*Special RAL/MMM Joint Seminar - Thursday, December 5, 2019 - 3:00pm
*Please note special time - 3:00pm
Speaker: Dr. David L. Darmofal
Affiliation: Department of Aeronautics & Astronautics, Massachusetts Institute of Technology
For phenomenon that exhibit a wide range of scales, adaptive methods can enable efficient yet accurate discretizations. In this talk, we consider the use of space-time adaptive methods to solve time-dependent, multi-scale phenomenon in which the space-time domain is discretized using simplices (i.e. pentatopes for 3D+time) that are not required to have face aligned with the temporal direction. The adaptive method utilizes an goal-oriented approach in which an adjoint solution and dual-weighted residual is employed to estimate the local contribution to the discretization error of a desired output. The dependence of the error estimate on the mesh is then synthesized into a model using the Metric Optimization through Error Sampling and Synthesis (MOESS) algorithm, and the resulting error model is then optimized to produce adapted meshes with minimal error at a fixed computational cost. We demonstrate this approach for higher-order finite element discretizations applied to convection-dominated flows and porous media. Also, similar to parallel-in-time strategies, we show that parallel solution of space-time adapted meshes are more scalable than time-marching approaches. We conclude with a discussion of remaining challenges and opportunities for space-time adaptive methods.
Refreshments: 2:45pm