# Questions tagged [domain-decomposition]

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.

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### 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.
342 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, ...
1k views

### Best Methodologies for Managing a Mesh in Parallel Finite Element Computation?

I am currently developing a domain decomposition method for the solution of the scattering problem. Basically I am solving a system of Helmholtz BVPs iteratively. I discretize the equations using ...
145 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 ...
218 views

### Domain decomposition w/Lagrange multipliers

I'm looking at FEM discretizations of $$u_i - \Delta u_i = f$$ for $u_1, u_2$ on subdomains $\Omega_1, \Omega_2$ with interface $\Gamma$. A Neumann-Neumann transmission condition can be formulated by ...
835 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 ...
139 views

### Effect of subdomain topologies on overlapping additive Schwarz?

Is there a reference on the effect of subdomain topology on performance of the overlapping additive Schwarz method for (high order) finite elements? For example, taking subdomains to be vertex ...
119 views

### Load balancing/partitioning with unknown weights

For a grid-based numerical simulation, I am looking for a load balancing/partitioning algorithm that not only distributes my grid elements, but also determines (approximates) their respective weights. ...
262 views

### Is it possible to predict the null space of a structure from contributing elements null spaces?

I am trying to solve an almost incompressible problem with heterogeneous properties by domain decomposition. Solution with CG converges slowly or divergerces completely. My problem becomes ill-...
141 views

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### How to precondition FEM problems using domain decomposition?

Let's say that I have a FEM code which yields the following problem: $$\mathbf{A}\mathbf{x} = \mathbf{b}.$$ In order to solve this more efficiently with an iterative method, I would like to ...
996 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 volume....
376 views

### Direct Solver and domain decomposition

In finite element method, in order to use MPI, we need to decompose the domain into sub-domains first. Then my question is whether we can solve each sub-domain using a direct solver? Of course, unlike ...
85 views

### why overlapping technique can accelerate the additive/multiplictive Schwarz

Overlapping technique can make each subdomain contain more nodes, and the overlapped subdomains are nonlonger disjoint, is it taking the average value of the multiple nodes as the result. After ...
118 views

### scalable parallel mesh/amr on unstructured grid

I am trying to code a scalable parallel AMR for unstructured grid. There seems to be three approaches for this a) Store some global grid info on each processor and partition with parmetis (The ...
197 views

### Efficient evaluation of $BQ^{-1}B^T$ (Domain Decomposition Implementation)

I have implemented a schur complement domain decomposition method for solving large scale problems in Matlab. It works well but I think there should be some alternative approaches to implement some ...