# Tag Info

Accepted

### The rate of convergence for finite difference methods for Poisson's equation with piecewise constant data

Let's examine the one-dimensional three-point stencil case in detail, because I think it's important to be clear just how this behaviour arises, and what it means to set a point to a certain value in ...
Accepted

### Solving Ax = b with sparse A and sparse b

When looking at the solution of your system, you will find that almost all entries of $x$ are nonzero although the right-hand side is "sparse". Hence, whatever algorithm you use, it'll have to visit ...
Accepted

Accepted

### How to solve a Poisson equation using the finite difference method when there is an object inside a domain?

If you have simple, grid-aligned interior objects or accuracy is not crucial then stick with the method you have described. If you need to accurately represent arbitrary boundary shapes then you're ...

### 1D inhomogeneous Poisson PDE with Dirichlet BCs, slow convergence

The answers so far seem to me to be completely off target. The boundary conditions you have are consistent with the r.h.s. of the equation and the matrix $L$, so they are not the problem. Instead, ...

### Poisson equation with Neumann boundary conditions

I think this happened because $L$ is a finite-difference operator that approximates your equation with some error (it is $\mathcal O(dx^2)$). To get small error your should increase ...

### explain the difference between 1D Poisson solvers

First, some notation for clarity. We're talking about solving $u_{xx}=f(x)$. So $u$ is the solution and $f$ is the right hand side. What makes you think either of your solutions is or is not correct? ...
Accepted

### Is it necessary to use Poisson - Boltzmann equation if I only need to build electrostatic potential from a PQR file?

So Is it neccesary to use Poisson - Boltzmann equation if I only need to build electrostatic potential from a PQR file? No. You can use Poisson. Since you know the positions of each point charge, ...
Accepted

### Discrete Poisson Equation with Pure Neumann Boundary Conditions

Previous comments gave you good suggestions, I try to add some more. Firstly, your example 2x2 really does not correspond to zero Neumann boundary conditions. In fact, one can show that your choice ...

### Discretize Poisson equation with derivative of delta function as source

As noted by others, this PDE is not well-posed in the Strong Form. However, you can take some function which asymtopically approximates the Dirac Delta and use that (where the error in the ...
One of the standard ways to handle singular problems like Poisson with Neumann boundary conditions which lead to a sinuglar problem $Ax=b$ is to make the obtained solution orthogonal to the kernel (...