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Merge branch 'develop' of https://github.com/feelpp/book.feelpp.org into develop
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‎.github/workflows/main.yml

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# python-version: '3.10'
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# cache: 'pip' # caching pip dependencies
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- name: Python install
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run: pip install -r requirements.txt
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run: |
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python -m venv --system-site-packages .venv
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source .venv/bin/activate
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pip install -r requirements.txt
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- name: Npm Install
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run: |
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npm i
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asciidoctor -v
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- name: Build
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run: npm run antora
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run: |
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source .venv/bin/activate
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npm run antora
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env:
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FEELPP_GITHUB_TOKEN: ${{ secrets.DOCS_GITHUB_KEY }}
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GITHUB_OAUTH: ${{ secrets.DOCS_GITHUB_KEY }}

‎.gitignore

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/**/node_modules/
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/**/build/
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/**/feelppdb/
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/**/toto/
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/**/*DS_Store
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‎docs/mor/modules/opusheat/assets/images/eads_geometry.png renamed to ‎docs/mor/modules/ROOT/assets/images/opusheat/eads_geometry.png

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‎docs/mor/modules/ROOT/assets/images/thermalbuilding/3d_building.png

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‎docs/mor/modules/ROOT/assets/images/thermalbuilding/heat_3d.png

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‎docs/mor/modules/ROOT/nav.adoc

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* xref:toolboxmor.adoc[ToolboxMor]
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** xref:toolboxmor.adoc#_creating_a_model_from_scratch[Creating a model from scratch]
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** xref:toolboxmor.adoc#_creating_a_model_from_a_toolbox[Creating a model from a toolbox]
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** xref:toolboxmor.adoc#_configuration[Configuration]
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* xref:pbdw.adoc[PBDW]
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** xref:pbdw.adoc#_sensors[Sensors]
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** xref:pbdw.adoc#_using_pbdw[Using PBDW]
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* xref:index.adoc#_cases[Cases]
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** xref:opusheat:index.adoc[OpusHeat]
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** xref:thermalfin:index.adoc[ThermalFin]

‎docs/mor/modules/ROOT/pages/index.adoc

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= Model Order Reduction
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:page-layout: case-study
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:page-tags: toolbox
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Welcome to the documentation of the Feel++ Model Order Reduction.
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== Introduction
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Feel++ provides a framework for model order reduction. +
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One easy way to use it, is to use the xref:toolboxmor.adoc[ToolboxMor] class.
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The Parametrized Background Data Weak (xref:pbdw.adoc[PBDW]) method has also been implemented in Feel++.
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== Cases
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- xref:opusheat:index.adoc[OpusHeat]
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- xref:thermalfin:index.adoc[ThermalFin]

‎docs/mor/modules/opusheat/pages/index.adoc renamed to ‎docs/mor/modules/ROOT/pages/opusheat/index.adoc

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= Opus Heat
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:page-tags: case
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:page-illustration: opusheat/eads_geometry.png
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:description: We consider a reduced 2D model of the surroundings of an electronic component submitted to a cooling air flow.
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This test case has been proposed by mailto:[email protected][Annabelle Le-Hyaric] and
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mailto:[email protected][Michel Fouquembergh] formerly at AIRBUS.
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ICs dissipate heat, so the volumic heat dissipated stem:[Q_1] and stem:[Q_2] are also parameters of the model, while stem:[Q_3=Q_4=0].
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image::eads_geometry.png[]
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image::opusheat/eads_geometry.png[]
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One should notice that the convection term in heat transfer equation
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may lead to spatial oscillations which can be overcome by

‎docs/mor/modules/ROOT/pages/pbdw.adoc

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= Parametrized Background Data Weak
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:page-tags: manual
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:description: PBDW manual
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:page-illustration: pass:[toolboxes::manual.svg]
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== Sensors
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‎docs/mor/modules/ROOT/pages/thermalbuilding/index.adoc

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= Thermal simulation of 3D building
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:stem: latexmath
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:page-tags: case
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:page-illustration: thermalbuilding/3d_building.png
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:description: We create a reduced order model for the thermal simulation of a 3D building using the stationary heat equation.
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:uri-data: https://github.com/feelpp/feelpp/blob/develop/mor/examples/thermalbuilding/
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== Description
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Based on the solution of the stationary heat equation, we create a reduced order model for the simulation of heat exchanges in a 3D building.
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The building is composed of a corridor and 5 rooms, each of which contains a heating unit. Internal walls and doors are modelled as having finite thickness, while external walls properties (thickness and insulation) are encoded in the boundary conditions of the problem.
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// Image
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=== Mathematical model
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Let stem:[\Omega \subset \mathbb{R}^3] be the region occupied by the building, and denote stem:[\Omega_i], stem:[i=0,1,2] its subregions occupied by the air, the internal walls and the internal doors, such that stem:[\Omega = \cup_{i=0}^2 \Omega_i]. Let stem:[k_i] be the thermal conductivities associated with the subregions.
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The external boundary of the domain stem:[\partial \Omega] is decomposed into two parts: stem:[\partial \Omega_{ext}], which corresponds to external walls, and stem:[\partial \Omega_D] which corresponds to the front door. We denote by stem:[\Gamma_i] the boundary of the stem:[i-]th heating unit, stem:[i=0,...,4]. The problem writes as
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[stem]
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++++
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\begin{equation}
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\begin{aligned}
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- \nabla \cdot (k_i\nabla u) &= 0, \quad &\text{on }\Omega_i \\
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u &= \mu_i \quad &\text{on }\Gamma_i, i=0,...,4, \\
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- k_0 \nabla u \cdot \vec{n} &= \mu_6 (u - \mu_5), \quad &\text{on }\partial \Omega_{ext},\\
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- k_0 \nabla u \cdot \vec{n} &= \sigma (u - \mu_5), \quad &\text{on }\partial \Omega_{D}.
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\end{aligned}
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\end{equation}
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++++
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where stem:[\sigma] is the convective heat exchange coefficient associated with the front door.
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The parameters stem:[\mu_i] correspond to
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* stem:[\mu_i \in (300,340)], for stem:[i=0,...,4], are the surface temperatures of the heating units (in Kelvin);
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* stem:[\mu_5 \in (270,290)] is the external temperature (in Kelvin);
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* stem:[\mu_6] is a function of the external wall thickness. The wall is composed of two layers: a cinder layer of thickness stem:[l_{cinder} \in (0.1,0.3) m] and an insulation layer of thickness stem:[l_{insulation} \in (0.1,0.2) m], and
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[stem]
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++++
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\mu_6 = \frac{1}{0.06 + \frac{0.01}{0.5} + \frac{l_{cinder}}{0.8} + \frac{l_{insulation}}{0.032} + \frac{0.016}{0.313} + 0.14}.
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++++
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=== Construction of the affine decomposition
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The problem presents an affine dependence on the parameters, hence we can explicity compute the terms of the correspondent affine decomposition
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[stem]
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++++
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\sum_{i = 0}^{N_A} \theta^A_i(\mu) A_i(u,v) = \sum_{j = 0}^{N_F} \theta^F_j(\mu) F_j(v),
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++++
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where stem:[N_A = 1] and stem:[N_F = 6].
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The first product on the left-hand side is given by stem:[\theta^A_0(\mu) = 1] and
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[stem]
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++++
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\begin{equation}
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\begin{aligned}
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A_0(u,v) &= \sum_{i=0}^{N_m} \int_{\Omega_i} k_i \nabla u \cdot \nabla v + \\
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& - \int_{\partial \Omega_{ext}} k_0 (\nabla u v + \nabla v u )\cdot \vec{n} + \\
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& + \int_{\partial \Omega_{ext}} k_0 \frac{\gamma}{h} u v +\\
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& + \int_{\partial \Omega_D} uv,
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\end{aligned}
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\end{equation}
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++++
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where stem:[\gamma] is the Nitsche penalty parameter and stem:[h] is the local mesh size.
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The second product is given by stem:[\theta^A_1(\mu) = \mu_6] and
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[stem]
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++++
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A_1(u,v) = \int_{\partial \Omega_{ext}} u v.
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++++
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The terms on the right-hand side are stem:[\theta^F_i(\mu) = \mu_i] for stem:[i=0,...,4], corresponding to the temperatures of the heating units, stem:[\theta^F_5(\mu) = \mu_5\mu_6], corresponding to the temperature on the internal surface of the external walls, and stem:[\theta^F_6(\mu) = \mu_5], corresponding to the external temperature. The corresponding linear forms are
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[stem]
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++++
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\begin{equation}
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\begin{aligned}
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F_i (v) &= k_0 \int_{\Gamma_i} -\nabla v \cdot \vec{n} + \frac{\gamma}{h} v, \quad i = 0,...,4\\
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F_5 (v) &= \int_{\partial \Omega_{ext}} v,\\
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F_6 (v) &= \int_{\partial \Omega_D} \sigma v.
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\end{aligned}
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\end{equation}
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++++
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=== Geometry
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image::thermalbuilding/heat_3d.png[]
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The geometry file can be found in Github link:{uri-data}/thermalbuilding/thermalbuilding.geo[here].
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== Output
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The output corresponds to the air mean temperature, and it is computed as
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[stem]
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++++
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\begin{equation}
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s(\mu) = \frac{1}{|\Omega_0|} \int_{\Omega_0} u.
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\end{equation}
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++++
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== Parameters
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The table displays the various fixed and variables parameters of this test-case.
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.Table of model order reduction parameters
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[width="100%"]
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|=======================================================================
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| Name | Description | Range | Units
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| stem:[\mu_0] | Heater temperature living room | stem:[[300,340]] | stem:[K]
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| stem:[\mu_1] | Heater temperature kitchen | stem:[[300,340]] | stem:[K]
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| stem:[\mu_2] | Heater temperature bedroom 1 | stem:[[300,340]] | stem:[K]
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| stem:[\mu_3] | Heater temperature bedroom 2 | stem:[[300,340]] | stem:[K]
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| stem:[\mu_4] | Heater temperature bathroom | stem:[[300,340]] | stem:[K]
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| stem:[\mu_5] | External temperature | stem:[[270,290]] | stem:[K]
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| stem:[\mu_6] | Exchange coefficient external walls | |
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|=======================================================================
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.Table of constant parameters
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[width="100%"]
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|=======================================================================
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| Name | Description | Range | Units
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| stem:[\gamma] | Boundary conditions using Nitsche method | stem:[[10]] |
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| stem:[\k_0] | Air conductivity | stem:[1] |
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| stem:[\k_1] | Conductivity - internal walls | stem:[0.25] |
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| stem:[\k_2] | Conductivity - internal doors | stem:[0.13] |
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| stem:[\sigma] | Heat transfer coefficient - front door | stem:[\frac{1.0}{0.06+\frac{0.06}{0.150}+\frac{0.1}{0.029}+0.14}] |
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|=======================================================================

‎docs/mor/modules/ROOT/pages/thermalfin/index.adoc

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= Thermal fin
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:page-tags: case
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:page-illustration: pass:[toolboxes::wip/wip-1.svg]
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:description: Work in progress.
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The redaction of this page is in progress.

‎docs/mor/modules/ROOT/pages/toolboxmor.adoc

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= ToolboxMor
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:page-tags: manual
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:description: ToolboxMor manual
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:page-illustration: pass:[toolboxes::manual.svg]
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ToolboxMor is a class aiming to ease the use of the model order reduction framework of Feel++.
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Usually, you would need to define a class which would handle the initialization of the model, its affine decomposition and possibly the use of the EIM methods.

‎docs/mor/modules/opusheat/nav.adoc

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‎docs/mor/modules/thermalfin/nav.adoc

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‎docs/mor/modules/thermalfin/pages/index.adoc

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‎docs/user/modules/python/pages/pyfeelpp/filters.adoc

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[%dynamic,python]
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----
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import feelpp
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import sys
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import sys,os
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import spdlog as spd
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from feelpp.timing import tic, toc
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logger = spd.ConsoleLogger('Logger', False, True, True)
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logger.set_level(spd.LogLevel.TRACE)
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tic()
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app = feelpp.Environment(["myapp"],config=feelpp.localRepository("")) # <1>
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toc("init Feel++")
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logger.info(f"Feel++ version: {feelpp.Info.version()}")
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<1> The {feelpp} environment is initiated with the name of the application and the path to the local repository where the results will be stored.
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app.setLogVerbosityLevel(0) # <1>
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geofilename=feelpp.download( "github:{repo:feelpp,path:feelpp/quickstart/laplacian/cases/feelpp2d/feelpp2d.geo}", worldComm=app.worldCommPtr() )[0]
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tic()
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mesh = feelpp.load(feelpp.mesh(dim=2,realdim=2), name=geofilename, h=0.1, verbose=1) # <2>
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toc("load mesh")
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logger.info(f"mesh loaded")
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Xh=feelpp.functionSpace(mesh=mesh,space="Pch",order=1) # <3>
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P0h=feelpp.functionSpace(mesh=mesh,space="Pdh",order=0) # <4>
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u=Xh.element() # <5>
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u.on(range=feelpp.elements(mesh), expr=feelpp.expr("sin(2*pi*x)*cos(pi*y):x:y")) # <6>
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logger.info(f"functionspace built and u created")
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e = feelpp.exporter(mesh=mesh) # <7>
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e.add("a_scalar", 1.) # <8>
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e.add("u",u) # <9>
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e.add("pid",feelpp.pid( P0h )) # <10>
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e.save() # <11>
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logger.info(f"export done")
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----
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<1> The verbosity level is set to 0 (only `VLOG(level)` with `level <= 0` are displayed)
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<2> The mesh is loaded from the {uri-github-feelpp} repository
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mesh = reader.read()
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return mesh
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def pv_plot(mesh, field="u", clim=None, cmap='viridis', cpos='xy', show_scalar_bar=True, show_edges=True):
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mesh.plot(scalars=field, clim=clim, cmap=cmap, cpos=cpos, show_scalar_bar=show_scalar_bar, show_edges=show_edges)
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plotter = pv.Plotter()
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plotter.show_axes()
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mesh = pv_get_mesh(f"exports/ensightgold/Exporter/Exporter.case")
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plotter.add_mesh(mesh, scalars="u", clim=None, cmap="viridis", show_scalar_bar=True, show_edges=True)
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plotter.camera_position = 'xy'
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axes = pv.create_axes_marker(
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line_width=4,
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ambient=0.0,
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x_color="#378df0",
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y_color="#ab2e5d",
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z_color="#f7fb9a",
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xlabel="X Axis",
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ylabel="Y Axis",
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zlabel="Z Axis",
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label_size=(0.1, 0.1), label_color="#aaaaaa",
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)
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plotter.add_actor(axes)
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plotter.show()
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----
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‎lib/dynamic-notebook.js

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let source = response[index].stdout.toString('utf8')
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if (block.isOption('raw')) {
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if (block.getAttribute('output') === 'pyvista') {
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logger.debug(source)
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source = source.replace(pyvistaContainerRx, `var container = document.getElementById('pyvista-${index}')`)
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source = source.replace(pyvistaFaviconRx, '')
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const found = source.match(pyvistaScriptRx)

‎requirements.txt

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xvfbwrapper
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ipykernel
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pythreejs
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plotly
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plotly
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trame-vtk
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trame
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spdlog

‎site-dev.yml

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title: Feel++ // Docs
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url: https://docs.feelpp.org
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start_page: home::index.adoc
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runtime:
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log:
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level: debug
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content:
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sources:
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- url: ./
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- url: ./
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branches: develop
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start_path: docs/salome/
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- url: ../Antora/antora-ui
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branches: mais
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start_path: docs/
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# - url: ../Antora/antora-ui
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# branches: mais
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# start_path: docs/
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# - url: ./
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# branches: mor-module
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# start_path: docs/mor/

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