Domain decomposition and multilevel methods

The development of fast solution techniques to effectively solve the algebraic (linear) system of equations arising from the approximation of partial differential equations is a fundamental problem in scientific computing. The research at MOX in this context focuses on 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.

Valley of Grenoble: decomposed computational domain for the numerical simulation of seismic wave propagation in near-fault conditions

Valley of Grenoble: decomposed computational domain for the numerical simulation of seismic wave propagation in near-fault conditions

Fast solution techniques for large scale problems

Sequence of agglomerated polygonal meshes for geometric multigrid.

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.