Numerical Web

Tag: numerical analysis

  • OpenRadioss

    Introduction OpenRADIOSS is a software package for nonlinear and linear structural analysis. It is a solver for finite element analysis and includes support for various elements such as truss, beam, shell, and solid elements. OpenRADIOSS is an open-source software package, which means that it is free to use, distribute, and modify. It is developed and…

  • Open Source Modelling and Visualization Libraries

    Introduction Open source 3D modeling and visualization refers to the use of software and tools that are freely available and can be modified and distributed by anyone. These tools and libraries provide a wide range of functionality for 3D modeling and visualization, including the ability to create and edit 3D models, perform numerical simulations, and…

  • 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…

  • MFEM Tutorials (4) Simple Electromagnetic Diffusion Part B

    Read and refined the mesh from the given mesh file We can handle triangular, quadrilateral, tetrahedral, hexahedral, surface and volume meshes with the same code. Refine the mesh to increase the resolution. In this example we do ‘ref_levels’ of uniform refinement. We choose ‘ref_levels’ to be the/ largest number that gives a final mesh with…

  • 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 (3) Simple Linear Elasticity Problem Describing a Multi-Material Cantilever Beam Part B

    Define a finite element space on the mesh. Here we use vector finite elements, i.e. dim copies of a scalar finite element space. The vector dimension is specified by the last argument of the FiniteElementSpace constructor. For NURBS meshes, we use the (degree elevated) NURBS space associated with the mesh nodes. This code sets up…

  • MFEM Tutorials (3) Simple Linear Elasticity Problem Describing a Multi-Material Cantilever Beam Part A

    Description This example code solves a simple linear elasticity problem describing a multi-material cantilever beam. Specifically, we approximate the weak form of where is the stress tensor corresponding to displacement field $\textit{\textbf{u}}$, and lambda and mu // are the material Lame constants. The boundary conditions are $\textit{\textbf{u}}=0$ on the fixed part of the boundary with…

  • 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…

  • 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…

  • Proper Orthogonal Decomposition(POD)

    Proper Orthogonal Decomposition (POD) is a mathematical technique that can be used to extract the most important modes of a system from a set of snapshots of the system’s state. It is a data-driven method and it can be used to identify the most important features of a system regardless of whether the system is…