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Colloquium: Prof. James Adler, Tufts University

Event Type: 
Prof. James Adler
Event Date: 
Tuesday, February 16, 2021 -
3:30pm to 4:45pm

Event Description: 

Title:  Monolithic Multigrid for a Reduced-Quadrature Discretization of Poroelasticity

Advanced finite-element discretizations and preconditioners for models of poroelasticity have attracted significant attention in recent years.  The equations of poroelasticity offer significant challenges in both areas, due to the potentially strong coupling between unknowns in the system, saddle-point structure, and the need to account for wide ranges of parameter values, including limiting behavior such as incompressible elasticity.  The work presented in this talk was motivated by an attempt to develop monolithic multigrid preconditioners for a novel P1-P0-RT-stabilized discretization; we show here why this is a difficult task and, as a result, we modify the discretization through the use of a reduced quadrature approximation, yielding a more ``solver-friendly'' discretization.  Local Fourier analysis is used to optimize parameters in the resulting monolithic multigrid method, allowing a fair comparison between the performance and costs of methods based on Vanka and Braess-Sarazin relaxation.  Numerical results are presented to validate the LFA predictions and demonstrate efficiency of the algorithms.  Finally, a comparison to existing block-factorization preconditioners is also given.



Event Contact

Contact Name: Jacob Schroder

Contact Email: