Numerical Web

Category: NGSolve

  • NGSOLVE Tutorial (4) Static Condensation Part B. Inhomogeneous Dirichlet B.C and Automatic utility

    Inhomogeneous Dirichlet Boundary Conditions In case of inhomogeneous Dirichlet boundary conditions, we combine the technique of Dirichlet data extension with the above static condensation principle in the following code. The code you provided is solving a Poisson equation with a manufactured solution and then calculates the error between the manufactured solution and the numerical solution…

  • 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…

  • 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…

  • NGSolve Example for Heat Transfer using Complex Geometries Part B

    These lines of code are using the Mesh class from the ngsolve module to create a finite element mesh of the 3D model of the package. The Mesh class is used to create a discretization of the 3D model that can be used to perform finite element analysis (FEA). The OCCGeometry class from the netgen.occ…

  • NGSolve Example for Heat Transfer using Complex Geometries Part A

    these lines of code are importing several modules that are used for performing boolean operations on 3D shapes and visualizing the resulting shapes in a web browser. These modules can be used together to perform boolean operations on 3D shapes, perform FEA simulations on the resulting shapes, and visualize the resulting shapes in a web…

  • Boolean Operation Examples for Netgen

    In computer-aided design (CAD), boolean operations are a set of functions that allow you to create new shapes by combining or modifying existing shapes. These operations are called boolean because they are based on the logical values of true and false, and they use the concepts of union, intersection, and difference to create new shapes.…

  • NGSolve Tutorials (2) CoefficientFunctions Example Part B

    6. Integrate a CoefficientFunction The Integrate function in ngsolve is used to compute the integral of a function over the domain of a given mesh. The function to be integrated is specified as a CoefficientFunction, and the mesh over which the integral is to be computed is specified as a Mesh object. In this case,…

  • NGSolve Tutorials (2) CoefficientFunctions Example Part A

    In the ngsolve library, a coefficient function is a function that is used to specify the coefficients of a PDE or boundary condition. Coefficient functions can be either symbolic or numerical. Symbolic coefficient functions are defined using mathematical expressions and can depend on the coordinates of the domain. They are used to define the weak…