Krylov subspace iterative method for large sparse matrix

In summary, the conversation is about a project for a Circuits Simulation class where the goal is to program a small spice software. The program must be able to solve for dc solutions and do transient analysis using iterative Krylov subspace methods. The professor recommended using the Βi-CG algorithm and GMRES, but the person is considering using other methods such as restarting GMRES or Bi-CGSTAB for better performance. They are also asking for recommendations and sources for further research on the topic.
  • #1
Constantinos
83
1
Hey!

I have a project for a Circuits Simulation class which is basically the programming of a small spice software. So the program must be able to find dc solutions and do transient analysis. This means it can solve Ax = b for a large (think 10^6 X 10^6) sparse non-symmetric matrix A which is derived after a Modified Nodal Analysis of the circuit. This is achieved with iterative Krylov subspace methods

So the professor says that I should go for Βi-CG algorithm and he is satisfied. He also recommended GMRES if I have the time to program it (in C).

Because of a fortunate turn of events, it seems I have a lot of time in my hands, and perhaps I should go for something even better! The restarting GMRES method seems good, but there are others that can solve the system like Bi-CGSTAB or others that I don't know.

So I want to ask you for a recommendation on what method to use for best performance.
 
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  • #2
It would be great if you could provide me with sources as well, as I am still new to this topic.Thanks in advance!
 

What is the Krylov subspace iterative method for large sparse matrix?

The Krylov subspace iterative method is a numerical algorithm used to solve large sparse linear systems of equations. It is based on constructing a sequence of approximations to the solution by finding vectors in the Krylov subspace, which is a subspace of the original matrix generated by applying the matrix to a starting vector multiple times.

How does the Krylov subspace iterative method work?

The Krylov subspace iterative method works by starting with an initial approximation to the solution and then iteratively improving it by projecting the residual vector onto the Krylov subspace. This process continues until the desired level of accuracy is achieved.

What are the advantages of using the Krylov subspace iterative method?

One advantage of the Krylov subspace iterative method is its ability to efficiently handle large, sparse matrices. This method also requires less storage space compared to direct methods, making it more suitable for problems with limited memory. Additionally, it can be easily parallelized for faster computation.

What are the limitations of the Krylov subspace iterative method?

The Krylov subspace iterative method may converge slowly or fail to converge for certain types of matrices, particularly those that are ill-conditioned or have highly varying eigenvalues. It also requires a good initial approximation to the solution for faster convergence.

What are some applications of the Krylov subspace iterative method?

The Krylov subspace iterative method is commonly used in various scientific and engineering fields, including computational fluid dynamics, structural mechanics, and electromagnetics. It is also used in data analysis and machine learning algorithms, such as principal component analysis and linear regression.

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