A MESHFREE METHOD FOR A PDE-CONSTRAINED OPTIMIZATION PROBLEM

A MESHFREE METHOD FOR A PDE-CONSTRAINED OPTIMIZATION PROBLEM

We describe a new approximation method for solving a PDE-constrained optimization problem numerically. Our method is based on the adjoint formulation of the optimization problem, leading to a system of weakly coupled, elliptic PDEs. These equations are then solved using kernel-based collocation. We...

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Veröffentlicht in:SIAM journal on numerical analysis 2021-01, Vol.59 (4), p.1896-1917
Hauptverfasser: Hoff, Daniel, Wendland, Holger
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics, Applied
Physical Sciences
Science & Technology
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Zusammenfassung:We describe a new approximation method for solving a PDE-constrained optimization problem numerically. Our method is based on the adjoint formulation of the optimization problem, leading to a system of weakly coupled, elliptic PDEs. These equations are then solved using kernel-based collocation. We derive an error analysis and give numerical examples.
ISSN:0036-1429
1095-7170
DOI:10.1137/20M1363510