Category: Finite Element
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How to Use Geometry Generation Functions of GMSH by Python (1) Basics
You can export Gmsh geometry in a Python environment by using the Python bindings that are provided with Gmsh. The process for doing this is as follows: Here is an example of a script that exports a 3D geometry to a .stl file: STL format is typically used for solid models. If you want to…
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MFEM Tutorials (2) Simplest MFEM of Laplace Problem with Various Options Part B
Set up the bilinear form a(.,.) on the finite element space Set up the bilinear form a(.,.) on the finite element space corresponding to the Laplacian operator -Delta, by adding the Diffusion domain integrator. This code is the same as I explained earlier, it creates a BilinearForm object, “a”, which is used to represent the…
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MFEM Tutorials (2) Simplest MFEM of Laplace Problem with Various Options Part A
Descriptions MFEM’s ex1 is a basic example of solving a linear elliptic PDE (partial differential equation) problem using the MFEM library. The problem is a simple scalar diffusion equation on a 2D mesh. The equation is defined as: where $u$ is the solution, $k$ is a scalar coefficient and $f$ is a source term. The…
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MFEM Tutorials (1) Simplest MFEM of Laplace Problem
Description This example code demonstrates the most basic usage of MFEM to define a simple finite element discretization of the Laplace problem with zero Dirichlet boundary conditions. General 2D/3D mesh files and finite element polynomial degrees can be specified by command line options. Parse command line options This code includes the header files for the…
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NGSolve Tutorials (3) Dirichlet Boundary Conditions Part C
Solve for the free dofs¶ We need to assemble the right hand side of $A_{FF}u_{0,F}=f_F-\left[ Au_D \right]_F$, namely This code creates a linear form f, and it represents the left hand side of the weak form of a PDE. In this case, a constant function 1 is used as a forcing term and multiplied by…
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NGSolve Tutorials (3) Dirichlet Boundary Conditions Part B
Extension of boundary data¶ We use the standard technique of reducing a problem with essential non-homogeneous boundary conditions to one with homogeneous boundary condition using an extension. The solution $u$ in $H_1$ satisfiesu$\Gamma_D=g$ and for all $v_0$ in $\in H_{0,D}^1= { v \in H^1 : v|_{\Gamma_D} = 0 }$. Split the solution where $u_D$ is…
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NGSolve Tutorials (3) Dirichlet Boundary Conditions Part A
This tutorial goes in depth into the mechanisms required to solve the Dirichlet problem with a nonzero Dirichlet boundary condition The same mechanisms are used in solving boundary value problems involving operators other than the Laplacian. You will see how to perform these tasks in NGSolve: Spaces with Dirichlet conditions on part of the boundary The first…
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WebGUI Capability of Opensource Finite Element Tools
there are a few that have web-based graphical user interfaces (GUIs) available: Overall, while some of the open-source tools above can be used with web-based GUIs, it is not all of them have this capability, most of them require some programming knowledge to use, and they are mostly command line interface based. However, you can…
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Heat Transfer Analysis and Open Sourced Finite Element Tools (3) About Opensources
CodeAster: Code_Aster is an open-source software for finite element analysis (FEA) developed by EDF (French electric company). It can be used to solve a wide range of problems, including heat transfer problems. It is primarily written in Fortran language and provides a comprehensive set of features for solving both steady-state and transient heat transfer problems.…
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Heat Transfer Analysis and Open Sourced Finite Element Tools (2) About Opensources
MFEM: MFEM is an open-source library for solving partial differential equations using the finite element method. It is written in C++ and provides a wide range of features for solving both scalar and vector-valued problems, including heat transfer problems. MFEM provides several discretization options for solving heat transfer problems, including continuous and discontinuous Galerkin methods,…