{"action":"created","issue":{"url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl/issues/53","repository_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl","labels_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl/issues/53/labels{/name}","comments_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl/issues/53/comments","events_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl/issues/53/events","html_url":"https://github.com/JuliaDiffEq/DiffEqOperators.jl/issues/53","id":301964777,"number":53,"title":"BC Overhaul","user":{"login":"ChrisRackauckas","id":1814174,"avatar_url":"https://avatars2.githubusercontent.com/u/1814174?v=4","gravatar_id":"","url":"https://api.github.com/users/ChrisRackauckas","html_url":"https://github.com/ChrisRackauckas","followers_url":"https://api.github.com/users/ChrisRackauckas/followers","following_url":"https://api.github.com/users/ChrisRackauckas/following{/other_user}","gists_url":"https://api.github.com/users/ChrisRackauckas/gists{/gist_id}","starred_url":"https://api.github.com/users/ChrisRackauckas/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ChrisRackauckas/subscriptions","organizations_url":"https://api.github.com/users/ChrisRackauckas/orgs","repos_url":"https://api.github.com/users/ChrisRackauckas/repos","events_url":"https://api.github.com/users/ChrisRackauckas/events{/privacy}","received_events_url":"https://api.github.com/users/ChrisRackauckas/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":0,"created_at":"2018-03-03T03:39:49Z","updated_at":"2018-03-03T04:31:27Z","closed_at":null,"author_association":"OWNER","body":"Long discussions with @dlfivefifty and @jlperla led to a big shift in the way we are doing BCs. The idea is outlined https://github.com/JuliaDiffEq/DifferentialEquations.jl/issues/260#issuecomment-370111767 . For DiffEqOperators.jl to change to support this, we need to do the following:\r\n\r\n1. The DerivativeOperators should be the non-square `A` interior stencil calculations. All interior, no boundaries. `full`, `sparse`, `banded`, etc. should be defined on the stencil to make it easy to get matrices out.\r\n2. Lazy `R` should be created. That's super simple of course. And full/space/etc. here too.\r\n3. Lazy `Q` should be created for each of the FDM boundary types. So there should be a constructor `FDMExtension(...)` which takes in boundary types and spits out an operator which does this operation. `Q` can be an affine operator. We'll need to define that such that `(Qa,Qb) = full(Q)`. And full/space/etc. here too.\r\n4. In this form, `v_t = L*v` can be written at `v_t = A*Qa*v + A*Qb`.\r\n5. We should have a lazy `L`, dependent on the BCs, which is `L*v = A*Qa*v + A*Qb`. \r\n6. In this form, `(L1+L2)*v` is well-defined as `(A1+A2)*Qa*v + (A1+A2)*Qb`.\r\n\r\nEvery step of the way should get tests of course. "},"comment":{"url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl/issues/comments/370117085","html_url":"https://github.com/JuliaDiffEq/DiffEqOperators.jl/issues/53#issuecomment-370117085","issue_url":"https://api.github.com/repos/JuliaDiffEq/DiffEqOperators.jl/issues/53","id":370117085,"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":"2018-03-03T04:31:27Z","updated_at":"2018-03-03T04:31:27Z","author_association":"NONE","body":"@stevenzhangdx @FernandoKuwer   Note, even more description for your writeup and test cases."}}
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