Heterogeneous domain decomposition: Principles, algorithms, applications

Heterogeneous domain decomposition is a field of research bridging (homogeneous) domain decomposition and mathematical modeling. The underlying mathematical assumption is that differential equations of different kind are coupled one another across interfaces of disjoined subdomains. In several circumstances such an approach allows a more flexible description of the physical problem at hand and fosters the use of different numerical methods within different zones of the computational domain. Besides, it may sometimes yield a remarkable simplification of the solution algorithm. Here we review the basic issues of heterogeneous domain decomposition, discuss its main theoretical properties together with its algorithmical aspects, and present some applications to fluid dynamical problems for convective-dominated flows. Several numerical results sustain our theoretical conclusions