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Transformation matrix for global displacements derivates to local ones

The derivatives of the displacements in the coordinate system $\bar{x} \bar{y} \bar{z}$ is given by \begin{equation} \begin{aligned} \{\bar{L}\} & = \begin{Bmatrix} ...
Riobaldo Tatarana's user avatar
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How to get Gauss points for nodal force vector (surface integral) in tetrahedral elements in the isoparametric coordinate system $({\xi \eta \zeta})$?

I am aware of the following question Evaluating the surface integral in an FEM (Finite Elements Method) procedure. But they use the volumetric coordinates while I want to use the cartesian ...
Mr Thomas Anderson's user avatar
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FEM for a biphasic drying problem

I have the following PDE originating from a biphasic drying model, where $\xi \in [0,\Xi]$ is a radial coordinate attached to the dry skeleton of a wet cylindrical body: $$ \frac{\partial u}{\partial ...
IPribec's user avatar
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How to find the formula of a projected circle in a pencil of conics structure?

Hi this is my first question on the platform so feel free to comment if I have a mistake regarding the question. I'm working on an ellipse detection scheme in which I have markers consisted of 3 ...
kemal alperen cetiner's user avatar
2 votes
1 answer

How do you handle the singularity in polar or cylindrical coordinates?

Governing equations in polar or cylindrical coordinates often have terms with $\frac{1}{r}$ involved. At $r = 0$, such terms blow up to become a "singularity." The Cartesian version of such ...
Steve M's user avatar
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How does one obtain tortoise coordinates by integrating with GNU Scientific Library (GSL)?

I’m trying to to obtain the values of the tortoise coordinates (Eddington-Finkelstein Coordinates) integrating the expression: $\frac{dr^*}{dr} = (1 - rS/r)^{-1}$ using the GNU Scientific Library (GSL)...
JoséM's user avatar
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2 votes
2 answers

Semi-infinite domain transformation

Question is mostly related to literature or suggestions. Given a semi infinite domain: $x=[0; +\infty);y=[0; +\infty)$. Willing to transform it to computational domain of: $[0,1]\times[0,1]$. I did ...
2Napasa's user avatar
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Interpolation is correct for grid, but wrong for random points

I am using scipy interpolation to construct a map of two coordinates to two other coordinates --- effectively one set of coordinates are 2D cartesian coordinates (called X and Y), and the other are ...
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Nondifferentiable coordinate transforms

Suppose that we have coordinates $u=u(x,y)$ and $v=v(x,y)$ in $\mathbb{R}^2$ so that $v$ is not differentiable when $u(x,y)=u_0$ where $u_0$ is a constant. Can we solve a differential equation, such ...
tohoyn's user avatar
  • 331