{"action":"created","issue":{"url":"https://api.github.com/repos/mit-crpg/OpenMOC/issues/162","labels_url":"https://api.github.com/repos/mit-crpg/OpenMOC/issues/162/labels{/name}","comments_url":"https://api.github.com/repos/mit-crpg/OpenMOC/issues/162/comments","events_url":"https://api.github.com/repos/mit-crpg/OpenMOC/issues/162/events","html_url":"https://github.com/mit-crpg/OpenMOC/pull/162","id":92110999,"number":162,"title":"Secondary eigenvalue capabilities using Krylov subspace methods","user":{"login":"cjosey","id":354602,"avatar_url":"https://avatars.githubusercontent.com/u/354602?v=3","gravatar_id":"","url":"https://api.github.com/users/cjosey","html_url":"https://github.com/cjosey","followers_url":"https://api.github.com/users/cjosey/followers","following_url":"https://api.github.com/users/cjosey/following{/other_user}","gists_url":"https://api.github.com/users/cjosey/gists{/gist_id}","starred_url":"https://api.github.com/users/cjosey/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/cjosey/subscriptions","organizations_url":"https://api.github.com/users/cjosey/orgs","repos_url":"https://api.github.com/users/cjosey/repos","events_url":"https://api.github.com/users/cjosey/events{/privacy}","received_events_url":"https://api.github.com/users/cjosey/received_events","type":"User","site_admin":false},"labels":[{"url":"https://api.github.com/repos/mit-crpg/OpenMOC/labels/Enhancement","name":"Enhancement","color":"006b75"}],"state":"open","locked":false,"assignee":{"login":"PrezNattyGibbs","id":1434947,"avatar_url":"https://avatars.githubusercontent.com/u/1434947?v=3","gravatar_id":"","url":"https://api.github.com/users/PrezNattyGibbs","html_url":"https://github.com/PrezNattyGibbs","followers_url":"https://api.github.com/users/PrezNattyGibbs/followers","following_url":"https://api.github.com/users/PrezNattyGibbs/following{/other_user}","gists_url":"https://api.github.com/users/PrezNattyGibbs/gists{/gist_id}","starred_url":"https://api.github.com/users/PrezNattyGibbs/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/PrezNattyGibbs/subscriptions","organizations_url":"https://api.github.com/users/PrezNattyGibbs/orgs","repos_url":"https://api.github.com/users/PrezNattyGibbs/repos","events_url":"https://api.github.com/users/PrezNattyGibbs/events{/privacy}","received_events_url":"https://api.github.com/users/PrezNattyGibbs/received_events","type":"User","site_admin":false},"milestone":{"url":"https://api.github.com/repos/mit-crpg/OpenMOC/milestones/3","html_url":"https://github.com/mit-crpg/OpenMOC/milestones/v0.1.5","labels_url":"https://api.github.com/repos/mit-crpg/OpenMOC/milestones/3/labels","id":980734,"number":3,"title":"v0.1.5","description":"","creator":{"login":"wbinventor","id":209492,"avatar_url":"https://avatars.githubusercontent.com/u/209492?v=3","gravatar_id":"","url":"https://api.github.com/users/wbinventor","html_url":"https://github.com/wbinventor","followers_url":"https://api.github.com/users/wbinventor/followers","following_url":"https://api.github.com/users/wbinventor/following{/other_user}","gists_url":"https://api.github.com/users/wbinventor/gists{/gist_id}","starred_url":"https://api.github.com/users/wbinventor/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/wbinventor/subscriptions","organizations_url":"https://api.github.com/users/wbinventor/orgs","repos_url":"https://api.github.com/users/wbinventor/repos","events_url":"https://api.github.com/users/wbinventor/events{/privacy}","received_events_url":"https://api.github.com/users/wbinventor/received_events","type":"User","site_admin":false},"open_issues":8,"closed_issues":31,"state":"open","created_at":"2015-02-16T04:36:42Z","updated_at":"2015-07-26T20:52:25Z","due_on":"2015-05-31T04:00:00Z","closed_at":null},"comments":9,"created_at":"2015-06-30T14:34:46Z","updated_at":"2015-07-26T21:16:38Z","closed_at":null,"pull_request":{"url":"https://api.github.com/repos/mit-crpg/OpenMOC/pulls/162","html_url":"https://github.com/mit-crpg/OpenMOC/pull/162","diff_url":"https://github.com/mit-crpg/OpenMOC/pull/162.diff","patch_url":"https://github.com/mit-crpg/OpenMOC/pull/162.patch"},"body":"As per Will's request.\r\n\r\nThis modification allows the expression of the M and A operators of the  transport equation Ax = 1/k Mx as independent transport sweeps.  The method currently in OpenMOC represents a single operator on which a non-linear power iteration method is performed.\r\n\r\nAs separated operators, each can be cast as a SciPy LinearOperator and sparse matrix math can be performed.  In the example c5g7-krylov.py, I use a combination of GMRES and eigs (an IRAM implementation) to then solve for the first 6 eigenvalues and eigenvectors of the problem.\r\n\r\nThis method has a few caveats:\r\n* The method is not yet derived for any boundary condition other than vacuum.\r\n* It requires 2k+1 eigenvector-sized arrays to be stored, where k is the number of eigenvectors required.\r\n* Eigs does not output convergence information.\r\n* CMFD not only does not accelerate the method, but actively prevents it from working.\r\n* It is slower than unaccelerated non-linear power iteration for a single eigenvalue\r\n* GMRES must converge more tightly than IRAM, but I do not know by precisely how much.\r\n* I implemented it assuming double precision.  It can probably be rewritten to read the FP_PRECISION type and adjust accordingly.\r\n* Implementation was only done for CPUSolver"},"comment":{"url":"https://api.github.com/repos/mit-crpg/OpenMOC/issues/comments/125040953","html_url":"https://github.com/mit-crpg/OpenMOC/pull/162#issuecomment-125040953","issue_url":"https://api.github.com/repos/mit-crpg/OpenMOC/issues/162","id":125040953,"user":{"login":"cjosey","id":354602,"avatar_url":"https://avatars.githubusercontent.com/u/354602?v=3","gravatar_id":"","url":"https://api.github.com/users/cjosey","html_url":"https://github.com/cjosey","followers_url":"https://api.github.com/users/cjosey/followers","following_url":"https://api.github.com/users/cjosey/following{/other_user}","gists_url":"https://api.github.com/users/cjosey/gists{/gist_id}","starred_url":"https://api.github.com/users/cjosey/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/cjosey/subscriptions","organizations_url":"https://api.github.com/users/cjosey/orgs","repos_url":"https://api.github.com/users/cjosey/repos","events_url":"https://api.github.com/users/cjosey/events{/privacy}","received_events_url":"https://api.github.com/users/cjosey/received_events","type":"User","site_admin":false},"created_at":"2015-07-26T21:16:37Z","updated_at":"2015-07-26T21:16:37Z","body":"I'd probably just set it up so that the LinearOperator has two functions, the `matvec` which we already use, and `rmatvec` for the transpose.  I'd then set it up that whenever we switch between evaluating `matvec` and `rmatvec`, we'd call `Material::transposeProductionMatrices()` or `Solver::resetMaterials()` as needed.  "}}