Thursday, March 20, 2025 - 09:00 in V2-205
Asymptotic compatibility of parametrized optimal design problems
A talk in the Nonlocal Equations: Analysis and Numerics series by
Abner J. Salgado from Knoxville
| Abstract: |
We study optimal design problems where the design corresponds to a coefficient in
the principal part of the state equation. The state equation, in addition, is parameter dependent, and we allow it to change type in the limit
of this (modeling) parameter. We develop a framework that guarantees
asymptotic compatibility, that is unconditional convergence with respect
to modeling and discretization parameters to the solution of the corresponding limiting problems. This framework is then applied to two distinct
classes of problems where the modeling parameter represents the degree
of nonlocality. Specifically, we show unconditional convergence of optimal
design problems when the state equation is either a scalar-valued fractional
equation, or a strongly coupled system of nonlocal equations derived from
the bond-based model of peridynamics.
This is joint work with Tadele Mengesha (UTK) and Joshua Siktar (TAMU)
Within the CRC this talk is associated to the project(s): A7 |
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