Numerical Web

Tag: partial differential equation

  • MFEM Tutorials (4) Simple Electomagnetic Diffusion Part C

    Assemble the bilinear form and the corresponding linear system Assemble the bilinear form and the corresponding linear system, applying any necessary transformations such as: eliminating boundary conditions, applying conforming constraints for non-conforming AMR, static condensation, etc. This code first checks if the “static_cond” variable is true. If it is, it calls the EnableStaticCondensation method on…

  • NGSOLVE Tutorial (4) Static Condensation Part A

    Descriptions Static condensation is a technique used in the solution of partial differential equations (PDEs) to reduce the size of the system to be solved. In the context of the ngsolve example, it likely refers to the use of static condensation to reduce the size of the system of equations being solved by the solver…

  • 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…

  • 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…

  • Proper Generalized Decomposition(PGD)

    Proper Generalized Decomposition (PGD) is a mathematical technique that can be used to approximate the solution of partial differential equations (PDEs) by expanding it in a basis of simple functions. It’s a generalization of the Proper Orthogonal Decomposition (POD) method, which can be used when the solution of the PDE is not linear. PGD is…

  • 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…

  • 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…

  • 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…

  • 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…

  • 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.…