Interface Control Domain Decomposition (ICDD) is a method designed to address partial differential equations (PDEs) in computational regions split into overlapping subdomains. The “interface controls” are unknown functions used as Dirichlet boundary data on the subdomain interfaces that are obtained by solving an optimal control problem with boundary observation.
When the ICDD method is applied to classical (homogeneous) elliptic equations, it can be regarded as (yet) another domain decomposition method to solve elliptic problems.
However, what makes it interesting is its convergence rate that is grid independent, its robustness with respect to the possible variation of operator coefficients, and the possibility to use non-matching grids and non-conforming discretizations inside different subdomains.
ICDD methods become especially attractive when applied to solve heterogeneous PDEs (like those occurring in multi-physics problems). A noticeable example is provided by the coupling between (Navier) Stokes and Darcy equations, with application to surface-subsurface flows, or to the coupling of blood flow in large arteries and the fluid flow in the arterial wall. In this case, the minimization problem set on the interface control variables, that is enforced by ICDD method, can in principle assure the correct matching between the two “different physics” without requiring the a priori determination of the transmission conditions at their interface.
Politecnico di Milano (Italy)
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Este colóquio faz parte do ciclo anual Pedro Nunes Lectures, promovido pelo Centro Internacional de Matemática, e conta com o apoio científico e financeiro do Centro de Matemática da Universidade de Coimbra.