# Tag Info

### What programming language should I choose and why?

You should definitely check out Julia. Julia is a programming language which is similar to Python or MATLAB but utilizes a strong type-inference algorithm + JIT in order to optimize code. If types can ...
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### Without positive definiteness, does an iterative solver work?

No, positive definiteness (and symmetry) are only precondition to using the Conjugate Gradient method. But there are plenty of other iterative methods such as MinRes and GMRES that can be used for ...
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### What programming language should I choose and why?

What is it you want to achieve? If you want to develop methods/algorithms you might prefer a language that is flexible, and that you are familiar with. As you stated in your question, the Fortran ...
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### What programming language should I choose and why?

Start simple. Learn Python. I have been paid to write programms for over forty years and I have used all the languages mentioned in other answers (except Julia - I had never heard of it before now). ...
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### Why is the FVM traditionally used in CFD, and FEM in computational structures?

The finite element method is actually quite widely used in fluid flow problems, for example for the Stokes and Navier-Stokes equations. The delineation between the methods is more along the following ...
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### What are the conceptual differences between the finite element and finite volume method?

The basic difference is simply the meaning to be attached to the results. FDM predicts point values of any aspect of the solution. Interpolation between these values is often left to the imagination ...
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### Why FVM can handle unstructured meshes while FDM cannot?

The difference between finite volumes and finite differences is really more about the form of the equations solved. In typical FV methods, the conservative form is ...
Accepted

### Don't we care about the numerical diffusion in the diffusion term?

We have the following problem: $$\frac{\partial u}{\partial t}+v\color{red}{\frac{\partial u}{\partial x}}-\nu\color{blue}{\frac{\partial^2u}{\partial x^2}}=0 \tag{*}$$ The function $u$ may represent ...
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### What programming language should I choose and why?

I highly recommend to anyone, regardless of background, learning both low-level, "fast" language (C, Rust, C++, Go) high-level scripting language (Python, MATLAB, Mathematica, R, bash) As a general ...
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### Is mesh orthogonality important for FEM?

Yes. The constants that appear in the interpolation estimates upon which finite element error estimates are based contain minimum and maximum angles of triangles/tetrahedra (or similar geometric ...
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### Add User-defined/custom differential equations in OpenFoam (CFD)

The whole point of the OpenFOAM (OF hereinafter) libraries is exactly what you are inquiring for: PDE mimicking programming for CFD using the FV framework. In order to do what you are asking, you ...
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### Are FEM or DGFEM methods based on integrals or PDEs?

Basically, you have the following set of derivations: Strong form of the PDE -> Finite differences Integral form of the PDE -> Finite volumes Weak (variational) form of the PDE -> Galerkin methods (...
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### Initial Condition in a Numerical Problem

That depends on the equation you have, and on the situation you want to model. Imagine, for example, that you are considering the advection equation $$\partial_t u + c \partial_x u = 0,$$ i.e., ...
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