# 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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### How can I get more accurate electric scalar potential in 2D closed box?

I am trying to use poisson equation to plot the electric scalar potential in close 2D space. The details in in this video and this one The following in written in Matlab for quick prototype. ...
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### Asking advice for implementation of Conservative Finite Difference Scheme for numerically solving Gross-Pitaevskii equation

I am trying to numerically solve the Gross-Pitaevskii equation for an impurity coupled with a one-dimensional weakly-interacting bosonic bath, given by (in dimensionless units): \begin{align} i \frac{\...
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### What is the best finite volume method for the following equation?

I'm trying to create a partial differential equation that approximates 1-D climate in a rocky planet's atmosphere, which accounts for energy transport via radiation and convection. I am only ...
1 vote
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### How can I apply a mixed boundary condition to a multi-material heat transfer problem using Crank-Nicolson?

I am working on a mixed material model for a melting material and need to enforce both a Dirichlet and Neumann type condition at the interface. Subject to an external surface heat flux at the top of ...
1 vote
61 views

### How to constraint the tangential gradient on a boundary in FEniCS?

The problem I'm considering is a 2D scalar PDE. The domain $\Omega$ is a disk with two holes $\partial\Omega_1$ and $\partial\Omega_2$ and an external boundary $\partial\Omega_0$. The PDE and boundary ...
1 vote
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1 vote
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### Iterative PDE solver for 1D Burgers equation

I am looking for an Iterative Numerical PDE solver for 1D Burgers equation. I need to have access to the intermediate solutions of the Numerical Solver. By iterative methods, I mean techniques which ...
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1 vote
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### Boundary conditions of a 2D explosion case

I want to solve this problem explosion test case. I was wondering about what are usual the boundary conditions for this type of problems. I want the wave to bounce of the boundary of the domain (let's ...
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1 vote
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### Monotonicity of Errors with Respect to Step Sizes in Numerical Methods for PDEs

Consider a non-linear partial differential equation (PDE) (e.g., Burgers' equation) that is solved numerically using a finite difference method (or a similar approach). Suppose a grid search is ...
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### numerical schemes for 1D PDE: for smaller grid size there is an increased roundoff error, larger size more truncation, so sweet spot in between?

I had a discussion with a colleague today. He claimed that usually for a general numerical scheme for solving a general 1D PDE, for smaller grid size there is an increased roundoff error because of ...
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### What exactly is a "unit-torus"?

I've seen references to the "unit torus" in papers such as this (Start of Sec 3.3, page 5). So, what exactly is a unit torus? Is it just a square or cube in d-dimensions with periodic ...
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### How to implement boundary conditions for the Thomas algorithm

For my variable $U(t,x)$, I have implemented the thomas algorithm with $U_j^i$: $$a(x)U_{j-1}^{i+1}+ b(x)U_j^{i+1} + c(x)U_{j+1}^{i+1} = d(x)U_j^{i}$$ Then $\textbf{A}$ is a tridiagonal vector with ...
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### Prof A. Stanoyevitch's finite difference based PDE matlab code

Where can one find Prof A. Stanoyevitch's finite difference based PDE matlab code? They have a book on such a topic but can't find the accompanying code. Is it well received? It's not commonly talked ...
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### Prof Lawrence Shampine's hpde matlab code

Where can one find Prof Lawrence Shampine's hpde matlab code? Is it well received? It's not commonly talked about.
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### Why the following discrete inequality are equal?

When reviewing papers on the numerical solutions of Partial Differential Equations (PDEs), I observed the following equation: $$(1-C\tau)||\theta^n||^2 \leq ||\theta^{n-1}||^2 + C\tau (h^{2r+2}),$$ ...
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1 vote
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### Seeking open-source PDE Solver for inhomogeneous material properties

I'm currently in search of an open-source PDE solver (Finite Element Method is preferred) that can effectively handle the challenge of material properties coefficients associated with each element in ...
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### Literature request covering Chebyshev's pseudospectral collocation method

I would like to request some literature recommendations covering Chebyshev's pseudospectral collocation method for solving space-time PDEs. It would be nice if it even contained some example problems ...
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### FVM for non-regular domain with triangular mesh

Setup The 1D convection-diffusion equation is given by: \tag{1} \frac{\partial u}{\partial t} + v \frac{\partial u}{\partial x} - \mu \frac{\partial^2 u}{\partial x^2} = 0, \end{...
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### Is a sort of "z-drift" the result of numerical precision errors in FDM?

Upon solving the 2D wave equation with Neumann boundary conditions $u_x = u_y = 0$ on a rectangular $10 \times 10 \times 10$ grid, I noticed something odd - $u$ seemed to shift upwards with time. This ...
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### PETSC: Solving a simpler PDE results in error while solving the original equation works in snes/tutorials/ex13.c

In snes/tutorials/ex13.c, there is a function SetupPrimalProblem(), which sets up the $f_0$ and $f_1$ in ...
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### How to get damping matrix for structural model in FE analysis

I need to implement in C a method of obtaining transient solution of damped FE models based on modal results for a structural model (imported CAD geometry) defined with hysteretic (structural) damping....