time stepping and introduces energy into the domain using a …
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Parallel and Adaptive Galerkin Methods for Radiative Transfer Problems
Finite element methods for radiative transfer problems are developed and their implementation on parallel computer architectures is discussed. A posteriori error estimates allow for efficient grid adaptation in two and three space dimensions.
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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 …
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INTERPOLATION OF RIGID-BODY MOTION AND GALERKIN METHODS FOR FLEXIBLE MULTIBODY DYNAMICS
… for both initial and boundary value problems. Galerkin methods provide a suitable framework for the development of such solvers. Galerkin methods require interpolation schemes that approximate the unknown rigid-body motion fields. Novel interpolation schemes for rigid-body motions are proposed …
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Invariant-region-preserving discontinuous Galerkin methods for systems of hyperbolic conservation laws
… invariant-region-preserving (IRP) discontinuous Galerkin (DG) schemes solving hyperbolic conservation law systems. In particular, our focus is on designing an IRP limiter to modify the numerical solution and identifying sufficient conditions for IRP DG schemes by extending Zhang and Shu's work on …
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Discontinuous Galerkin methods for compressible and incompressible flows on space-time adaptive meshes
… flows is dealt within the discontinuous Galerkin (DG) framework along space-time adaptive meshes. Two main research fields can be distinguished: (1) fully explicit DG methods on collocated grids and (2) semi-implicit DG methods on edge-based staggered grids. DG methods became increasingly …
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Refined theories and Discontinuous Galerkin methods for the analysis of multilayered composite structures
… it can be obtained employing several numerical methods that can provide very detailed results at an high computational cost. This approach is well suited for small parts but cannot be applied to complex structures or for damage-tolerance analysis. Thus, accurate and computationally efficient …
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Spacetime meshing of stratified spaces for spacetime discontinuous Galerkin methods in arbitrary spatial dimensions
We introduce the spacetime discontinuous Galerkin method and motivate the need for supporting spacetime meshing on meshes comprised of multiple manifolds. We first discuss preliminary concepts behind simplices, simplicial complexes, and the generalization to oriented simplicies. Using these ideas, …
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Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations
With interior penalty discontinuous Galerkin methods well established as locking-free for lowo-rder triangular elements, and thus an effective alternative to the Standard Galerkin method for nearly incompressible materials, substantial numerical evidence in this work shows that this is not the case …
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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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A survey of discontinuous Galerkin methods for solving the time domain Maxwell's equations
The discontinuous Galerkin (DG) method with different numerical fluxes is applied to the square wave guide problem to avoid spurious modes that arise from the application of standard finite element methods. These numerical fluxes are the central, upwind and Lax-Friedrichs found in the literature. A …
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Optimization of Plane Wave Directions in Plane Wave Discontinuous Galerkin Methods for the Helmholtz Equation
… other than polynomials in Discontinuous Galerkin (DG) approaches has attracted a lot of attention and became known as DG-Trefftz methods. In particular, for the 2D Helmholtz equation, plane waves have been used to derive an Interior Penalty (IP) type Plane Wave DG (PWDG) method and to …
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Adaptive Discontinuous Galerkin Methods Applied to Multiscale & Multiphysics Problems towards Large-scale Modeling & Joint Imaging
… is based on a unified high-order discontinuous Galerkin (DG) method, with adaptive nonconformal meshes, for efficient wave propagation modeling. This algorithm is compatible with a diverse portfolio of real-world geophysical/biomedical applications, ranging from longstanding tough problems: such …
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Entropy-stable hybridized discontinuous Galerkin methods for large-eddy simulation of transitional and turbulent flows
… interest. In this thesis, we develop a series of methods and techniques to improve efficiency, accuracy and robustness of large-eddy simulations with the goal of making CFD a more powerful tool in the aerospace industry.
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High-order Discontinuous Galerkin Methods and Deep Reinforcement Learning with Application to Multiscale Ocean Modeling
… integration of observational data and adaptive methods. As scientists strive to better understand multiscale ocean processes, the thirst for comprehensive simulations has proceeded apace with concomitant increases in computing power, and submesoscale resolutions where nonhydrostatic effects are …
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A-Posteriori bounds on linear functionals of coercive 2nd order PDEs using discontinuous Galerkin methods
… we base our method on the Discontinuous Galerkin finite element method. For equations such as the convection-diffusion equation, the convection term is handled by the standard DG method for hyperbolic problems while the diffusion operator is discretized by the LDG scheme. This choice …
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Schur's Complement and Discontinuous Galerkin Methods for Domain Decomposition Solvers and Plasticity and Interface Evolution Analyses
Adaptive methods can be based on either conforming or non-conforming meshes. Though non-conforming meshes are easier to generate, they require the satisfaction of jump conditions across the non-conforming interface. In this work we develop a discontinuous Galerkin framework for such an adaptive …
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