A PDE-constrained optimization method for 3D-1D coupled problems with discontinuous solutions

Abstract A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on subject where only continuous were considered. Thanks to properly defined function spaces well posed problem obtained from original fully 3D solution then found by PDE-constrained optimization reformulation. domain decomposition strategy in which unknown interface variables are introduced suitably cost functional, expressing error fulfilling conditions, minimized constrained constitutive equations subdomains. The resulting discrete robust respect geometrical complexity thanks use of independent discretizations various Meshes different sizes can be used without affecting conditioning linear system, this peculiar aspect considered formulation. An efficient solving further proposed, based gradient solver yielding ready parallel implementation. experiment known analytical shows accuracy method, two examples more complex configurations proposed address applicability approach practical problems.