Documentation Bug Fix

docs/_rst/_installation.rst

@@ -1,7 +1,7 @@
 Installation
 ============
 
-The build of the code is currently tested on Python 3.8, 3.9, 3.10 and 3.11. The code is CI tested on enviroinments provided by Github Actions such as `ubuntu-20.04`, `ubuntu-latest`, `macos-latest`,`windows-latest` , 
+The build of the code is currently tested on Python 3.8, 3.9, 3.10 and 3.11. The code is CI tested on environments provided by Github Actions such as `ubuntu-20.04`, `ubuntu-latest`, `macos-latest`, `windows-latest`, 
 refer to `Compatibility-CI <https://github.com/cmgcds/fastvpinns/actions/workflows/integration-tests.yml>`_ page for more details.
 
 Setting up an Virtual Environment
@@ -11,15 +11,15 @@ It is recommended to create a virtual environment to install the package. You ca
 
 .. code-block:: bash
 
-    $ python3 -m venv venv
-    $ source venv/bin/activate
+    python3 -m venv venv
+    source venv/bin/activate
 
 For conda users, you can create a virtual environment using the following command:
 
 .. code-block:: bash
 
-    $ conda create -n fastvpinns python=3.8
-    $ conda activate fastvpinns
+    conda create -n fastvpinns python=3.8
+    conda activate fastvpinns
 
 
 Installing via PIP
@@ -29,13 +29,13 @@ You can simply install the package using pip as follows:
 
 .. code-block:: bash
 
-    $ pip install fastvpinns
+    pip install fastvpinns
 
 On ubuntu/mac systems with libGL issues caused due to matplotlib or gmsh, please run the following command to install the required dependencies.
 
 .. code-block:: bash
 
-    $ sudo apt-get install libgl1-mesa-glx
+    sudo apt-get install libgl1-mesa-glx
 
 
 Installing from source
@@ -45,10 +45,11 @@ The official distribution is on GitHub, and you can clone the repository using
 
 .. code-block:: bash
     
-    $ git clone https://github.com/cmgcds/fastvpinns.git
+    git clone https://github.com/cmgcds/fastvpinns.git
 
 To install the package just type:
 
 .. code-block:: bash
 
-    $ pip install -e .
+    cd fastvpinns
+    pip install -e .

docs/_rst/_team.rst

@@ -5,5 +5,5 @@ FastVPINNs is currently developed by `Thivin Anandh <https://github.com/thivinan
 under supervision of `Prof. Sashikumaar Ganesan <http://cds.iisc.ac.in/faculty/sashi/>`_ at `STARS LAB, Indian Institute of Science, Bangalore <https://cmg.cds.iisc.ac.in/>`_. 
 
 
-The Authors would like to acknowkedge the support of Shell Technology Centre, India for their partial funding, We are thankful to the MHRD Grant No. STARS-1/388 (SPADE)
+The Authors would like to acknowledge the support of Shell Technology Centre, India for their partial funding, We are thankful to the MHRD Grant No. STARS-1/388 (SPADE)
 for partial support. 

docs/_rst/fastvpinns.rst

@@ -75,7 +75,6 @@ Finite Element Setup
    :maxdepth: 2
    :titlesonly:
 
-      Fespace(Abstract) <library/fe2d/fe2d_fespace.rst>
       Fespace2D  <library/fe2d/fe2d_fespace2d.rst>
       FE2DSetupMain <library/fe2d/fe2d_fe2d_setup.rst>
       FE2DCell <library/fe2d/fe2d_fe2d_cell.rst>

docs/_rst/tutorials/forward_problems_2d/complex_mesh/cd2d/cd2d.rst

@@ -3,7 +3,7 @@ Convection Diffusion 2D Example on Circular Domain
 
 
 This example demonstrates how to solve a Poisson equation in 2D on a circular domain using the ``fastvpinns`` package.
-All the necesary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
+All the necessary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
 
 The Poisson equation is given by
 
@@ -301,7 +301,7 @@ special type of Jacobi polynomials defined by
 
 .. math:: J_{n} = J_{n-1} - J_{n+1}
 
-, where $J_{n} is the nth Jacobi polynomial.
+, where J :sub:`n` is the nth Jacobi polynomial.
 
 `Return to top <#contents>`__
 
@@ -596,7 +596,7 @@ Initialise the ``DataHandler`` class with the required parameters.
 Setup model
 ^^^^^^^^^^^
 
-Setup the necesary parameters for the model and initialise the ``Model``
+Setup the necessary parameters for the model and initialise the ``Model``
 class. Before that fill the ``params`` dictionary with the required
 parameters.
 

docs/_rst/tutorials/forward_problems_2d/complex_mesh/cd2d_gear/cd2d_gear.rst

@@ -4,7 +4,7 @@ Convection-Diffusion 2D Example on Circular Domain
 
 This example demonstrates how to solve a Poisson equation in 2D on a
 circular domain using the ``fastvpinns`` package. 
-All the necesary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
+All the necessary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
 The Poisson equation is given by
 
 .. math::  -\epsilon \nabla^2 u  + \mathbf{b} \cdot \nabla u + cu = f \quad \text{in} \quad \Omega 
@@ -308,7 +308,7 @@ special type of Jacobi polynomials defined by
 
 .. math:: J_{n} = J_{n-1} - J_{n+1}
 
-, where $J_{n} is the nth Jacobi polynomial.
+, where J :sub:`n` is the nth Jacobi polynomial.
 
 `Return to top <#contents>`__
 
@@ -597,7 +597,7 @@ Initialise the ``DataHandler`` class with the required parameters.
 Setup model
 ^^^^^^^^^^^
 
-Setup the necesary parameters for the model and initialise the ``Model``
+Setup the necessary parameters for the model and initialise the ``Model``
 class. Before that fill the ``params`` dictionary with the required
 parameters.
 

docs/_rst/tutorials/forward_problems_2d/complex_mesh/helmholtz2d/helmholtz2d.rst

@@ -4,7 +4,7 @@ Helmholtz 2D Example on Circular Domain
 
 This example demonstrates how to solve a Poisson equation in 2D on a
 circular domain using the ``fastvpinns`` package. 
-All the necesary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
+All the necessary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
 
 The Poisson equation is given by
 
@@ -305,7 +305,7 @@ special type of Jacobi polynomials defined by
 
 .. math:: J_{n} = J_{n-1} - J_{n+1}
 
-, where $J_{n} is the nth Jacobi polynomial.
+, where J :sub:`n` is the nth Jacobi polynomial.
 
 `Return to top <#contents>`__
 
@@ -596,7 +596,7 @@ Initialise the ``DataHandler`` class with the required parameters.
 Setup model
 ^^^^^^^^^^^
 
-Setup the necesary parameters for the model and initialise the ``Model``
+Setup the necessary parameters for the model and initialise the ``Model``
 class. Before that fill the ``params`` dictionary with the required
 parameters.
 

docs/_rst/tutorials/forward_problems_2d/complex_mesh/poisson2d/poisson2d.rst

@@ -4,7 +4,7 @@ Poisson 2D Example on Circular Domain
 
 This example demonstrates how to solve a Poisson equation in 2D on a
 circular domain using the ``fastvpinns`` package. 
-All the necesary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
+All the necessary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
 
 The Poisson equation is given by
 
@@ -33,8 +33,6 @@ The computational domain is a circular domain with radius 1 centered at
 .. figure:: mesh.png
    :alt: alt text
 
-   alt text
-
 Contents
 -----------
 
@@ -307,7 +305,7 @@ special type of Jacobi polynomials defined by
 
 .. math:: J_{n} = J_{n-1} - J_{n+1}
 
-, where $J_{n} is the nth Jacobi polynomial.
+, where J :sub:`n` is the nth Jacobi polynomial.
 
 `Return to top <#contents>`__
 
@@ -597,7 +595,7 @@ Initialise the ``DataHandler`` class with the required parameters.
 Setup model
 ^^^^^^^^^^^
 
-Setup the necesary parameters for the model and initialise the ``Model``
+Setup the necessary parameters for the model and initialise the ``Model``
 class. Before that fill the ``params`` dictionary with the required
 parameters.
 

docs/_rst/tutorials/forward_problems_2d/hard_boundary_constraints/poisson_2d/poisson2d_hard.rst

@@ -2,7 +2,7 @@ Solving forward problems with FastVPINNs : Enforcing hard boundary constraints w
 =======================================================================================================
 
 In this example, we will learn how to use hard boundary constraints using FastVPINNs.
-All the necesary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
+All the necessary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
 
 .. math::
 

docs/_rst/tutorials/forward_problems_2d/uniform_mesh/helmholtz_2d/helmholtz2d_uniform.rst

@@ -2,7 +2,7 @@ Solving forward problems with FastVPINNs : Helmholtz - 2D
 =========================================================
 
 In this example, we will learn to solve the Helmholtz equation in 2D
-All the necesary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
+All the necessary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
 
 .. math::
 
@@ -13,8 +13,8 @@ where
 .. math::
 
 
-   f(x,y) = 2 \pi cos(\pi y)sin(\pi x) + 2 \pi cos(\pi x) sin(\pi y) 
-            + (x+y) sin(\pi x) sin(\pi y) - 2 \pi^2 (x+y) sin(\pi x) sin(\pi y),
+   f(x,y) = 2 \pi cos(\pi y)sin(\pi x) + 2 \pi cos(\pi x) sin(\pi y) + (x+y) sin(\pi x) sin(\pi y) - \\
+   2 \pi^2 (x+y) sin(\pi x) sin(\pi y),
 
 
 For this problem, the parameters are

docs/_rst/tutorials/forward_problems_2d/uniform_mesh/poisson_2d/poisson2d_uniform.rst

@@ -2,7 +2,7 @@ Solving forward problems with FastVPINNs : Poisson - 2D
 =======================================================
 
 In this example, we will learn how to solve a 2-dimensional Poisson problem using FastVPINNs. 
-All the necesary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
+All the necessary files can be found in the examples folder of the `fastvpinns GitHub repository <https://github.com/cmgcds/fastvpinns>`_
 
 .. math::
 
@@ -124,7 +124,7 @@ The input file, ``input.yaml``, is used to define inputs to your solver.
 These will usually parameters that will changed often throughout your
 experimentation, hence it is best practice to pass these parameters
 externally. The input file is divided based on the modules which use the
-parameter in question, as follows - ### ``experimentation`` This
+parameter in question, as follows - ``experimentation`` This
 contains ``output_path``, a string which specifies which folder will be
 used to store your outputs.
 
@@ -346,8 +346,8 @@ PDE.
 
 `Back to contents <#contents>`__
 
-## Solution
------------
+Solution
+--------
 .. image:: exact_solution.png
    :alt: Exact Solution
    :align: center
@@ -365,8 +365,8 @@ PDE.
 
 `Back to contents <#contents>`__
 
-## References
--------------
+References
+----------
 
 1. `FastVPINNs: Tensor-Driven Acceleration of VPINNs for Complex
    Geometries. <https://arxiv.org/abs/2404.12063>`__

docs/_rst/tutorials/inverse_problems_2d/const_inverse_poisson2d/inverse_constant.rst

@@ -47,7 +47,7 @@ actual value of the parameter that needs to be estimated (if the error
 between the actual and estimated parameter needs to be calculated) ###
 Defining boundary values The current version of FastVPINNs only
 implements Dirichlet boundary conditions. The boundary values can be set
-defining a function for each boundary,
+by defining a function for each boundary,
 
 .. code:: python
 
@@ -431,12 +431,6 @@ Solution
 
          Error
 
-      .. figure:: sensor_points.png
-         :alt: Sensor points
-         :align: center
-
-         Sensor points
-
       .. figure:: inverse_eps_prediction.png
          :alt: inverse_eps_prediction
          :align: center

docs/_rst/tutorials/inverse_problems_2d/domain_inverse_cd2d/domain_inverse.rst

@@ -46,7 +46,7 @@ Defining boundary values
 
 The current version of FastVPINNs only
 implements Dirichlet boundary conditions. The boundary values can be set
-defining a function for each boundary,
+by defining a function for each boundary,
 
 .. code:: python
 

docs/index.rst

@@ -36,7 +36,7 @@ Welcome to FastVPINNs's documentation!
 A robust tensor-based deep learning framework for solving PDE's using hp-Variational Physics-Informed Neural Networks (hp-VPINNs). The framework supports handling complex geometries and uses tensor-based loss computation to accelerate the training of conventional hp-VPINNs. 
 The framework is based on the work by `FastVPINNs Paper <https://arxiv.org/abs/2404.12063>`_. The framework is written on `Tensorflow 2.0 <https://www.tensorflow.org/>`_ and has support for handling external meshes. 
 
-*Note: This framework is an highly optimised version of the the initial implementation of hp-VPINNs by* `kharazmi <https://github.com/ehsankharazmi/hp-VPINNs>`_. Ref `hp-VPINNs(arXiv) <https://arxiv.org/abs/2003.05385>`_.
+*Note: This framework is a highly optimised version of the the initial implementation of hp-VPINNs by* `kharazmi <https://github.com/ehsankharazmi/hp-VPINNs>`_. Ref `hp-VPINNs(arXiv) <https://arxiv.org/abs/2003.05385>`_.
 
 Variational Physics-informed neural network
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

fastvpinns/FE/fe_transformation_2d.py

@@ -35,7 +35,7 @@ def __init__(self):
     @abstractmethod
     def set_cell(self):
         """
-        Set the cell co-ordinates, which will be used to calculate the Jacobian and actual values.
+        Set the cell coordinates, which will be used to calculate the Jacobian and actual values.
 
         :return: None
         """
@@ -56,13 +56,13 @@ def get_original_from_ref(self, xi, eta):
     @abstractmethod
     def get_original_from_ref(self, xi, eta):
         """
-        This method returns the original co-ordinates from the reference co-ordinates.
+        This method returns the original coordinates from the reference coordinates.
 
-        :param xi: The xi value of the reference co-ordinates.
+        :param xi: The xi value of the reference coordinates.
         :type xi: float
-        :param eta: The eta value of the reference co-ordinates.
+        :param eta: The eta value of the reference coordinates.
         :type eta: float
-        :return: The original co-ordinates corresponding to the given reference co-ordinates.
+        :return: The original coordinates corresponding to the given reference coordinates.
         :rtype: tuple
         """
 

fastvpinns/FE/quad_affine.py

@@ -35,7 +35,7 @@ def __init__(self, co_ordinates) -> None:
 
     def set_cell(self):
         """
-        Set the cell co-ordinates, which will be used to calculate the Jacobian and actual values.
+        Set the cell coordinates, which will be used to calculate the Jacobian and actual values.
 
         :param None:
             There are no parameters for this method.
@@ -49,7 +49,7 @@ def set_cell(self):
         self.x2 = self.co_ordinates[2][0]
         self.x3 = self.co_ordinates[3][0]
 
-        # get the y-co-ordinates of the cell
+        # get the y-coordinates of the cell
         self.y0 = self.co_ordinates[0][1]
         self.y1 = self.co_ordinates[1][1]
         self.y2 = self.co_ordinates[2][1]
@@ -65,12 +65,12 @@ def set_cell(self):
 
     def get_original_from_ref(self, xi, eta):
         """
-        Returns the original co-ordinates from the reference co-ordinates.
+        Returns the original coordinates from the reference coordinates.
 
         :param float xi: The xi coordinate.
         :param float eta: The eta coordinate.
         :return: numpy.ndarray
-            The original co-ordinates.
+            The original coordinates.
         """
         x = self.xc0 + self.xc1 * xi + self.xc2 * eta
         y = self.yc0 + self.yc1 * xi + self.yc2 * eta
@@ -96,7 +96,7 @@ def get_jacobian(self, xi, eta):
 
     def get_orig_from_ref_derivative(self, ref_gradx, ref_grady, xi, eta):
         """
-        Returns the derivatives of the original co-ordinates with respect to the reference co-ordinates.
+        Returns the derivatives of the original coordinates with respect to the reference coordinates.
 
         :param ref_gradx: The reference gradient in the x-direction.
         :type ref_gradx: numpy.ndarray
@@ -107,7 +107,7 @@ def get_orig_from_ref_derivative(self, ref_gradx, ref_grady, xi, eta):
         :param eta: The eta coordinate.
         :type eta: float
 
-        :return: The derivatives of the original co-ordinates with respect to the reference co-ordinates.
+        :return: The derivatives of the original coordinates with respect to the reference coordinates.
         :rtype: tuple
         """
         gradx_orig = np.zeros(ref_gradx.shape)
@@ -121,7 +121,7 @@ def get_orig_from_ref_derivative(self, ref_gradx, ref_grady, xi, eta):
 
     def get_orig_from_ref_second_derivative(self, grad_xx_ref, grad_xy_ref, grad_yy_ref, xi, eta):
         """
-        Returns the second derivatives (xx, xy, yy) of the original co-ordinates with respect to the reference co-ordinates.
+        Returns the second derivatives (xx, xy, yy) of the original coordinates with respect to the reference coordinates.
 
         :param grad_xx_ref: The reference second derivative in the xx-direction.
         :type grad_xx_ref: numpy.ndarray
@@ -134,7 +134,7 @@ def get_orig_from_ref_second_derivative(self, grad_xx_ref, grad_xy_ref, grad_yy_
         :param eta: The eta coordinate.
         :type eta: float
 
-        :return: The second derivatives (xx, xy, yy) of the original co-ordinates with respect to the reference co-ordinates.
+        :return: The second derivatives (xx, xy, yy) of the original coordinates with respect to the reference coordinates.
         :rtype: tuple
         """
         GeoData = np.zeros((3, 3))