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ADAPTIVE SPACETIME MESHING FOR DISCONTINUOUS GALERKIN METHODS
| Content Provider | CiteSeerX |
|---|---|
| Author | Thite, Shripad |
| Abstract | Abstract. Spacetime-discontinuous Galerkin (SDG) finite element methods are used to compute numerical solutions of hyperbolic spacetime partial differential equations (PDEs) for accurately modeling wave propagation phenomena arising in important applications in science and engineering. Tent Pitcher [20, 19, 8, 9, 1] is a specialized algorithm to construct an unstructured simplicial (d + 1)dimensional spacetime mesh over an arbitrary d-dimensional space domain. It supports an accurate, local, and parallelizable solution by interleaving mesh generation with an SDG solver. When solving nonlinear PDEs, Tent Pitcher must make conservative worst-case assumptions about the physical parameters which limit the duration of spacetime elements. Thus, it creates a mesh with many more elements than necessary. In this paper, we extend Tent Pitcher to give the first spacetime meshing algorithm suitable for efficient simulation of nonlinear phenomena using SDG methods. Given a triangulated 2-dimensional Euclidean space domain M corresponding to time t = 0 and initial conditions of the underlying hyperbolic spacetime PDE, we construct an unstructured tetrahedral mesh in the spacetime domain E 2 × R. For every target time T � 0, our algorithm meshes the spacetime volume M × [0, T] with a bounded number of nondegenerate tetrahedra. A recent extension of Tent Pitcher [1] adapts the size of spacetime elements to a posteriori numerical error estimates. Our improvement of Tent Pitcher retains this ability to perform adaptive refinement and coarsening of the mesh. We thus obtain the first adaptive algorithm to build spacetime meshes over arbitrary 2-dimensional triangulated spatial domains suitable for solving nonlinear hyperbolic PDEs. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Spacetime Mesh Physical Parameter Mesh Generation Efficient Simulation Numerical Solution Nondegenerate Tetrahedron Initial Condition Unstructured Tetrahedral Mesh Arbitrary D-dimensional Space Domain Posteriori Numerical Error Estimate Sdg Method Spacetime Domain Target Time Sdg Solver Hyperbolic Spacetime Pde Spacetime Volume Conservative Worst-case Assumption Element Method Triangulated 2-dimensional Euclidean Space Domain First Adaptive Algorithm Specialized Algorithm Recent Extension Tent Pitcher Nonlinear Phenomenon Bounded Number First Spacetime Hyperbolic Spacetime Partial Differential Equation Adaptive Refinement Spacetime-discontinuous Galerkin Nonlinear Hyperbolic Pdes Dimensional Spacetime Mesh Spatial Domain Wave Propagation Phenomenon Unstructured Simplicial Spacetime Element Parallelizable Solution |
| Content Type | Text |
| Resource Type | Article |
