MMM/RAL Special Joint Seminar | December 2019 - Discretizations for Multi-Scale - David Darmofal
Channel: NSF NCAR Research Applications Laboratory
Date: 06/12/2019

Special RAL/MMM Joint Seminar: Goal-Orient, Adaptive Space-Time Discretizations For Multi-Scale Phenomenon

Dr. David L. Darmofal
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.

Thursday, December 5, 2019 - 3:00pm