1 research outputs found
Domain decomposition methods for domain composition purpose: Chimera, overset, gluing and sliding mesh methods
Domain composition methods (DCM) consist in
obtaining a solution to a problem, from the formulations of the same problem expressed on various subdomains. These methods have therefore the opposite objective of domain
decomposition methods (DDM). Indeed, in contrast to
DCM, these last techniques are usually applied to matching
meshes as their purpose consists mainly in distributing the
work in parallel environments. However, they are sometimes
based on the same methodology as after decomposing,
DDM have to recompose. As a consequence, in the
literature, the term DDM has many times substituted DCM.
DCM are powerful techniques that can be used for different
purposes: to simplify the meshing of a complex geometry
by decomposing it into different meshable pieces; to perform
local refinement to adapt to local mesh requirements;
to treat subdomains in relative motion (Chimera, sliding
mesh); to solve multiphysics or multiscale problems, etc.
The term DCM is generic and does not give any clue about
how the fragmented solutions on the different subdomains
are composed into a global one. In the literature, many
methodologies have been proposed: they are mesh-based,
equation-based, or algebraic-based. In mesh-based formulations,
the coupling is achieved at the mesh level, before the governing equations are assembled into an algebraic
system (mesh conforming, Shear-Slip Mesh Update,
HERMESH). The equation-based counterpart recomposes
the solution from the strong or weak formulation itself, and
are implemented during the assembly of the algebraic
system on the subdomain meshes. The different coupling
techniques can be formulated for the strong formulation at
the continuous level, for the weak formulation either at the
continuous or at the discrete level (iteration-by-subdomains,
mortar element, mesh free interpolation). Although
the different methods usually lead to the same solutions at
the continuous level, which usually coincide with the
solution of the problem on the original domain, they have
very different behaviors at the discrete level and can be
implemented in many different ways. Eventually, algebraic-
based formulations treat the composition of the
solutions directly on the matrix and right-hand side of the
individual subdomain algebraic systems. The present work
introduces mesh-based, equation-based and algebraicbased
DCM. It however focusses on algebraic-based
domain composition methods, which have many advantages
with respect to the others: they are relatively problem
independent; their implicit implementation can be hidden
in the iterative solver operations, which enables one to
avoid intensive code rewriting; they can be implemented in
a multi-code environment