update author

chapter0/bezier-curves.md

@@ -1,4 +1,5 @@
 # Bézier curves
+*Author: Ahmed Ratnani*
 
 We recall the definition of a Bézier curve:
 

chapter0/bezier.md

@@ -1,4 +1,5 @@
 # Bernstein polynomials
+*Author: Ahmed Ratnani*
 
 Without loss of generality, we restrict to the case of the unit interval, namely $a=0$ and $b=1$.
 In figure (Fig. \ref{fig:bernstein-polynomials}), we plot the first sixth Bernstein polynomials.

chapter0/bsplines-curves.md

@@ -1,4 +1,5 @@
 # B-Splines curves
+*Author: Ahmed Ratnani*
 
 Let $(\mathbf{P}_i)_{ 0 \leqslant i \leqslant n}\in \mathbb{R}^d$  be a sequence of control points. Following the same approach as for Bézier curves, we define B-Splines curves as
 

chapter0/bsplines-operations.md

@@ -1,5 +1,5 @@
 # Fundamental geometric operations for B-Splines
-
+*Author: Ahmed Ratnani*
 
 Having more control on a curve, adding new control points, can be done in two different ways:
 

chapter0/bsplines-surfaces.md

@@ -1,4 +1,5 @@
 # B-Splines surfaces
+*Author: Ahmed Ratnani*
 
 The B-spline surface in $\mathbb{R}^d$ associated to knots $(T_u, T_v)$ where $T_u=(u_i)_{0\leqslant i \leqslant n_u + p_u + 1}$ and $T_v=(v_i)_{0\leqslant i \leqslant n_v + p_v + 1}$, and control points $(\mathbf{P}_{ij})_{ 0 \leqslant i \leqslant n_u,  0 \leqslant j \leqslant n_v}$ is defined by :
 

chapter0/bsplines.md

@@ -1,4 +1,5 @@
 # B-Splines
+*Author: Ahmed Ratnani*
 
 Given a subdivision $\{x_0 <  x_1 < \cdots < x_r\}$ of the interval $I = [x_0, x_r]$, the \textbf{Schoenberg space} is the space of piecewise polynomials of degree $p$, on the interval $I$ and given regularities $\{k_1, k_2, \cdots, k_{r-1}\}$ at the internal points $\{x_1, x_2, \cdots, x_{r-1}\}$. 
 

chapter0/cad.md

@@ -1,3 +1,4 @@
 # Computer Aided Design
+*Author: Ahmed Ratnani*
 
 TODO

chapter0/data-structure.md

@@ -1,4 +1,5 @@
 # Data Structure
+*Author: Ahmed Ratnani*
 
 In the sequel, we shall use **StencilMatrix** and **StencilVector** from the **psydac** library.
 

chapter0/fem.md

@@ -1,4 +1,5 @@
 # Introduction to B-Splines FEM
+*Author: Ahmed Ratnani*
 
 Let $\Omega \subset \mathbb{R}^d$ be a computational domain that is the image of a logical domain $\mathcal{P}$, *i.e.* a unit line (in *1d*), square (in *2d*) or a cube (in *3d*) with a **mapping** function 
 

chapter0/howto.md

@@ -1,2 +1,2 @@
 # What to expect from IGA-Python
-
+*Author: Ahmed Ratnani*

chapter0/iga.md

@@ -1,3 +1,4 @@
 # Isogeometric Analysis 
+*Author: Ahmed Ratnani*
 
 TODO

chapter0/performance-acceleration.md

@@ -1,4 +1,5 @@
 # Performance and Acceleration
+*Author: Ahmed Ratnani*
 
 In this section, we shall see how to accelerate our Python code assembly and get native speed.
 We will be using [Numba](https://numba.pydata.org/) and [Pyccel](https://github.com/pyccel/pyccel).

chapter0/poisson-1d.md

@@ -1,4 +1,5 @@
 # B-splines FEM solver for Poisson equation (1D)
+*Author: Ahmed Ratnani*
 
 Following the previous [section](http://nbviewer.jupyter.org/github/ratnania/IGA-Python/blob/main/lessons/Chapter1/01_introduction_fem.ipynb), we implement here a B-Splines FEM for the Poisson problem in 1D, with homogeneous boundary conditions.
 

chapter0/poisson-2d.md

@@ -1,4 +1,5 @@
 # B-splines FEM solver for Poisson equation (2D)
+*Author: Ahmed Ratnani*
 
 In this section, we show hoa to use **simplines** to solve a 2D Poisson problem with homogeneous boundary conditions
 $$

chapter1/install.md

@@ -1,4 +1,5 @@
 # Installation
+*Author: Ahmed Ratnani*
 
 It is recommanded to use a virtual environement.
 

chapter1/poisson.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Your first code using SymPDE & PsyDAC\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "We first start by writing our first example using SymPDE.\n",
     "Let $\\Omega := (0,1)^2$. We consider the Poisson problem with homogeneous Dirichlet boundary conditions.  \n",

chapter1/rules.md

@@ -1,4 +1,5 @@
 # Algebraic and differential operators evalution rules
+*Author: Ahmed Ratnani*
 
 ## Evaluation of the $\mathrm{grad}$ operator 
 

chapter1/space.md

@@ -1,4 +1,5 @@
 # Function Space concepts
+*Author: Ahmed Ratnani*
 
 SymPDE provides two Python classes to describe scalar and vector function spaces, respectively. There is no notion of a discrete representation; for example, we do not need to mention that a space is a Brezzi-Douglas-Marini (BDM) space. In fact, these kind of function spaces can be seen as parametric types having as a basic type **ScalarFunctionSpace** or **VectorFunctionSpace**. SymPDE only needs to know if an element of the space can be indexed or not. A BDM space would then be identified by an annotation added by a third party library to uniquely define a function space at the discrete level.
 

chapter1/sympde.md

@@ -1,4 +1,5 @@
 # SymPDE concepts and their mathematical meaning
+*Author: Ahmed Ratnani*
 
 ## Domain
 

chapter1/topology.md

@@ -1,4 +1,5 @@
 # Topology concepts
+*Author: Ahmed Ratnani*
 
 ## Domain
 

chapter2/advection-diffusion-stabilized.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Stabilized advection-diffusion equation\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "In the sequel we consider two different stabilization methods, leading to formulations of the form\n",
     "\n",

chapter2/advection-diffusion.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Advection-diffusion equation\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "We consider the advection-diffusion problem consisting of finding a scalar-valued function $u$ such that\n",
     "\n",

chapter2/biharmonic.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# The Biharmonic problem\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "We consider the (inhomogeneous) biharmonic equation with homogeneous essential boundary conditions,\n",
     "\n",

chapter2/elliptic-curl.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Elliptic-curl Problem\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "Let $\\Omega \\subset \\mathbb{R}^d$ be an open Liptschitz bounded set, and we look for the solution of the following problem\n",
     "\n",

chapter2/elliptic-div.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Elliptic-div Problem\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "Let $\\Omega \\subset \\mathbb{R}^d$ be an open Liptschitz bounded set, and we look for the solution of the following problem\n",
     "\n",

chapter2/elliptic-general-form.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Elliptic equation in the general form\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "We consider here, the following general form of an elliptic partial differential equation,\n",
     "\n",

chapter2/linear-elasticity.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Linear Elasticity Problem\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "Analysis of deformable structures is essential in engineering, with the equations of linear elasticity being fundamental in this field. In this section, we present the variational formulation of linear elasticity equations using the principle of virtual work.\n",
     "\n",

chapter2/poisson-mixed-v1.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# First mixed formulation of the Poisson problem\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "Instead of having one unknown, we now have two, along with the above two equations.\n",
     "In order to get a mixed variational formulation, we first take the dot product of the first one by $ \\mathbf{v}$ and integrate by parts\n",

chapter2/poisson-mixed-v2.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Second mixed formulation of the Poisson problem\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "Here, we get an alternative formulation by not integrating by parts, the mixed term in the first formulation but in the second. The first formulation simply becomes\n",
     "\n",

chapter2/poisson-mixed.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Mixed FEM for the Poisson problem\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "Let $\\Omega \\subset \\mathbb{R}^3$ and consider the Poisson problem\n",
     "\n",

chapter2/poisson-nitsche.ipynb

@@ -5,7 +5,8 @@
    "id": "119eb328",
    "metadata": {},
    "source": [
-    "# The Poisson equation with weak imposition of Dirichlet conditions"
+    "# The Poisson equation with weak imposition of Dirichlet conditions\n",
+    "*Author: Ahmed Ratnani*"
    ]
   },
   {

chapter2/poisson.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# The Poisson equation\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "As a first example, we consider the Poisson equation\n",
     "\n",

chapter2/stokes-v1.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# First mixed formulation of the Stokes problem\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "For the variational formulation, we take the dot product of the first equation with $v$ and integrate over the whole domain\n",
     "\n",

chapter2/stokes-v2.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Second mixed formulation of the Stokes problem\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "Another possibility to obtained a well posed variational formulation, is to integrate by parts the\n",
     "$\\int_{\\Omega} \\nabla p \\cdot \\mathbf{v} ~\\mathrm{d} \\mathbf{x}$ term in the first formulation:\n",

chapter2/stokes.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Mixed FEM for the Stokes problem \n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "We consider now the Stokes problem for the steady-state modelling of an incompressible fluid\n",
     "\n",

chapter2/vector-poisson.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Vector Poisson equation \n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "In this example we consider the vector Poisson equation with homogeneous Dirichlet boundary conditions:\n",
     "\n",

chapter3/burgers.md

@@ -1,4 +1,5 @@
 # 1D Burgers equation
+*Author: Ahmed Ratnani*
 
 We consider the 1d Burgers equation
 

chapter3/navier-stokes-steady-streamfunction-velocity.md

@@ -1,4 +1,5 @@
 # The streamfunction-velocity formulation of the steady-state Navier-Stokes equations for incompressible fluids
+*Author: Ahmed Ratnani*
 
 When $\Omega$ is a simply connected 2D domain, there exists a unique function $\psi$ such that $\mathbf{u} = \boldsymbol{\nabla} \times \psi:= \left( \partial_y \psi, - \partial_x \psi \right)$;
 substituting this expression for $\mathbf{u}$ into \eqref{eq:steady-navier-stokes} leads to the so-called ``streamfunction-velocity formulation'' of the steady-state Navier-Stokes equations for an incompressible fluid.

chapter3/navier-stokes-steady.md

@@ -1,4 +1,5 @@
 # the steady-state Navier-Stokes equations for incompressible fluids
+*Author: Ahmed Ratnani*
 
 The steady-state Navier Stokes problem for an incompressible fluid, with homogeneous Dirichlet boundary conditions (``no slip'' condition), is defined as
 

chapter3/poisson.md

@@ -1,4 +1,5 @@
 # Nonlinear Poisson in 2D
+*Author: Ahmed Ratnani*
 
 In this section, we consider the non-linear Poisson problem:
 

chapter4/poisson-multi-subdomains-nitsche.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# The Poisson problem using Nitsche method on multiple subdomains\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "We consider a 2D domain $\\Omega$, that is subdivided into a grid of small squares, using the **meshgrid** function.\n",
     "Each subdomain has the form $(x_{i}, x_{i+1}) \\times (y_{j}, y_{j+1})$, where $x_1, ..., x_{n_x}$ and $y_1, ..., y_{n_y}$ are subdivisions in each axis.\n"

chapter4/poisson-two-subdomains-nitsche.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# The Poisson problem using Nitsche method on two subdomains\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "We consider a domain $\\Omega = \\Omega_1 \\bigcup \\Omega_2 = (0,1)^2$, where $\\Omega_1 = (0,\\frac{1}{2}) \\times (0,1)$ and $\\Omega_2 = (\\frac{1}{2}, 1) \\times (0,1)$\n",
     "\n",

chapter5/bingham_plastic_flow_in_a_pipe.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Bingham Plastic Flow in a Pipe\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "## Mathematical Model\n",
     "\n",

chapter5/buoyancy-driven_natural_convection.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Buoyancy-Driven Natural Convection\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "## Mathematical Model\n",
     "\n",

chapter5/casson_fluid_flow_in_a_channel.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Casson Fluid Flow in a Channel\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "## Mathematical Model\n",
     "\n",

chapter5/cfd.md

@@ -1 +1,2 @@
 # Computational Fluid Dynamics
+*Author: Ahmed Ratnani*

chapter5/compressible_flow_in_a_nozzle.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Compressible Flow in a Nozzle\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "## Mathematical Model\n",
     "\n",

chapter5/convection-diffusion_equation_in_a_channel.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Convection-Diffusion Equation in a Channel\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "## Mathematical Model\n",
     "\n",

chapter5/cross_power_law_fluid_flow_in_a_channel.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Cross Power Law Fluid Flow in a Channel\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "## Mathematical Model\n",
     "\n",

chapter5/electromagnetics.md

@@ -1,4 +1,5 @@
 # Electromagnetics
+*Author: Ahmed Ratnani*
 
 Electromagnetic problems are commonly described by Maxwell's equations, which govern the behavior of electric and magnetic fields. The Finite Element Method (FEM) provides a powerful numerical approach for solving these equations in complex geometries. This section provides a concise overview of the mathematical formulation for electromagnetic problems using finite elements.
 

chapter5/free_surface_flow.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Free Surface Flow (Navier-Stokes with Free Surface)\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "## Mathematical Model\n",
     "\n",

chapter5/fsi.md

@@ -1,4 +1,5 @@
 # Fluid-Structure Interaction
+*Author: Ahmed Ratnani*
 
 Fluid-Structure Interaction (FSI) involves the coupled interaction between a fluid and a structure, where the motion of one influences the behavior of the other. The Finite Element Method (FEM) is a powerful tool for simulating FSI problems. This section provides an overview of the mathematical formulation for fluid-structure interaction using finite elements.
 

chapter5/heat_conduction_in_a_solid.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Heat Conduction in a Solid\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "## Mathematical Model\n",
     "\n",

chapter5/herschel-bulkley_fluid_flow_in_a_pipe.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Herschel-Bulkley Fluid Flow in a Pipe\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "## Mathematical Model\n",
     "\n",

chapter5/incompressible_flow_past_a_cylinder.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Incompressible Flow Past a Cylinder\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "## Mathematical Model:\n",
     "\n",

chapter5/magnetohydrodynamics_flow.ipynb

@@ -6,6 +6,7 @@
    "metadata": {},
    "source": [
     "# Magnetohydrodynamics (MHD) Flow\n",
+    "*Author: Ahmed Ratnani*\n",
     "\n",
     "## Mathematical Model\n",
     "\n",

chapter5/material-science.md

@@ -1 +1,2 @@
 # Material Science
+*Author: Ahmed Ratnani*