• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,054 questions , 2,207 unanswered
5,345 answers , 22,719 comments
1,470 users with positive rep
818 active unimported users
More ...

  Connections of iterative solvers for large systems of equation in Physics?

+ 2 like - 0 dislike

I am trying to find the domains in physics where solving large systems of equations is computationally expensive. The sparse systems are of my particular interest, where the input matrix A is in GBs (up to 100 GBs).

This post has been migrated from (A51.SE)
asked Oct 16, 2011 in Theoretical Physics by Lukasz (10 points) [ no revision ]
retagged Mar 7, 2014 by dimension10
What type of equations?

This post has been migrated from (A51.SE)
What would the purpose of such a list?

This post has been migrated from (A51.SE)
You should edit your question and expand a bit. In its current form, it is impossible to answer it. Can you provide examples of what you have in mind?

This post has been migrated from (A51.SE)
Sure. Say you have PDE equations which you linearize with FEM or FVM. You end up with a system of linear equations that can be later turned into famoous Ax=b where A is huge (tens of GBs) and sparse. You can solve it with direct methods and have to use iterative solvers such as CG/BCGSTAB/GMRES/multi-grid. Does it answer to your question?

This post has been migrated from (A51.SE)
Marcin, physists would like to have their supercomputers under the desk instead of using clusters with complicated submission process. With GPUs this is possible.

This post has been migrated from (A51.SE)

1 Answer

+ 1 like - 0 dislike

For one thing, the solution of any PDE using the finite elements method yields a large sparse system of equations. In the nonlinear case the method is iterative so you need to solve a linear system many times. The applications in physics are countless. To name a few:

  • Numerical general relativity
  • Hydrodynamics
  • Magnetohydrodynamics
  • Stellar structure and evolution
  • Scattering and propagation of electromagnetic radiation

Then you have differential-integral equations such as those coming from computational quantum mechanics (Hartree-Fock, Density Functional), electrostatics and countless other places. These transform to systems of linear equations under most numerical methods

All in all, without additional qualifications the list is simply too long. Equation systems are everywhere!

This post has been migrated from (A51.SE)
answered Dec 26, 2011 by Squark (1,725 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights