{"action":"created","issue":{"url":"https://api.github.com/repos/firedrakeproject/tsfc/issues/158","repository_url":"https://api.github.com/repos/firedrakeproject/tsfc","labels_url":"https://api.github.com/repos/firedrakeproject/tsfc/issues/158/labels{/name}","comments_url":"https://api.github.com/repos/firedrakeproject/tsfc/issues/158/comments","events_url":"https://api.github.com/repos/firedrakeproject/tsfc/issues/158/events","html_url":"https://github.com/firedrakeproject/tsfc/pull/158","id":297173762,"number":158,"title":"Support averaging operators (fixes #107)","user":{"login":"wence-","id":1126981,"avatar_url":"https://avatars2.githubusercontent.com/u/1126981?v=4","gravatar_id":"","url":"https://api.github.com/users/wence-","html_url":"https://github.com/wence-","followers_url":"https://api.github.com/users/wence-/followers","following_url":"https://api.github.com/users/wence-/following{/other_user}","gists_url":"https://api.github.com/users/wence-/gists{/gist_id}","starred_url":"https://api.github.com/users/wence-/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/wence-/subscriptions","organizations_url":"https://api.github.com/users/wence-/orgs","repos_url":"https://api.github.com/users/wence-/repos","events_url":"https://api.github.com/users/wence-/events{/privacy}","received_events_url":"https://api.github.com/users/wence-/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":4,"created_at":"2018-02-14T17:06:14Z","updated_at":"2018-02-15T10:39:44Z","closed_at":null,"author_association":"CONTRIBUTOR","pull_request":{"url":"https://api.github.com/repos/firedrakeproject/tsfc/pulls/158","html_url":"https://github.com/firedrakeproject/tsfc/pull/158","diff_url":"https://github.com/firedrakeproject/tsfc/pull/158.diff","patch_url":"https://github.com/firedrakeproject/tsfc/pull/158.patch"},"body":"Done by just integrating the averaged expression over the relevant\r\nentity.\r\n\r\nNeeds a matching UFL merge."},"comment":{"url":"https://api.github.com/repos/firedrakeproject/tsfc/issues/comments/365888762","html_url":"https://github.com/firedrakeproject/tsfc/pull/158#issuecomment-365888762","issue_url":"https://api.github.com/repos/firedrakeproject/tsfc/issues/158","id":365888762,"user":{"login":"wence-","id":1126981,"avatar_url":"https://avatars2.githubusercontent.com/u/1126981?v=4","gravatar_id":"","url":"https://api.github.com/users/wence-","html_url":"https://github.com/wence-","followers_url":"https://api.github.com/users/wence-/followers","following_url":"https://api.github.com/users/wence-/following{/other_user}","gists_url":"https://api.github.com/users/wence-/gists{/gist_id}","starred_url":"https://api.github.com/users/wence-/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/wence-/subscriptions","organizations_url":"https://api.github.com/users/wence-/orgs","repos_url":"https://api.github.com/users/wence-/repos","events_url":"https://api.github.com/users/wence-/events{/privacy}","received_events_url":"https://api.github.com/users/wence-/received_events","type":"User","site_admin":false},"created_at":"2018-02-15T10:39:44Z","updated_at":"2018-02-15T10:39:44Z","author_association":"CONTRIBUTOR","body":"I don't think so.  Here's my reasoning.  For a function `f`, the mean over some compact domain U is `1/Vol(U) \\int f dU`.  Which, with quadrature, is `(\\sum_q w_q f_q) / (\\sum_q w_q)`.\r\n\r\nNow consider integrating `cell_avg(f)*dx`.\r\n\r\nThis is `\\int_\\Omega \\bar{f} dx = \\sum_e \\int_e \\bar{f} dx_e`.\r\n\r\nNow I pull back to reference space:\r\n\r\n`\\sum_e \\int_e \\bar{f} dx_e = \\sum_e \\int_E \\bar{\\tilde{f}} \\det J dX`\r\n\r\nand `\\bar{\\tilde{f}} = \\int_E \\tilde{f} dX / Vol(dX)` (because we're already in reference space).\r\n\r\nI think the only thing I assumed here was that averaging commutes will pullback.\r\n\r\nDoes this make sense?"}}
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