# 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.

352 questions
Filter by
Sorted by
Tagged with
339 views

### Dirichlet boundary conditions in the 1D Heat Equation

Please consider the assignment I have uploaded on the picture. I am confused about the functions $g_L(t)$, $g_R(t)$ and $\eta(x)$. What are they and how do I find them... My question: Is it possbile ...
1k views

### Boundary conditions in conjugate gradient method for poisson's equation

I want to use the conjugate gradient method to solve poisson's equation in an electrostatic setup: \begin{align} \rho=-\nabla^2\phi \end{align} I am however a little confused when it comes to the ...
359 views

### Satisfying Periodic Boundary Conditions while plotting spherical particles inside a cube

I am trying to plot spherical particles in a cube of fixed dimension in matlab. I face a problem here where the center of the sphere is too close to the edge of the cube in this case the rest of the ...
294 views

### Relation between Stress/Strain and normal derivative of displacement

I calculated the stress $\sigma$ and strain $\varepsilon$ for a solid plate with dirichlet boundary conditions $u = g$, where $u$ is the displacement. With these I want to calculate $\nabla_n u = t$ ...
91 views

### Harmonic oscillators with periodic boundary conditions

I am trying to simulate multiple harmonic oscillators in periodic boundary conditions (subsequently visualizing the process in VMD). I have successfully simulated multiple HOs by using the Leapfrog ...
584 views

### Well-posedness of linear elasticity boundary conditions

I have several questions regarding suitable boundary conditions for linear elasticity. I have read that in order for modeling linear elasticity to be well-posed, the entire boundary cannot be ...
146 views

### 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 ...
275 views

63 views

### Where could error terms that blow up in SWE come from?

I have been working on a solver for shallow water equations with reflective boundary conditions. I have found that it diverges very fast. As a workaround I noticed yesterday that if I smooth the ...
111 views

### traction boundary conditions in elasticity

I have a question about implementing traction boundary conditions in 2D and 3D linear elasticity. Consider the picture above. I want to apply traction boundary conditions on the boundary in red. My ...
74 views

### Simulating pressure waves at an impedance boundary

I am trying to simulate pressure waves crossing a boundary from one medium to another (e.g., water to air) in Matlab. The code that I have got so far, which is largely taken from Wikipedia on Partial ...
83 views

### FEM diffusion: inaccurate results small time steps

I wrote some FEM code and found some strange results when using a very small time step. So, I decided to analyze the discrete equations. Consider the following linear diffusion problem in 1 dimension:...
93 views

### Dealing with boundary conditions using Fourier spectral methods

I am currently working on a project where I need to use Fourier spectral methods to solve the KS equation. I found this code which is using the Fourier spectral methods to solve the classic 1D heat ...
462 views

54 views

### Solving Laplace equation with constraint on boundary

I have found the following PDE problem in a paper: Essentially, we have a rectangular domain where there is a unknown interface $z=\xi(x)$ (liquid-air interface) separating the domain into two medium ...
46 views

### Integrating a wavelike equation with absorbing boundary conditions

I am trying to numerically solve the following equation: $\frac{\partial^{2} \phi}{\partial t^{2}}-\frac{\partial^{2} \phi}{\partial x^{2}}+V(x) \phi(x, t)=0$ On some domain, with: $\phi(x, 0) = I(x)$ ...
38 views

### Discretization formula for a system of two differential equations. “Solution to one of these is the initial condition of the other”. In which sense?

Consider the following stochastic differential equation \begin{equation} dy=\left(A-\left(A+B\right)y\right)dt+C\sqrt{y\left(1-y\right)}dW\tag{1} \end{equation} where $A$, $B$ and $C$ are parameters ...
42 views

### Euler Explict Method for solving the PDE for option prices under the Schwartz mean reverting model. Numerical Finance

I have to solve the following PDE for a Call option : $\partial_tV + \{ \alpha - (\mu - \lambda/ \alpha -log(S))\}S\partial_SV + 1/2 \sigma^{2}S^{2}\partial_{S}^{2}V - rV = 0$ Where V(S,t) is the ...