# All Questions

7,522 questions
27 views

### Numerical stability while modeling wave equation in staggered grid

I have modeled a simple wave equation given by: \begin{align} & \begin{cases} u_t = v_x \\ v_t = u_x \end{cases} \end{align} Boundary conditions given on interval $M=[-1,1]$ by: \begin{align} u(...
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### ODE: should Euler implicit be more accurate than Euler explicit for a given computational step?

I am aware than Euler explicit is conditionally stable, and Euler implicit is unconditionally stable. And I am aware that it is probably pointless to use Euler implicit with a small computational step ...
130 views

### Libraries to deal with unstructured grids

I am dealing with a *.cgns file. This mesh format, when saved as an unstructured grid, holds nodes coordinates, nodes connectivity per element and boundary ...
62 views

### Wrong result of 'ddot' from BLAS

I am having trouble with a C/C++ program that uses the BLAS routine ddot. I am running Linux and so far LAPACK routines worked without any problems. I get a wrong ...
20 views

I am trying to solve a nonlinear diffusion-type problem using the finite element method which has the following terms: $-\nabla\cdot k_1\nabla u - \nabla\cdot k_2\nabla\mathrm{ln}(u) = 0$ in $\Omega$ ...
82 views

### what is Sherman-Morrison formula

Can someone please explain what is the Sherman-Morrison formula and it's specialities when it comes to matrix calculations? I'm a little bit confused on understanding how the preconditioning works ...
89 views

### How to simulate basic semiconductor models using the Drift-diffusion model on Python?

I'm trying to simulate basic semiconductor models for pedagogical purposes--starting from the Drift-diffusion model. Although I don't want to use an off-the-shelf semiconductor simulator--I'll be ...
62 views

### Element Preconditioner

Im just working on a preconditioner for the linear equation system $Ax = b$ arising in FEM for elliptic PDE. $A$ is a s.p.d Matrix with real valued entries. I read something about the element by ...
128 views

### How good are current implementations of rand() in C?

There is a lot of literature that indicates using rand() for simulations might be harmful. A couple of them are as follows: https://www.sciencedirect.com/science/...
133 views

### Double potential well with Python

I'm trying to understand the Schrödinger equation and solving it a bit better, and I'm running into some doubts while coding, even though I am adapting the code to this situation. Also I tried asking ...
41 views

### Thermal stress to displacement through finite volume method

I am attempting to solve for a displacement field where I know the thermal stresses on my discretized domain, which consists of hex cells. My first question is: is easier way to solve for the ...
42 views

100 views

### Fast and Numerically Stable Pairwise Distance Algorithms

I'm looking for resources on fast, numerically stable pairwise euclidean distance algorithms. In particular, suppose $A \in \mathbb{R}^{M \times D}$ and $B \in \mathbb{R}^{N \times D}$ are two sets of ...
80 views

### Inverting small matrices: canned factorization versus explicit formula

I am interested in solving a large number of small linear systems of equations, $Ax=b$, with $A$ either $2\times2$ or $3\times3$. Assuming none of these systems are actually singular, is there ...