# Domain decomposition and multilevel methods

**domain decomposition methods**as well as

**multigrid and multilevel algorithm**that can be used as solvers as well as preconditioners.

**Domain decomposition** **methods** consists in decomposing the original mathematical problem into a collection of smaller (and computationally cheaper) subproblems, each of which can be solved independently. The divide-and-conquer philosophy at the basis of iterative domain decomposition methods has been proved to be the ideal paradigm for large-scale simulation on massively parallel computers.

View a list of journal publications and MOX Reports related to domain decomposition methods.

View a list of theses related to domain decomposition methods.

**Multigrid and multilevel methods** employs a hierarchy of discretizations to solve differential problems. The main idea at the basis of these techniques is to accelerate the convergence of basic iterative solvers employing (recursively) a global coarse correction. For a certain class of problems, multigrid methods are among the fastest solution techniques known today since they feature optimal computational complexity and scaling properties.

View a list of journal publications and MOX Reports related to domain decomposition methods.

View a list of theses related to domain decomposition methods.