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Showing 1 to 12 of 12 for “"spacetime discontinuous"”.
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A Spacetime Discontinuous Galerkin Method for Hyperbolic Conservation Laws
… in the immediate vicinity of shocks and other discontinuous solution features. We address this requirement with a diffusion operator whose intensity is controlled by a shock indicator that measures the relative strength of the high-frequency components of the SDG approximation. Results …
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Analysis of a Spacetime Discontinuous Galerkin Method for Elastodynamics
We prove error estimates for the case of both element-wise and patch-wise causal partitions.
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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 …
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Asynchronous parallel solver for hyperbolic problems via the Spacetime Discontinuous Galerkin method
This thesis presents a parallel Space Time Discontinuous Galerkin (SDG) finite element method which makes use of the method's unstructured mesh generation and localized solution technique to achieve a high level of parallel scalability. Our SDG method is different from most traditional adaptive …
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Analysis of a Spacetime Discontinuous Galerkin Method for Systems of Conservation Laws
… of this dissertation is analysis of a causal spacetime discontinuous Galerkin (CSDG) method for one-dimensional hyperbolic systems of conservation laws. The CSDG method is based on causal spacetime discretizations, and the Galerkin basis herewith consists of piecewise constant functions. The …
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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 …
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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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A scalable distributed framework for parallel—adaptive spacetime discontinuous Galerkin solvers with application to multiscale earthquake simulation
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms
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Spacetime Meshing for Discontinuous Galerkin Methods
… to construct an unstructured simplicial spacetime mesh over an arbitrary simplicial space domain. Our algorithm is the first adaptive spacetime meshing algorithm suitable for efficient solution of nonlinear phenomena using spacetime discontinuous Galerkin finite element methods. Given a …
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A Spacetime, Balance-Law Formulation of Coupled Atomistic and Continuum Dynamics for Solids
… coupled formulation is composed of the continuum spacetime discontinuous Galerkin (SDG) method and the mathematically consistent, time finite element, atomistic discontinuous Galerkin (ADG) method. On the continuum side I develop a two- and three-field SDG formulations for linearized …
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Spacetime damage-based cohesive model for elastodynamic fracture with dynamic contact
… materials. The model is implemented within a spacetime discontinuous Galerkin (SDG) finite element method. An adaptive meshing procedure generates %When implemented on suitable spacetime grids that satisfy a special causality constraint to enable an efficient patch-by-patch, advancing-front …