Elucidating the Conformal Structure of the Brinkman Penalisation Method for Geometry-Adapted, Structure-Preserving Operator Learning of Hamiltonian PDEsNew

This paper investigates the mathematical structure of the Brinkman penalisation method when applied to Hamiltonian PDEs. The method embeds boundary-value problems on complex geometries into simple computational boxes by modeling solid regions as strongly dissipative media, eliminating the need for body-fitted mesh generation. The researchers demonstrate that multi-symplectic Hamiltonian PDEs regularized by Brinkman-type penalisation retain a multi-conformal symplectic structure under a specific compatibility condition, yielding an exact local conservation law.