{"action":"created","issue":{"url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl/issues/51","repository_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl","labels_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl/issues/51/labels{/name}","comments_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl/issues/51/comments","events_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl/issues/51/events","html_url":"https://github.com/JuliaDiffEq/DiffEqOperators.jl/issues/51","id":301940763,"number":51,"title":"Document the new discretization and boundary values","user":{"login":"jlperla","id":13106721,"avatar_url":"https://avatars2.githubusercontent.com/u/13106721?v=4","gravatar_id":"","url":"https://api.github.com/users/jlperla","html_url":"https://github.com/jlperla","followers_url":"https://api.github.com/users/jlperla/followers","following_url":"https://api.github.com/users/jlperla/following{/other_user}","gists_url":"https://api.github.com/users/jlperla/gists{/gist_id}","starred_url":"https://api.github.com/users/jlperla/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jlperla/subscriptions","organizations_url":"https://api.github.com/users/jlperla/orgs","repos_url":"https://api.github.com/users/jlperla/repos","events_url":"https://api.github.com/users/jlperla/events{/privacy}","received_events_url":"https://api.github.com/users/jlperla/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":{"login":"stevenzhangdx","id":30738391,"avatar_url":"https://avatars0.githubusercontent.com/u/30738391?v=4","gravatar_id":"","url":"https://api.github.com/users/stevenzhangdx","html_url":"https://github.com/stevenzhangdx","followers_url":"https://api.github.com/users/stevenzhangdx/followers","following_url":"https://api.github.com/users/stevenzhangdx/following{/other_user}","gists_url":"https://api.github.com/users/stevenzhangdx/gists{/gist_id}","starred_url":"https://api.github.com/users/stevenzhangdx/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/stevenzhangdx/subscriptions","organizations_url":"https://api.github.com/users/stevenzhangdx/orgs","repos_url":"https://api.github.com/users/stevenzhangdx/repos","events_url":"https://api.github.com/users/stevenzhangdx/events{/privacy}","received_events_url":"https://api.github.com/users/stevenzhangdx/received_events","type":"User","site_admin":false},"assignees":[{"login":"stevenzhangdx","id":30738391,"avatar_url":"https://avatars0.githubusercontent.com/u/30738391?v=4","gravatar_id":"","url":"https://api.github.com/users/stevenzhangdx","html_url":"https://github.com/stevenzhangdx","followers_url":"https://api.github.com/users/stevenzhangdx/followers","following_url":"https://api.github.com/users/stevenzhangdx/following{/other_user}","gists_url":"https://api.github.com/users/stevenzhangdx/gists{/gist_id}","starred_url":"https://api.github.com/users/stevenzhangdx/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/stevenzhangdx/subscriptions","organizations_url":"https://api.github.com/users/stevenzhangdx/orgs","repos_url":"https://api.github.com/users/stevenzhangdx/repos","events_url":"https://api.github.com/users/stevenzhangdx/events{/privacy}","received_events_url":"https://api.github.com/users/stevenzhangdx/received_events","type":"User","site_admin":false},{"login":"FernandoKuwer","id":35511185,"avatar_url":"https://avatars2.githubusercontent.com/u/35511185?v=4","gravatar_id":"","url":"https://api.github.com/users/FernandoKuwer","html_url":"https://github.com/FernandoKuwer","followers_url":"https://api.github.com/users/FernandoKuwer/followers","following_url":"https://api.github.com/users/FernandoKuwer/following{/other_user}","gists_url":"https://api.github.com/users/FernandoKuwer/gists{/gist_id}","starred_url":"https://api.github.com/users/FernandoKuwer/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/FernandoKuwer/subscriptions","organizations_url":"https://api.github.com/users/FernandoKuwer/orgs","repos_url":"https://api.github.com/users/FernandoKuwer/repos","events_url":"https://api.github.com/users/FernandoKuwer/events{/privacy}","received_events_url":"https://api.github.com/users/FernandoKuwer/received_events","type":"User","site_admin":false}],"milestone":null,"comments":3,"created_at":"2018-03-02T23:43:45Z","updated_at":"2018-03-20T17:29:36Z","closed_at":null,"author_association":"NONE","body":"@stevenzhangdx  @FernandoKuwer \r\nI added in a placeholder `.tex` file in `/docs/linear_operators_overview.tex` which you can compile.  The idea is that you can write up all of the algebra required to understand the discretization of the operators and boundary values.  Remember that the main description is the https://github.com/JuliaDiffEq/DifferentialEquations.jl/issues/260 issue.  In particular, figuring out the B, Q, R, A, etc. matrices.\r\n\r\nInstead of worrying about the solutions to the full PDEs, we should start by just looking at the stationary problems.  The PDEs can come later once we figure out how the discretization works.  \r\n\r\nI also put the julia code for at least one or two of them in the `/docs/operator_examples` directory.  We should put all of the code there that implements our descriptions."},"comment":{"url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl/issues/comments/374686607","html_url":"https://github.com/JuliaDiffEq/DiffEqOperators.jl/issues/51#issuecomment-374686607","issue_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl/issues/51","id":374686607,"user":{"login":"jlperla","id":13106721,"avatar_url":"https://avatars2.githubusercontent.com/u/13106721?v=4","gravatar_id":"","url":"https://api.github.com/users/jlperla","html_url":"https://github.com/jlperla","followers_url":"https://api.github.com/users/jlperla/followers","following_url":"https://api.github.com/users/jlperla/following{/other_user}","gists_url":"https://api.github.com/users/jlperla/gists{/gist_id}","starred_url":"https://api.github.com/users/jlperla/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jlperla/subscriptions","organizations_url":"https://api.github.com/users/jlperla/orgs","repos_url":"https://api.github.com/users/jlperla/repos","events_url":"https://api.github.com/users/jlperla/events{/privacy}","received_events_url":"https://api.github.com/users/jlperla/received_events","type":"User","site_admin":false},"created_at":"2018-03-20T17:29:36Z","updated_at":"2018-03-20T17:29:36Z","author_association":"NONE","body":"Some comments from editing the document:\r\n- Need a notation for the extension of the domain and the domain itself.  This will become especailly important with jumps\r\n  - Use $i=1,... I$ as the grid in the interior.  So the solution to the discretized function is $u \\in R^I$ if stationary\r\n  - The total size if $\\hat{I} > I$.\r\n  - In general, use a hat when looking at the extension.  Then $\\hat{u} \\in R^{\\hat{I}}$ is the extension of $u \\in R^I$.  Replace the current $v$ with $\\hat{u}$\r\n  - For the steady state, just drop the $t$ for now.\r\n  - When dealing with a univariate function with 2 sides, can denote the extra points as $I_L$ and $I_H$ so that $\\hat{I} = I + I_L + I_H$.  For example, with a univariate diffusion operator, $I_L = I_H = 1$\r\n  - $R$ is a $I \\times \\hat{I}$ matrix, etc.\r\n  - Change the basic notation to stack the BC1 and BC2 on the bottom instead of on the top and bottom.\r\n  - Rename BC1 and BC2.   \r\n- When we start writing up the examples, we can make the main description more generic\r\n  -  As we go through the first example, we can convert the main description to be fully generic in terms of $\\hat{I}, I,$ etc.\r\n  - Move the Dirichlet, etc. to the examples sections to map into the B, Q, etc.\r\n  - I think (6) and (7) will be clearer with the generic notation.\r\n  - Try to get rid of the $v_t$, etc. notation for the discretization?.  Too easy to confuse with a partial...  Can abuse the $u$ vector and the $u$ function notation?\r\n  - Lets get rid of the $f$ and just use $u$..."}}
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