All Questions
Tagged with sparse-matrix finite-difference
15 questions
1
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1
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522
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Crank Nicolson Method with closed boundary conditions
I want to simulate 1D diffusion with a constant diffusion coefficient using the Crank-Nicolson method.
$$\frac{\partial u (x,t)}{\partial t} = D \frac{\partial^2 u(x,t)}{\partial x^2}.$$
I take an ...
- 111
2
votes
1
answer
120
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How to numerically solve differential equations involving sines, cosines and inverses of the unknown function?
I'm very new to finite difference method and I am just introduced to methods of solving differential equation using finite difference method via sparse matrix method.
I find that the main idea is to ...
- 35
3
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0
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267
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solve Ax=b for outrigger A matrix python
I implement Crank-Nicolson 2D finite-difference method.
I get a matrix A which is banded with 1 band above and below the main diagonal, but also contains 2 additional bands , further apart from the ...
- 141
3
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0
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107
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Solving PDEs: What is the best way to deal with non-banded/dense jacobians?
I have a system of PDEs describing atmospheric chemistry and transport. I use finite-differences to make my system of PDEs into a system of ~10,000 ODEs. I then integrate the ODEs forward in time with ...
- 317
0
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276
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How to make a directed graph symmetric?
Say I have a directed graph given as an adjacency matrix $A$ in CSR format represented by the arrays ia (row indexes) and ja (...
- 645
0
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1
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312
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How to fill matrix entries for two-dimensional implicit finite-difference for the general case
If I have derived a finite-difference formula for a 2D problem, for example something like:
$af_{i,j}+bf_{i-1,j}+cf_{i,j-1}+df_{i-1,j-1}=g_{i,j}$
where f is the unknown function on a grid and ...
- 111
2
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0
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136
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How to determine the finite difference coefficient matrix in 2D with periodic BC?
I'm solving a PDE in matlab using ode15s, and since the spatial dimension is 2, and number of variables grow large very quickly, I need to supply the structure of ...
- 217
4
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2
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1k
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Solving Ax = b with sparse A and sparse b
Let's suppose I'm numerically solving the Poisson equation for a delta function source:
$$ \nabla^2 f(x) = \delta(x-x') $$
I can represent the Laplacian $\nabla^2$ using the finite difference method ...
- 213
4
votes
1
answer
4k
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Iteratively solving 3D Poisson equation in MATLAB
I have written a function that sets up a sparse matrix A and RHS b for the 3D Poisson equation in a relatively efficient way. The set-up is nothing fancy: I have extended the 2D 5-point stencil to an ...
- 143
0
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2
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312
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CHOLMOD implementation
I am working on a domain decomposition code in C that uses CHOLMOD to approximate grid values for a PDE in each sub-domain. The issue I have is that the methods use Matrix Market format, which is not ...
- 37
1
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1
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724
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How efficient (compared to "normal" methods) is using a sparse finite difference matrix to solve differential equations?
Any differential operator can be written as a finite difference matrix acting on a vector of values. I recently used it to solve $\Delta A = j$ by writing the Laplacian as a finite difference ...
- 111
3
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0
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354
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Efficient assembly of finite element matrix(coupled equations case)
I noticed this post, where spalloc and sparse are recommended for efficient assembly in Matlab. I personally use sparse ...
- 593
2
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0
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1k
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How to solve singular non symmetric poisson equation with Neumann boundary condtions?
I am trying to solve 2D Poisson equations with Neumann boundary conditions. When the mesh is uniform, Poisson equation is singular and symmetric, so the method listed in Null Space Projection for ...
- 21
2
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1
answer
664
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Assembling sparse matrix in PETSC for Poisson equation
I am a novice at PETSC, and I have been trying to write an FVM code for steady heat conduction in 2D using PETSC (square, regular grid, Dirichlet boundaries)
Since the large matrix , say A, will be ...
- 445
18
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6
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2k
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How to reorder variables to produce a banded matrix of minimum bandwidth?
I'm trying to solve a 2D Poisson equation by finite differences. In the process, I obtain a sparse matrix with only $5$ variables in each equation. For example, if the variables were $U$, then the ...
- 12.2k