Questions tagged [pde]
Partial differential equations (PDEs) are equations that relate the partial derivatives of a function of more than one variable. This tag is intended for questions on modeling phenomena with PDEs, solving PDEs, and other related aspects.
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Meaning of Degree of Freedom in FEM
Assume we want to solve the Poisson eq. with the FEM on some Domain $\Omega$, i.e.
$$\begin{cases} -\Delta u = f, \; \Omega\\
u = 0, \; \partial \Omega \end{cases}$$
For the sake of the discussion let ...
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Linear PDE solution with constraints
Consider the following linear PDE:
$$\nabla_q V(q) - M_d(q)M^{-1}(q)\nabla_q V_d(q) = 0,$$
where $V(q)$ and $M(q)$ are known and $M_d(q)$ is a grey box function (e.x., $M_d(q)$ is fitted using a ...
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Discrete laplacian 9 point
I am trying to write a code for 9 point discrete laplacian. I would like to write a matrix and solve the linear system $AU=F$ with gradient conjugate method.
I wrote the matrix this way
...
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Upwind scheme with periodic conditions
I am struggling with this assignment.
I have to write an upwind scheme for the following PDE:
$$u_t+a Du=0 \quad\mathrm{on}\;(-1,3)$$
$a$ is said to be positive, the initial condition is $\sin(2\pi x)$...
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Solving second order coupled differential equations in python
as I have to design a reactor and therefore have to get its length x, I have to solve the following differential equations:
$$D_{eg}\tfrac{d^2A_g}{dx^2}-u_g\tfrac{dA_g}{dx} = k_la_b\left(\tfrac{A_g}{...
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Can I use MOL to solve 2D steady state PDE in terms of r and z spatial coordinates?
recently I need to solve a 2D steady state PDE equation.
It’s not time dependent, and the only two independent variables are z and r direction.
So far for this solution, I was thinking using Method ...
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Applying spectral method to a damped, driven 2D bending-mode wave equation on an irregular domain with heterogeneous boundary conditions
I'm trying to model some two-dimensional waves, and am unsure how to combine my boundary conditions with spectral methods. The PDE I'd like to explore resembles the equations for damped, driven ...
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Can successive over-relaxation (SOR) method deal with ill-posed PDE BVP?
Recently, I've been struggling to understand the limitations and capabilities of the successive over-relaxation (SOR) method for boundary value problems which are ill-posed, such as, for instance, ...
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Poisson equation with discontinuous variable coefficient
Trying to solve numerically the 2D Poisson equation with variable diffusion coefficient $K$, that in general can be discontinuous.
$$ \frac{\partial}{\partial x} ( K(x,y)\frac{\partial C}{\partial x}) ...
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Crank-Nicolson vs Spectral Methods for the TDSE
The time-dependent Schroedinger equation (TDSE) depends linearly on the system's initial state $\vert \psi(0) \rangle$, such that the solution can be generally written as
$$ \vert \psi(t) \rangle = \...
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Convergence stall when solving 2D Poisson PDE with pure Neumann boundaries (finite differences)
I recently started coding a small library of 2D PDE solvers (time dependent and time independent), and my first attempt was a 2D Poisson equation of the form:
$$\nabla(\epsilon\nabla\varphi)=\nabla\...
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Spurious oscillations in solving diffusion problems using finite elements
I've been struggling with this problem for a while so I hope someone can help me here.
I'm trying to solve the McNabb-Foster equations for hydrogen diffusion in metals using a simple 1D finite element ...
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One dimensional $C^1$ finite elements
I tried to solve a one dimensional biharmonic equation with finite elements. I wanted to use a conforming approach (as I simply do not know a lot about other approaches) and therefore was looking for ...
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Numerical solution of PDE with uniform initial condition
I have a PDE like this
$$
\frac{\partial h}{\partial t} = \bigg(\frac{\dot{L}}{L}\bigg)x\frac{\partial h}{\partial x} - \alpha\bigg[h^3\frac{\partial^3 h}{\partial x^3}\bigg]
$$
With boundary and ...
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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 ...
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