# All Questions

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127 views

### How to implement flexible gmres in matlab?

About the flexible GMRES (fgmres), we know that it is a variant of right preconditioned gmres. And the robust command gmres in matlab as follows: ...
41 views

### Heat diffusion simulation in a 3D piston using FENICS

I'm trying to simulate the heat diffusion in a 3D piston. I marked the boundaries on GMSH. I have used a Dirichlet BC of 300 on the top face of piston. But the results look abnormal. There is a ...
51 views

### What is the reason for this finite-difference high errors on non-uniform grid?

tl;dr Using a Taylor-matched method to find coefficients for the discretized equation $\mathbf{A} \vec{f}'' = \mathbf{B} \vec{f}$, a Fortran code has been implemented to find the second derivative ...
159 views

79 views

### Solve a nonlinear system of equations with condition symbolically

Consider the following system of nonlinear non-dimensional ODE : \begin{align*} \frac{d\bar{x}(\tau)}{d\tau}=\quad&\bar{x}\left[1-\bar{x}-\frac{\bar {y}_{1}}{\bar{m}_{1}\bar {y}_{1}+\bar{x}}-\...
42 views

58 views

### Optimization with the constraint of rank=1

I have the following matrix $$A = [x_1, x_2, ..., x_n],$$ where $x_i \in \mathbb R^n$. But I know the relationship that \begin{align} x_2 = s_2 x_1 \\ x_3 = s_3 x_3 \\ ... \end{align} where $s_i$...
115 views

### Fastest way to calculate the $2$-norm (or an upper bound for the $2$-norm) of the inverse of a matrix $A\in \mathbb{C}^{N\times N}$

I have a matrix $A\in \mathbb{C}^{N\times N}$ and I need to calculate $||A^{-1}||_{2}$ efficiently. Can it be done without having to evaluate the inverse explicitly? In general, I am looking for ...
575 views

### Help with Fourier beam propagation method

I am working on implementing the Fourier beam propagation method in C++. I am really more of a programmer than a physicist but I think I have a good understanding of what I am trying to do. Here is ...
172 views