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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How to choose MPI topology for uniform 3D Cartesian grid that is not cubical?
When writing an MPI-parallelised code, I need to split a global Cartesian domain of $(N_x, N_y, N_z)$ cells among $M$ MPI ranks. For simplicity, we can assume that the decomposition is "simple&...
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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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Metis: how to use and tutorial recommendation
I am new to METIS and trying to use it in my fortran code. I read the manual online. But still, I am not sure about how to implement it my code. I tried the test cases in the graphs directory. For ...
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Partitioning SPD matrix with METIS to preserve block SPD-ness
I am using the METIS to partition a matrix and then using domain decomposition to solve the subdomains in parallel using the Restricted Additive Schwarz method.
I am currently trying to solve some ...
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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 ...
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overlapping additive schwarz [closed]
I am solving 1D laplace problem discretized with finite differences (3-point stencil).
I would like to use additive Schwarz method in classical form:
$U_{k+1}=U_{k}+M^{−1} r_k,$
where $r_k=F−A U_k$...
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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 ...
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Alternating Schwarz does not converge without Dirichlet conditions on physical boundaries
Note: Thanks to comments, I realized that I have two problems, each which can be described more clearly on its own. This revised question covers the first.
I would like to solve
$$
-\Delta u - 1=0,\...
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What is the global problem in the two-level additive Schwarz?
The two-level additive Schwarz method (additive Schwarz with a coarse space correction) is often written like this:
$$
\mathbf{v} = \sum_{i=0}^N \mathbf{R}_i^T \mathbf{A}^{-1}_i\mathbf{R}_i\mathbf{w}
$...
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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 ...
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Direct solvers and domain decomposition for FEM
In the 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, ...
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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. ...
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Non-overlaping Domain decomposition - assemble of Laplacian
I am dealing with following 2-dimensional problem in the unit square domain $S_2$
$$- \Delta u (x,y) = f \ \text{in} \ S_2, \hspace{1.5cm} u(x,y) = 0 \ \text{on} \ \partial S_2$$
where $f$ is ...
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how to partition a graph(matrix) into subdomains with different sizes
i am studying the solver for PageRank problems which drived from the web link graph.
I have tried using METIS to divided the matrix into subdomains, but METIS can only produce subdomains with nearly ...
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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 ...
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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-...
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Steklov-Poincaré operator for overlapping domain decomposition
For non-overlapping domain decomposition methods for elliptic problems there is an associated Steklov-Poincaré definite positive operator defined on the interface, allowing a direct computation of the ...
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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 ...
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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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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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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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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 $f(x=0,t)...
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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....
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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, ...
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