# Tag Info

Accepted

Accepted

### Memory issues with iterative solvers

As you pointed out, your matrices are sparse which means that the number of non-zeros is small compared to the number of zeros. There are several formats to store such matrices, e.g. COO, CSC, CSR etc....

### Discretization of Poisson's equation with 2d permittivity tensor

You have \begin{align} \nabla \cdot \left(\begin{pmatrix} a & b \\ c & d\end{pmatrix} \nabla \phi \right) &= \nabla\cdot\begin{pmatrix} a \partial_x\phi + b\partial_{y}\phi \\ c\partial_{x}...
Accepted

### Solving Poisson's Equation with Periodic Boundary Conditions

Here's what I think the problem is. You have the equation: $$\Delta u(x) = f(x), \, x\in \Omega.$$ where $\Omega$ is a circle/torus. First you have some compatibility constraints you have to satisfy. ...
Accepted

### Solving new linear system that comes from an $p$ enrichment

What you are thinking of is something that uses the structure of the augmented matrix to make solution of the system simpler. For example, one could be tempted to think of forming the Schur complement ...
Accepted

### Laplace's equation with periodic Dirichlet boundary conditions

This is not just a "numerical discontinuity". Are you sure that this is the problem you want to solve? $\Phi$ looks like a phase, which is defined up to $2\pi$. That may be what you refer to as "...
Accepted