A parallel algorithm design approach in which the data is divided into pieces and then computations are associated with the data. This contrasts to 'functional decomposition', in which tasks or computations are divided first, then data is associated to them.
4
votes
3answers
123 views
implicit vs. explicit domain decomposition methods
I've been working on a finite element code on unstructured methods, which I've parallelized using the Schur complement method. Here's a summary of how I did it:
Assign each triangle of the mesh to a ...
1
vote
0answers
60 views
Enforcing continuity conditions in pseudospectral domain decomposition methods for time dependent PDEs
I have a partial differential equation of the form
$$ \frac{d}{dt}f(x,t) = \Theta(x) f(x,t) \qquad \Theta(x) \sim \left[\frac{d^2}{dx^2} + k^2(x)\right] $$
subject to $f(x,t=0) = f_0(x)$, and ...
2
votes
2answers
192 views
Mesh domain decompositions / mesh partitioning
I have some experience with mpmetis from METIS. It is pretty good software which offers unstructured mesh grid partitioning. But obtained results always minimize edgecuts or total communication ...
5
votes
1answer
46 views
Compability conditions in domain decomposition methods
Suppose we want to solve the Poisson equation $\Delta u = f$ on a domain $\Omega$ with Dirichlet boundary conditions. One possible way to do is by a domain decomposition method.
There is a condition ...
9
votes
5answers
655 views
What is the advantage of multigrid over domain decomposition preconditioners, and vice versa?
This is mostly aimed for elliptic PDEs over convex domains, so that I can get a good overview of the two methods.
7
votes
3answers
161 views
In what application cases are additive preconditioning schemes superior to multiplicative ones?
In both domain decomposition (DD) and multigrid (MG) methods, one may compose the application of the block updates or coarse corrections as either additive or multiplicative. For pointwise solvers, ...
