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comparison Notes.md @ 1382:1aee4e6206c2 feature/variable_derivatives

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Merge
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 08 Jun 2023 15:51:52 +0200
parents e9dfc1998d31
children bdcdbd4ea9cd 88e738d807cb
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1376:2ad2de55061a 1382:1aee4e6206c2
69 If possible the goal should be for the parsing to get all the way to the 69 If possible the goal should be for the parsing to get all the way to the
70 stencils so that a user calls `read_stencil_set` and gets a 70 stencils so that a user calls `read_stencil_set` and gets a
71 dictionary-structure containing stencils, tuples, scalars and other types 71 dictionary-structure containing stencils, tuples, scalars and other types
72 ready for input to the methods creating the operators. 72 ready for input to the methods creating the operators.
73 73
74 ## Variable second derivative
75
76 2020-12-08 after discussion with Vidar:
77 We will have to handle the variable second derivative in a new variant of
78 VolumeOperator, "SecondDerivativeVariable?". Somehow it needs to know about
79 the coefficients. They should be provided as an AbstractVector. Where they are
80 provided is another question. It could be that you provide a reference to the
81 array to the constructor of SecondDerivativeVariable. If that array is mutable
82 you are free to change it whenever and the changes should propagate
83 accordingly. Another option is that the counter part to "Laplace" for this
84 variable second derivate returns a function or acts like a functions that
85 takes an Abstract array and returns a SecondDerivativeVariable with the
86 appropriate array. This would allow syntax like `D2(a)*v`. Can this be made
87 performant?
88
89 For the 1d case we can have a constructor
90 `SecondDerivativeVariable(D2::SecondDerivativeVariable, a)` that just creates
91 a copy with a different `a`.
92
93 Apart from just the second derivative in 1D we need operators for higher
94 dimensions. What happens if a=a(x,y)? Maybe this can be solved orthogonally to
95 the `D2(a)*v` issue, meaning that if a constant nD version of
96 SecondDerivativeVariable is available then maybe it can be wrapped to support
97 function like syntax. We might have to implement `SecondDerivativeVariable`
98 for N dimensions which takes a N dimensional a. If this could be easily
99 closured to allow D(a) syntax we would have come a long way.
100
101 For `Laplace` which might use a variable D2 if it is on a curvilinear grid we
102 might want to choose how to calculate the metric coefficients. They could be
103 known on closed form, they could be calculated from the grid coordinates or
104 they could be provided as a vector. Which way you want to do it might change
105 depending on for example if you are memory bound or compute bound. This choice
106 cannot be done on the grid since the grid shouldn't care about the computer
107 architecture. The most sensible option seems to be to have an argument to the
108 `Laplace` function which controls how the coefficients are gotten from the
109 grid. The argument could for example be a function which is to be applied to
110 the grid.
111
112 What happens if the grid or the varible coefficient is dependent on time?
113 Maybe it becomes important to support `D(a)` or even `D(t,a)` syntax in a more
114 general way.
115
116 ```
117 g = TimeDependentGrid()
118 L = Laplace(g)
119 function Laplace(g::TimeDependentGrid)
120 g_logical = logical(g) # g_logical is time independent
121 ... Build a L(a) assuming we can do that ...
122 a(t) = metric_coeffs(g,t)
123 return t->L(a(t))
124 end
125 ```
126
127 ## Known size of range and domain? 74 ## Known size of range and domain?
128 Is there any reason to use a trait to differentiate between fixed size and unknown size? 75 Is there any reason to use a trait to differentiate between fixed size and unknown size?
129 76
130 When do we need to know the size of the range and domain? 77 When do we need to know the size of the range and domain?
131 * When indexing to provide boundschecking? 78 * When indexing to provide boundschecking?