Tag: numerical analysis
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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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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 (1) List of Tools
There are many open-source tools available for solving heat transfer problems. These include: All these software packages are open-source, and they provide a wide range of features and capabilities, and can be used to solve a wide range of heat transfer problems. Some are written in Python, others in C++,Fortran, and all have active user…
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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…
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Boundary Conditions for Partial Differential Equations (1) Types of Boundaries
Here is a summary of the different types of boundary conditions that are commonly used in partial differential equation (PDE) problems: where $u$ is the variable (such as temperature or velocity) and $g$ is the fixed value specified by the boundary condition. where $u$ is the variable (such as temperature or velocity) and ${du/dn}$ is…
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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,…
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NGSolve Tutorials (1) First NG Solve Example Part B
In NGSolve, the BilinearForm class represents a bilinear form defined on a finite element space. A bilinear form is a function that takes two finite element functions as input and returns a scalar. It is used to define the left-hand side of a weak formulation of a PDE. In the code you provided, a bilinear…
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Linear Algebra for Rust and Examples (3) Parallel Linear Solver
To use the multi-frontal solver in a parallel fashion, you can use the rayon crate to parallelize the factorization and solution steps of the solver. Here is an example in Rust: This code creates a random sparse 3×3 matrix A with approximately 50% non-zero elements and a random 3D vector B, and then solves the…