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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Domain Decomposition with PETSc

Does anyone have any experience on Domain Decomposition using PETSc library? I have used PETSc for creating my vectors and matrix within my C++ code. I also used KSP to solve the linear system. I ...
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101 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 ...
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60 views

nonoverlapping domain decomposition

I solved a simple test example by overlapping domain decomposition. The problem domain is a rectangular that is decomposed to two domains. So the value on the intersection boundary is guessed at the ...
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349 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 ...
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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 ...
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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 ...
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389 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 ...
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77 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 ...
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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.
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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, ...