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Adaptive Meshing with Zero Projection Error

Jeff Erickson, Shuo-Heng Chung and Shripad Thite, Department of Computer Science

Jayandran Palaniappan, Reza Abedi and Robert B. Haber, Theoretical & Applied Mechanics

Spacetime tetrahedron

Edge-flip operation in space requires error-prone projection. We obtain an analogous change in connectivity using a single spacetime tetrahedron with two inflow (blue) and two outflow (red) faces. Zoom

Animation of adaptive spacetime meshing

Adaptive spacetime meshing captures expanding shock and contact discontinuity while maintaining mesh quality and exact conservation properties.


Adaptive meshing is crucial for resolving multiple length and time scales in transient numerical simulations. When implemented as an instantaneous operation in space, it introduces projection error as the solution is transferred from the old to new mesh. This limits solution accuracy, the primary goal of adaptive analysis. Global remeshing can hinder parallel execution. We seek new techniques that circumvent these problems.


We adapt unstructured spacetime meshes using strictly local remeshing operations to avoid serial bottlenecks in parallel codes. We implement the common remeshing operations (edge flips, vertex deletion, smoothing, etc.) within spacetime elements to improve element quality while eliminating all solution projections and associated errors. This preserves the element-wise conservation properties of spacetime discontinuous Galerkin methods.


Our adaptive method offers improved performance and accuracy, especially for models with extremely sensitive energetics, as are common in simulations of materials microstructure.

This material is also available in a Powerpoint slide "nugget".

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