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Remove notes on boundary conditions. They are now obsolete.
author Vidar Stiernström <vidar.stiernstrom@gmail.com>
date Sun, 09 Jun 2024 16:46:40 -0700
parents d68d02dd882f
children 8141c184cc2f
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1608:8315c456e3b4 1611:8ebcac8edd9d
1 # Notes 1 # Notes
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3 ## Boundary Conditions and SATs
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5 Types for boundary conditions:
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7 * abstract type `BoundaryData`
8 * abstract type `BoundaryCondition{T<:BoundaryData}`
9 * concrete types `ConstantBoundaryData <: BoundaryData` and similar
10 * concrete types `NeumannCondition{BD<:BoundaryData} <: BoundaryCondition{BD}` and similar
11 The concrete `BoundaryData` subtypes are "thin types" wrapping the boundary data, and are used to indicate how the boundary data should be used in e.g. sat routines. The concrete `BoundaryCondition{BD}` subtypes are used for assembling the tensors used to construct e.g. a SAT.
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13 SAT methods:
14 There are multiple options for what the SAT methods could return.
15 * (Current) a function which returns a `LazyTensorApplication`, e.g. `f = sat(grid,op,bc)`. The the resulting `LazyTensorApplication` can then be added to scheme i.e. `scheme = op*u + f(u)`. Depdending on the type of data in the BC, e.g. time-depdendent etc one can return f(u,t).
16 * `LazyTensor`s `closure, penalty = sat(grid,op,bc)` like in the matlab version. Probably the most general one. Up to the user to make use of the returned `LazyTensor`s. One can for example then easily include the closures to the operator and have eg. `D = (op + closure)*u`.
17 * A `LazyTensor` for closure, and a `LazyArray` for `penalty*data`. Mix of the above.
18 * Same as first but of the form sat = `sat_op*(L*u-g)`. This is how one typically would write the SAT in the litterature. The function `sat_tensors` would return `sat_op` and `L`. Need to get compositions working before we can implement this approach.
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20 2
21 ## Reading operators 3 ## Reading operators
22 4
23 Jonatan's suggestion is to add methods to `Laplace`, `SecondDerivative` and 5 Jonatan's suggestion is to add methods to `Laplace`, `SecondDerivative` and
24 similar functions that take in a filename from which to read stencils. These 6 similar functions that take in a filename from which to read stencils. These