PDE-Constrained Optimization Models and Pseudospectral Methods for Multiscale Particle Dynamics

Mildred Aduamoah, Benjamin D Goddard, John W Pearson, Jonna Roden

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we investigate problems where the control acts as an advection 'flow' vector or a source term of the partial differential equation, and the constraint is equipped with boundary conditions of Dirichlet or no-flux type. After deriving continuous first-order optimality conditions for such problems, we solve the resulting systems by developing a link with computational methods for statistical mechanics, deriving pseudospectral methods in both space and time variables, and utilizing variants of existing fixed point methods. Numerical experiments indicate the effectiveness of our approach for a range of problem set-ups, boundary conditions, as well as regularization and model parameters.
Original languageEnglish
Number of pages28
JournalBit numerical mathematics
Publication statusAccepted/In press - 18 May 2022


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