# Questions tagged [boundary-conditions]

For questions regarding the choice and/or appropriateness of conditions necessary to model a particular phenomenon with a partial differential equations.

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### Structural mechanics - traction free = Zero displacement gradient?

This is a follow up question to my question yesterday Structural mechanics traction boundary condition question Does a traction free boundary condition also mean that the displacement gradient is 0 ...
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### Structural mechanics traction boundary condition question

In structural mechanics, are the boundary conditions "free surface," "Traction free", "stress free" all equivalent Neumann boundary conditions?
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### Understanding Boundary Condition in FEM

I am trying to understand Dirichlet and Neumann boundary conditions in FEM and I wanted to know if my inference is correct. To articulate my understanding, lets consider a simple case of TE and TM ...
2answers
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### How do you apply boundary conditions in a time-stepping problem?

It looks to me like a very common problem, yet I haven't been able to find any practical guide on the subject despite many hours searching. Here is a clearer statement of my question: I have a ...
1answer
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### Parallel calculation in finite elements

I am trying to solve a 1 Dimensional eigenvalue of poisson problem: $$\nabla \phi ^2 +\nabla \phi = k\phi$$ with the boundary condition: $\phi (0)=0 , \nabla \phi(1) = 0$. I could solve this ...
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### FEM current toy problem

I am solving the Dirichlet problem $$\begin{cases} \Delta u = 0, \\ u|_{\partial D} = f, \end{cases}$$ in a $2d$ domain $D$ using the finite element method. What I want to get is the ...
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### Neumann boundary conditions for the upwind scheme applied to the advection equation (Python)

I'm trying to solve the linear advection equation $$u_{t} = cu_{x}, \\ x \in [x_{0}, x_{e}], \quad t \in (0, T], \quad c \in \mathbb{R} \\ u(x,0) = f(x)$$ Note that for $c > 0$, the solution is ...
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### How would you specify mixed boundary conditions for a 2D PDE in the matrix used for finite differences

I have the following PDE in 2D: $U_{x} + U_{xx} + U_y + U_{yy} + U_{xy} = f$ where $f$ is a constant. And I'm trying to create a matrix $A$ to solve the PDE through finite differences: $AU = f$. I ...
1answer
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### Line integral along the edge of an isoparametrically mapped triangle

I need to integrate the following function on the line segment from $P_{1} = \begin{bmatrix} -2\\-1 \end{bmatrix}$ to $P_{2} = \begin{bmatrix} 1\\2 \end{bmatrix}$: $$\int_{P_{1}}^{P_{2}} 4x + y \ ds$$...
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### Simulating periodic boundary condition with long_range interaction

Consider 2 particles in a 2D plane. There is a long-range interaction between two particles: $$f (r_i-r_j)= \frac{\vec{r_i} - \vec{r_j}}{|r_i-r_j|^3}$$ $$\vec{r_i} =(x_i,y_i)$$ $r_i$ determines the ...
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