From 22c5f5c38670eb235f60f5378a8afc0620cd6587 Mon Sep 17 00:00:00 2001 From: mbouyges Date: Wed, 13 Mar 2024 15:37:21 +0100 Subject: [PATCH 1/9] how to build custom operator --- docs/make.jl | 2 +- docs/src/howto/howto.md | 39 +++++++++++++++++++++++++++++++++++---- 2 files changed, 36 insertions(+), 5 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index 75473390..b2a032c9 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -39,7 +39,7 @@ makedocs(; "api/dof/dof.md", "api/output/vtk.md", ], - "How to..." => "howto/howto.md", + "How to... (FAQ)" => "howto/howto.md", ], ) diff --git a/docs/src/howto/howto.md b/docs/src/howto/howto.md index b0e4f91d..b6ab8042 100644 --- a/docs/src/howto/howto.md +++ b/docs/src/howto/howto.md @@ -1,17 +1,48 @@ -# How to +# How to... (FAQ) -To be completed to answer common user questions. +## Build your own `LazyOperator` +Imagine that you want some kind of function (~operator) that has a different behavior depending on the cell (or face) it is applied to. The `PhysicalFunction` won't do the job since it is assumed that the provided function applies the same way in all the different cells. What you want is a `LazyOperator`. Here is how to build a custom one. + +For the example, let's say that you want an operator whose action is to multiply `x`, the evaluated point, by the index of the cell surrounding `x`. Start importing some Bcube material and by declaring a type corresponding to this operator: +```julia +using Bcube +import Bcube: CellInfo, CellPoint, get_coord, LazyOperators +struct DummyOperator <: Bcube.AbstractLazy end +``` + +Then, specify what happens when `Bcube` asks for the restriction of your operator in a given cell. This is done before applying it to any point. In most case, you don't want to do anything special, so just return the operator itself: +```julia +LazyOperators.materialize(Op::DummyOperator, ::CellInfo) = Op +``` + +Now, specify what to return when `Bcube` wants to apply this operator on a given point in a cell. As said earlier, we want it the return the point, multiplied by the cell index (but it could be anything you want): +```julia +function LazyOperators.materialize( + ::DummyOperator, + cPoint::CellPoint, +) + x = get_coord(cPoint) + cInfo = Bcube.get_cellinfo(cPoint) + index = Bcube.cellindex(cInfo) + return x * index +end +``` + +That's it! To see your operator in action, take a look at the related [section](@ref Evaluate-a-LazyOperator-on-a-specific-point). + +In this short example, note that we restricted ourselves to `CellPoint` : the `DummyOperator` won't be applicable to a face. To do so, you have to specialize the materialization on a `Side` of a `FaceInfo` and on a `Side` of a `FacePoint`. Checkout the source code for `TangentialProjector` to see this in action. Besides, the `CellPoint` is parametrized by a `DomainStyle`, allowing to specify different behavior depending on if your operator is applied to a point in the `ReferenceDomain` or in the `PhysicalDomain`. ## Evaluate a `LazyOperator` on a specific point Suppose that you have built a mesh and defined a `LazyOperator` on this mesh and you want, for debug purpose, evaluate this operator on a point of your choice. First, let's define our example operator: ```julia +using Bcube mesh = circle_mesh(10) -op = Bcube.TangentialOperator() +op = Bcube.TangentialProjector() ``` Then, let's define the point where we want to evaluate this operator. For this, we need to create a so-called `CellPoint`. It's structure is quite basic : it needs the coordinates, the mesh cell owning these coordinates, and if the coordinates are given in the `ReferenceDomain` or in the `PhysicalDomain`. Here, we will select the first cell of the mesh, and choose the coordinates `[0.5]` (recall that we are in 1D, hence this vector of one component): ```julia cInfo = Bcube.CellInfo(mesh, 1) -cPoint = Bcube.CellPoint(SA[0.5], cInfo, Bcube.ReferenceDomain()) +cPoint = Bcube.CellPoint([0.5], cInfo, Bcube.ReferenceDomain()) ``` Now, they are always two steps to evaluate a `LazyOperator`. First we need to materialize it on a cell (or a face) and then to evaluate it on a cell-point (or face-point). The materialization on a cell does not necessarily triggers something, it depends on the operator. For instance, an analytic function will not have a specific behaviour depending on the cell; however a shape function will. ```julia From b812776cd4142d472ab21f773d96511f4e4f618f Mon Sep 17 00:00:00 2001 From: mbouyges Date: Wed, 13 Mar 2024 15:44:16 +0100 Subject: [PATCH 2/9] tiny typo --- docs/src/howto/howto.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/src/howto/howto.md b/docs/src/howto/howto.md index b6ab8042..538436b1 100644 --- a/docs/src/howto/howto.md +++ b/docs/src/howto/howto.md @@ -12,7 +12,7 @@ struct DummyOperator <: Bcube.AbstractLazy end Then, specify what happens when `Bcube` asks for the restriction of your operator in a given cell. This is done before applying it to any point. In most case, you don't want to do anything special, so just return the operator itself: ```julia -LazyOperators.materialize(Op::DummyOperator, ::CellInfo) = Op +LazyOperators.materialize(op::DummyOperator, ::CellInfo) = op ``` Now, specify what to return when `Bcube` wants to apply this operator on a given point in a cell. As said earlier, we want it the return the point, multiplied by the cell index (but it could be anything you want): From 410ede95839e7d20e144a6049219e35fcdc9dad7 Mon Sep 17 00:00:00 2001 From: mbouyges Date: Wed, 13 Mar 2024 16:06:41 +0100 Subject: [PATCH 3/9] tiny modif --- docs/src/howto/howto.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/src/howto/howto.md b/docs/src/howto/howto.md index 538436b1..d433e3ef 100644 --- a/docs/src/howto/howto.md +++ b/docs/src/howto/howto.md @@ -6,18 +6,18 @@ Imagine that you want some kind of function (~operator) that has a different beh For the example, let's say that you want an operator whose action is to multiply `x`, the evaluated point, by the index of the cell surrounding `x`. Start importing some Bcube material and by declaring a type corresponding to this operator: ```julia using Bcube -import Bcube: CellInfo, CellPoint, get_coord, LazyOperators +import Bcube: CellInfo, CellPoint, get_coord struct DummyOperator <: Bcube.AbstractLazy end ``` Then, specify what happens when `Bcube` asks for the restriction of your operator in a given cell. This is done before applying it to any point. In most case, you don't want to do anything special, so just return the operator itself: ```julia -LazyOperators.materialize(op::DummyOperator, ::CellInfo) = op +materialize(op::DummyOperator, ::CellInfo) = op ``` Now, specify what to return when `Bcube` wants to apply this operator on a given point in a cell. As said earlier, we want it the return the point, multiplied by the cell index (but it could be anything you want): ```julia -function LazyOperators.materialize( +function materialize( ::DummyOperator, cPoint::CellPoint, ) From 0364dfab3ce6edaac95bb36ebe98078ad0ddcd9b Mon Sep 17 00:00:00 2001 From: mbouyges Date: Wed, 13 Mar 2024 16:15:16 +0100 Subject: [PATCH 4/9] revert to Bcube.materialize --- docs/src/howto/howto.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/src/howto/howto.md b/docs/src/howto/howto.md index d433e3ef..47a3602d 100644 --- a/docs/src/howto/howto.md +++ b/docs/src/howto/howto.md @@ -12,12 +12,12 @@ struct DummyOperator <: Bcube.AbstractLazy end Then, specify what happens when `Bcube` asks for the restriction of your operator in a given cell. This is done before applying it to any point. In most case, you don't want to do anything special, so just return the operator itself: ```julia -materialize(op::DummyOperator, ::CellInfo) = op +Bcube.materialize(op::DummyOperator, ::CellInfo) = op ``` Now, specify what to return when `Bcube` wants to apply this operator on a given point in a cell. As said earlier, we want it the return the point, multiplied by the cell index (but it could be anything you want): ```julia -function materialize( +function Bcube.materialize( ::DummyOperator, cPoint::CellPoint, ) From 6c25998bd3447a2757fbc307a62832f316a84c40 Mon Sep 17 00:00:00 2001 From: bmxam Date: Tue, 26 Mar 2024 22:20:44 +0100 Subject: [PATCH 5/9] doc_integration_sketch --- .gitignore | 5 +++ docs/src/assets/sketch/sketch-integration.pdf | Bin 0 -> 49867 bytes docs/src/assets/sketch/sketch-integration.tex | 35 ++++++++++++++++++ 3 files changed, 40 insertions(+) create mode 100644 docs/src/assets/sketch/sketch-integration.pdf create mode 100644 docs/src/assets/sketch/sketch-integration.tex diff --git a/.gitignore b/.gitignore index aadca965..f7802c15 100644 --- a/.gitignore +++ b/.gitignore @@ -13,4 +13,9 @@ benchmark/Manifest.toml params.json .ipynb_checkpoints/ /example/private/ +*.aux +*.fls +*.log +*.synctex.gz +*.fdb_latexmk diff --git 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\sum_{i=1}^N \hat{\lambda}(\xi, \eta)M_i$ + } (LINE_E); + + \pgfmathsetmacro{\x}{\refXMax + 2*\arrowMarginX + \arrowWidth}; + \draw (\x, 0) to ++(1,1) to ++(0, 1) to ++(-1,0) to cycle; + + +\end{tikzpicture} +\end{document} \ No newline at end of file From 89c9943bec24134c1442423371cc560a2fdc3449 Mon Sep 17 00:00:00 2001 From: mbouyges Date: Wed, 27 Mar 2024 11:58:12 +0100 Subject: [PATCH 6/9] sketch --- .gitignore | 5 - docs/src/assets/sketch/.gitignore | 6 ++ docs/src/assets/sketch/sketch-integration.png | Bin 0 -> 44015 bytes docs/src/assets/sketch/sketch-integration.tex | 91 +++++++++++++++--- docs/src/manual/geometry.md | 2 + 5 files changed, 87 insertions(+), 17 deletions(-) create mode 100644 docs/src/assets/sketch/.gitignore create mode 100644 docs/src/assets/sketch/sketch-integration.png diff --git a/.gitignore b/.gitignore index f7802c15..aadca965 100644 --- a/.gitignore +++ b/.gitignore @@ -13,9 +13,4 @@ benchmark/Manifest.toml params.json .ipynb_checkpoints/ 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\usetikzlibrary{calc, backgrounds} +\documentclass[tikz,convert={density=600,size=1080x800,outext=.png}]{standalone} % we can also output .svg +\usetikzlibrary{backgrounds} \usepackage{amsmath} \newcommand{\bo}[1]{\boldsymbol{#1}} +\tikzset{background fill/.style={background rectangle/.style={fill=#1},show background rectangle}} \begin{document} -\begin{tikzpicture} +\begin{tikzpicture}[background fill=white] + % Background rectangle + % \fill[color=red] (-1,-1) rectangle (10,3); + % Globals \pgfmathsetmacro{\refXMin}{0} \pgfmathsetmacro{\refXMax}{2} - \pgfmathsetmacro{\arrowWidth}{4} - \pgfmathsetmacro{\arrowMarginX}{0.5} + % Ref quad \coordinate (REF_SW) at (\refXMin, \refXMin); \coordinate (REF_NE) at (\refXMax, \refXMax); + \draw[color=black] (REF_SW) rectangle (REF_NE); + + \pgfmathsetmacro{\x}{\refXMin}; + \pgfmathsetmacro{\y}{0}; + \coordinate (A) at (\x,\y); + \node[font=\tiny] at (A) {$\times$}; + \node[below, font=\tiny] at (A) {$(-1,-1)$}; + + \pgfmathsetmacro{\x}{\refXMax}; + \pgfmathsetmacro{\y}{0}; + \coordinate (B) at (\x,\y); + \node[font=\tiny] at (B) {$\times$}; + \node[below, font=\tiny] at (B) {$(1,-1)$}; + + \pgfmathsetmacro{\x}{\refXMax}; + \pgfmathsetmacro{\y}{\refXMax}; + \coordinate (C) at (\x,\y); + \node[font=\tiny] at (C) {$\times$}; + \node[above, font=\tiny] at (C) {$(1,1)$}; + + \pgfmathsetmacro{\x}{\refXMin}; + \pgfmathsetmacro{\y}{\refXMax}; + \coordinate (D) at (\x,\y); + \node[font=\tiny] at (D) {$\times$}; + \node[above, font=\tiny] at (D) {$(-1,1)$}; + + \pgfmathsetmacro{\x}{\refXMin - 0.7} + \pgfmathsetmacro{\y}{\refXMin - 0.6} + \draw[->] (\x,\y) -- ++(0.4, 0) node[below] {\tiny $\xi$}; + \draw[->] (\x,\y) -- ++(0, 0.4) node[left] {\tiny $\eta$}; + + + % Map line + \pgfmathsetmacro{\arrowWidth}{4} + \pgfmathsetmacro{\arrowMarginX}{0.5} \pgfmathsetmacro{\x}{\refXMax+\arrowMarginX} \pgfmathsetmacro{\y}{(\refXMax-\refXMin)/2} \coordinate (LINE_W) at (\x, \y); \pgfmathsetmacro{\x}{\x+\arrowWidth} \coordinate (LINE_E) at (\x, \y); - - \draw[color=black] (REF_SW) rectangle (REF_NE); - - \draw[->] (LINE_W) to[out=10,in=170] node[midway, above]{ + \draw[->] (LINE_W) to[bend left = 10] node[midway, above]{ $\bo{x} = F(\bo{\xi}) = \sum_{i=1}^N \hat{\lambda}_i(\bo{\xi})\bo{M}_i$ - % $\begin{pmatrix}x \\ y\end{pmatrix} = F(\xi, \eta) = \sum_{i=1}^N \hat{\lambda}(\xi, \eta)M_i$ } (LINE_E); + % Physical quad \pgfmathsetmacro{\x}{\refXMax + 2*\arrowMarginX + \arrowWidth}; - \draw (\x, 0) to ++(1,1) to ++(0, 1) to ++(-1,0) to cycle; + \pgfmathsetmacro{\y}{0}; + \coordinate (A) at (\x,\y); + \node[font=\tiny] at (A) {+}; + \node[below, font=\tiny] at (A) {$M_1$}; + + \pgfmathsetmacro{\x}{\x + 2}; + \pgfmathsetmacro{\y}{\y + 1}; + \coordinate (B) at (\x,\y); + \node[font=\tiny] at (B) {+}; + \node[right, font=\tiny] at (B) {$M_2$}; + + \pgfmathsetmacro{\x}{\x + 0.3}; + \pgfmathsetmacro{\y}{\y + 1.5}; + \coordinate (C) at (\x,\y); + \node[font=\tiny] at (C) {+}; + \node[right, font=\tiny] at (C) {$M_3$}; + + \pgfmathsetmacro{\x}{\x - 1.5}; + \pgfmathsetmacro{\y}{\y - 0.6}; + \coordinate (D) at (\x,\y); + \node[font=\tiny] at (D) {+}; + \node[left, font=\tiny] at (D) {$M_4$}; + + \pgfmathsetmacro{\x}{\x + 0.5}; + \pgfmathsetmacro{\y}{\y - 0.5}; + \coordinate (E) at (\x,\y); + \node[font=\tiny] at (E) {+}; + \node[below, font=\tiny] at (E) {$M_9$}; + + \draw[font=\tiny] (A) to[bend right = 15] node[midway] {+} node[midway,below] {$M_{5}$} (B) to[bend left = 15] node[midway] {+} node[midway,right] {$M_{6}$} (C) to[bend right = 20] node[midway] {+} node[midway,above] {$M_{7}$} (D) to[bend left=15] node[midway] {+} node[midway,left] {$M_{8}$} cycle; + \pgfmathsetmacro{\x}{\refXMax + 2*\arrowMarginX + \arrowWidth + 2} + \pgfmathsetmacro{\y}{0 - 0.6} + \draw[->] (\x,\y) -- ++(0.4, 0) node[below] {\tiny $x$}; + \draw[->] (\x,\y) -- ++(0, 0.4) node[left] {\tiny $y$}; \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/docs/src/manual/geometry.md b/docs/src/manual/geometry.md 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docs/src/manual/geometry.md | 2 +- docs/src/manual/integration.md | 4 ++-- src/mesh/entity.jl | 2 +- 5 files changed, 4 insertions(+), 4 deletions(-) rename docs/src/assets/sketch/{sketch-integration.png => sketch-mapping.png} (100%) rename docs/src/assets/sketch/{sketch-integration.tex => sketch-mapping.tex} (100%) diff --git a/docs/src/assets/sketch/sketch-integration.png b/docs/src/assets/sketch/sketch-mapping.png similarity index 100% rename from docs/src/assets/sketch/sketch-integration.png rename to docs/src/assets/sketch/sketch-mapping.png diff --git a/docs/src/assets/sketch/sketch-integration.tex b/docs/src/assets/sketch/sketch-mapping.tex similarity index 100% rename from docs/src/assets/sketch/sketch-integration.tex rename to docs/src/assets/sketch/sketch-mapping.tex diff --git a/docs/src/manual/geometry.md b/docs/src/manual/geometry.md index 4bd42ebf..b237be10 100644 --- a/docs/src/manual/geometry.md +++ b/docs/src/manual/geometry.md @@ -10,4 +10,4 @@ F(\xi) = \sum_{i=1}^n \hat{\lambda}_i(\xi)M_i where $(\lambda)_i$ are the Lagrange polynomials whose order matches the element order. -![sketch](../assets/sketch/sketch-integration.png) +![sketch](../assets/sketch/sketch-mapping.png) diff --git a/docs/src/manual/integration.md b/docs/src/manual/integration.md index 1e6677ee..c218cbff 100644 --- a/docs/src/manual/integration.md +++ b/docs/src/manual/integration.md @@ -8,10 +8,10 @@ To compute an integral on a geometrical element, for instance a curved element, where we recall that $$F$$ is the reference to physical mapping and $$J$$ is the determinant of the jacobian matrix of this mapping. Depending on the shape and element order, this determinant is either hard-coded or computed with `ForwardDiff`. -Now, to compute the right side, i.e the integral on the reference shape, quadrature rules are applied: +Now, to compute the right side, i.e the integral on the reference shape, quadrature rules are applied to $\hat{g} = g \circ F$: ```math -\int_{\hat{\Omega}} g(\hat{x}) \mathrm{\,d} \hat{\Omega} = \sum_{i =1}^{N_q} \omega_i g(\hat{x}_i) +\int_{\hat{\Omega}} \hat{g}(\hat{x}) \mathrm{\,d} \hat{\Omega} = \sum_{i =1}^{N_q} \omega_i \hat{g}(\hat{x}_i) ``` A specific procedure is applied to compute integrals on a face of a cell (i.e a surfacic integral on a face of a volumic element). diff --git a/src/mesh/entity.jl b/src/mesh/entity.jl index d1f12ea8..605a7a3b 100644 --- a/src/mesh/entity.jl +++ b/src/mesh/entity.jl @@ -512,7 +512,7 @@ struct isVolumic <: TopologyStyle end """ topology_style(::AbstractEntityType{topoDim}, ::Node{spaceDim, T}) where {topoDim, spaceDim, T} topology_style(::AbstractEntityType{topoDim}, ::AbstractArray{Node{spaceDim, T}, N}) where {spaceDim, T, N, topoDim} -) + Indicate the `TopologyStyle` of an entity of topology `topoDim` living in space of dimension `spaceDim`. 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\tikzset{background fill/.style={background rectangle/.style={fill=#1},show background rectangle}} @@ -44,8 +45,8 @@ \pgfmathsetmacro{\x}{\refXMin - 0.7} \pgfmathsetmacro{\y}{\refXMin - 0.6} - \draw[->] (\x,\y) -- ++(0.4, 0) node[below] {\tiny $\xi$}; - \draw[->] (\x,\y) -- ++(0, 0.4) node[left] {\tiny $\eta$}; + \draw[-{Latex[length=1mm, width=1mm]}] (\x,\y) -- ++(0.4, 0) node[below] {\tiny $\xi$}; + \draw[-{Latex[length=1mm, width=1mm]}] (\x,\y) -- ++(0, 0.4) node[left] {\tiny $\eta$}; % Map line @@ -95,8 +96,8 @@ \pgfmathsetmacro{\x}{\refXMax + 2*\arrowMarginX + \arrowWidth + 2} \pgfmathsetmacro{\y}{0 - 0.6} - \draw[->] (\x,\y) -- ++(0.4, 0) node[below] {\tiny $x$}; - \draw[->] (\x,\y) -- ++(0, 0.4) node[left] {\tiny $y$}; + \draw[-{Latex[length=1mm, width=1mm]}] (\x,\y) -- ++(0.4, 0) node[below] {\tiny $x$}; + \draw[-{Latex[length=1mm, width=1mm]}] (\x,\y) -- ++(0, 0.4) node[left] {\tiny $y$}; \end{tikzpicture} \end{document} \ No newline at end of file