Archives

Steps to install Salome

Step 1: Go to the official website of Salome https://www.salome-platform.org/?page_id=15 and download the setup. Step 2: Right-click on the setup and select run as administrator. Step 3: The license agreement window appears on the screen. Select on the accept the agreement button and then select the next button. Step 4: After that, select the destination […]

Steps to Install Gmsh

Step 1: Go to the official website of Gmsh https://gmsh.info/ and click on download Gmsh for windows. Step 2: The zip file of gmsh is downloaded. Unzip that zip file by clicking on it and selecting the extract button. Step 3: After extracting, right-click on the gmsh.exe button and select run as administrator. Step 4: […]

Steps to install Cmder

Step 1: Go to the official website of cmder https://cmder.app/ to download the setup. Step 2: A cmder.zip file is downloaded. Unzip that zip file by right click on it and clicking on Extract to the “cmder\” button. Step 3: After unzipping the cmder.zip file, right-click on the Cmder.exe and click on the run as […]

Steps to install Docker Desktop

Step 1: Go to the docker desktop official website https://www.docker.com/products/docker-desktop/ and click on download docker desktop for windows. Step 2: Once the setup has been installed, then right-click on the setup and click on the run as administrator. Step 3: The docker desktop installation process is started. The configuration window appears on the screen, click […]

Reasons and solutions for the optimization algorithm convergence

Various reasons are responsible when the optimization algorithm’s convergence is not ensured. Some of the following steps are beneficial in fixing this issue:  Ensure that the objective function and the constraints are appropriately formulated. Ensure that the objective and constraint functions are continuous and differentiable at least up to the second order. If the objective […]

Gradient vector: If the partial derivative of a function f(x) (function having $n$ variables) with respect to the $n$ variables $x_1$, $x_2$…..$x_n$ at a point $x^{\star}$ is taken, then that partial derivative vector of f(x) represents the “gradient vector” which is represented by symbols like $c$ or $\triangledown {f}$, as: \$\mathbf{c}=\nabla f\left(\mathrm{x}^{*}\right)=\left[\begin{array}{c}\frac{\partial f\left(\mathrm{x}^{*}\right)}{\partial x_{1}} \\ \frac{\partial f\left(\mathrm{x}^{*}\right)}{\partial […]

Norm and condition number of a matrix

In a numerical analysis with a vector involvement, norms are essential to predict the various errors involved in the numerical analysis. A norm is a function ||.|| in a vector space V. If A is a n*n matrix, then its norm is a real number and denoted by ||A||. A norm satisfies the following properties: […]

Dolfin-x: An upgraded version of Dolfin

FEniCSx is the new version of FEniCS that is currently actively developed. Dolfin-x is the computational environment of FEniCS and implements the FEniCS problem-solving environment in Python and C++. New features in Dolfin-x in addition to existing features of Dolfin include: Variational formulations with complex numbers support Support for quadrilateral and hexahedral elements Higher-order […]

Variational Calculus: Deriving the strong and weak form

There are many ways in which we can obtain the weak form and the strong form. We focus on the Variational Principles to derive them because FEniCS works on the variational form

Calculus with Sympy

Sympy is a python package through which we can perform calculus operations in mathematics like differentiation, integration, limits, infinite series, and so on. It is a python library used mainly for symbolic mathematics. The installation of this library is simple by using the following command: pip install sympy In order to write any symbolic expressions, […]