add multigrid doc

docs/source/cfd/examples/index.rst

@@ -44,3 +44,11 @@ CFD benchmark cases
 #. `国产CFD开源软件OneFLOW+Two-Dimensional Poisson Equation+Spectral method简单测试 <https://zhuanlan.zhihu.com/p/638970775/>`_
 #. `国产CFD开源软件OneFLOW+Two-Dimensional Poisson Equation+Spectral Vs CDS order简单测试 <https://zhuanlan.zhihu.com/p/639049947/>`_
 #. `国产CFD开源软件OneFLOW+Two-Dimensional Poisson Equation+Gauss-Seidel method简单测试 <https://zhuanlan.zhihu.com/p/641180890/>`_
+#. `国产CFD开源软件OneFLOW+One-Dimensional Poisson Equation+Gaussian elimination简单测试 <https://zhuanlan.zhihu.com/p/642688717/>`_
+#. `国产CFD开源软件OneFLOW+One-Dimensional Poisson Equation+Steepest Descent简单测试 <https://zhuanlan.zhihu.com/p/642749705/>`_
+#. `国产CFD开源软件OneFLOW+One-Dimensional Poisson Equation+Conjugate Gradients简单测试 <https://zhuanlan.zhihu.com/p/642790857/>`_
+#. `国产CFD开源软件OneFLOW+1d Poisson+Steepest Descent修正简单测试 <https://zhuanlan.zhihu.com/p/642924639/>`_
+#. `国产CFD开源软件OneFLOW+1d Poisson+Steepest Descent Version 2简单测试 <https://zhuanlan.zhihu.com/p/642945070/>`_
+#. `国产CFD开源软件OneFLOW+1d Poisson+Conjugate Gradients Version 2简单测试 <https://zhuanlan.zhihu.com/p/643019408/>`_
+#. `国产CFD开源软件OneFLOW+2d Poisson+Conjugate Gradients简单测试 <https://zhuanlan.zhihu.com/p/643463586/>`_
+#. `国产CFD开源软件OneFLOW+2d Poisson+Conjugate Gradients case2简单测试 <https://zhuanlan.zhihu.com/p/643684539/>`_

docs/source/cfd/matrix.rst

@@ -67,3 +67,59 @@ The classical adjoint matrix should not be confused with the adjoint matrix. The
   \vdots& \vdots &  &\vdots \\
   A_{1n}&A_{2n}  &\cdots   & A_{nn}\\
   \end{bmatrix}  
+  
+Transpose
+----------------------
+`Transpose <https://en.wikipedia.org/wiki/Transpose/>`_
+
+Formally, the :math:`i`-th row, :math:`j`-th column element of :math:`\mathbf{A}^{\text{T}}` is the :math:`j`-th row, :math:`i`-th column element of :math:`\mathbf{A}`:  
+
+.. math::
+  [\mathbf{A}^{\text{T}}]_{ij}=[\mathbf{A}]_{ji}
+  
+Properties
+````````````````````
+
+Let :math:`\mathbf{A}` and :math:`\mathbf{B}` be matrices and :math:`c` be a scalar.  
+
+1. 
+
+.. math::
+  {\displaystyle \left(\mathbf {A} ^{\operatorname {T} }\right)^{\operatorname {T} }=\mathbf {A} .}
+  
+2. 
+
+.. math::
+  {\displaystyle \left(\mathbf {A} +\mathbf {B} \right)^{\operatorname {T} }=\mathbf {A} ^{\operatorname {T} }+\mathbf {B} ^{\operatorname {T} }.}
+  
+3. 
+
+.. math::  
+  {\displaystyle \left(\mathbf {AB} \right)^{\operatorname {T} }=\mathbf {B} ^{\operatorname {T} }\mathbf {A} ^{\operatorname {T} }.}
+  
+  
+What are Eigenvalues?
+---------------------------------------
+The eigenvalue is explained to be a scalar associated with a linear set of equations which, when multiplied by a nonzero vector, equals to the vector obtained by transformation operating on the vector.
+
+Let us consider :math:`k \times k` square matrix :math:`A` and :math:`\mathbf{v}` be a vector, then :math:`\lambda` is a scalar quantity represented in the following way:
+
+.. math::
+  A\mathbf{v} = \lambda\mathbf{v}
+
+Here, :math:`\lambda` is considered to be the eigenvalue of matrix :math:`A`.
+
+The above equation can also be written as:
+
+.. math::
+  (A – \lambda I) = 0
+
+Where “:math:`I`” is the identity matrix of the same order as :math:`A`.
+
+This equation can be represented in the determinant of matrix form.
+
+.. math::
+  |A – \lambda I| = 0
+ 
+The above relation enables us to calculate eigenvalues :math:`\lambda` easily.
+

docs/source/cfd/method/index.rst

@@ -7,6 +7,5 @@ CFD Methods
    /cfd/method/spectrum
    /cfd/method/fourier
    /cfd/method/iterative
-
-
-
+   /cfd/method/multigrid
+   /cfd/method/multigrid1