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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Can domain decomposition methods also be applied to linear systems resulting from finite difference discretizations?
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In general, do domain decomposition methods (DDMs) require a linear system of equations $Au = f$ to be formed by finite element discretization/method (FEM) of a PDE? Or could one simply use a ...
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How is the Alternating Schwarz Method used as a Preconditioner to a Krylov Method?
I am reading "Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations" (Smith 1996), and I am confused as to how the below Alternating Schwarz algorithm ...
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Why aren't mortar domain decomposition techniques used as much as schwarts type DD?
Schwartz type domain decomposition techniques require a transmission condition which can be hard to come by. Mortar type techniques enforce continuity with a Lagrange multiplier across domains. Are ...
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Deconvolution of sinc function in spectrum calculation in FTS
In Fourier transform spectroscopy (FTS) I am calculating a broadband interferogram (e.m. frequency 190-300 GHz top-hat), then back-retrieving the spectrum by FT.
Here in the figure, you can see the ...
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"Optimal" domain partitioning in domain decomposition algorithms
When solving a PDE numerically by domain decomposition methods, what is the "optimal way" to split the domain? Are there any results stating that a particular partition of the domain yields &...
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What is the difference between Adittive Schwarz as a preprocessor and a solver?
As we all know, the Additive Schwarz approach can be used as either solver or preconditioner, however, my question is, what is the difference between the two? In other words, how to use AS as solver, ...
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Partition mesh into predetermined submeshes
I have a mesh already partitioned into disjoint groups of cells. What I want to achieve is the following.
Obtain the adjacency graph for the cell groups.
Partition the mesh, i.e. generate submeshes ...
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preconditioner for $u''(x)=\sin(x)$
I am interested in finding preconditioner to solve the problem for one dimensional problem $u''(x)=\sin(x), u(0)=u(1)=0$ using Dirichlet-Neumann method.
The preconditioner $M$ coming from Dirichlet-...
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can you give me some information of tools for load reblance
I want a tool for load rebalances.
I have a distributed grid. Each process can handle a part of the global grid. Each process has a different node and I want to rebalance it. I want a tool that can ...
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Parallelisation strategies for mixed FE formulations
Mixed FE formulations with LBB-stable elements require two different meshes for the primary and the constraint variables, for example, displacement and pressure. With continuous approximation for the ...
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Solve wave equation with discontinuous coefficients numerically?
I would like to solve the following equation
$$\frac{\partial^2 y}{\partial t^2} - c^2(x,t)\frac{\partial^2 y}{\partial x^2}=0,$$
for $y=y(x,t)$ numerically. The wave speed, $c(x,t)$, is of the form
$$...
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interface value on the error equation
https://www.jstor.org/stable/pdf/2157482.pdf, here I have a problem in last equation of (2.6) in section (2.1). When they are considering error equation on the interface $\Gamma$ they get $e_v^{(n)} = ...
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fixed point iteration on DD method
I have to solve the the problem $u_t+\Delta^2u=f(u)$, where $f(u)$ is non-linear, using domain-decomposition method.
My approach is first using fixed point iteration on mixed form i.e to say $u^{k+1}...
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problem in interface operator
https://www.unige.ch/~gander/Preprints/42540.pdf. here I have a problem in section $4,$ of approximating the symbol $\sigma_i(k)$. My understanding is, to get back the operator $S_i$ we have to use ...
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understanding Domain Decomposition with example
I am new in Domain Decomposition method. I am started to solve $-\Delta u = f$ in $\Omega$ and $u = 0$ on $\partial\Omega$.
From that I get in $\Omega _1$
$$\begin{bmatrix}4&-1\\-1&4\end{...
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