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### How to write these function with disciplined convex programming rule to use CVX? x*(2^(y/x)-1)

I have the following functions in an optimization problem. $x\times 2^{(y/x)-1}$ $x \log (a+b\times 2^{(y/cx)-1} )$ Here, x,y>0, and also a,b,c>0, and b>a. For these conditions, I checked ...
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### How GMRES method finds smallest singular value and the corresponding singular vectors of a matrix?

https://stackoverflow.com Krylov solvers for iterative computation of the smallest singular value and the corrensponding singular vectors of a matrix Edit: This is a follow-up question to How to ...
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### Calculate stable time step DG method for advection-diffusion

For stable time steps for the RKDG method for transport equations we require that $$\Delta t \le \frac{\Delta x CFL}{(2k + 1)|\lambda|},$$ where $\lambda$ is the eigenvalue of our conservation law ...
83 views

### Efficient way to solve a set of linear equations $Ax=b$ when $A$ is sparse and some elements of $b$ are equal to zero

I have a set of linear equations, $Ax=b$. And about half of the elements in the right-hand side (vector $b$) are equal to zero. My system matrix $A$ is a sparse complex matrix. And $A$ is in the size ...
49 views

### Solving large sparse system

I am working on a problem with very large sparse matrices. I'd like to compute $A^{-1} B$, that is a crucial part of converting DAE to ODE (and there is no workaround). Here size of $A$ is 2E+5 x 2E+5 ...
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### Methods for solving discrete PDEs using algorithmic differentiation results

I'm looking for a method to solve a 20000 variable, 20000 residual non-linear PDE with a Galerkin method. I have Fortran subroutines for: The residuals: $\vec{r}(\vec{x})$; Their Jacobian multiplied ...
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### Flux boundary condition in solute transport

I have a pretty naive question, though important to me. Usually when solving the following PDE in solute transport: $\frac{{\partial C}}{\partial t } = \nabla. (D\nabla C -vC )=0,$ one can be asked to ...
7k views

### Use of machine learning in computational fluid dynamics

Background: I have only built one working numeric solution to 2d Navier-Stokes, for a course. It was a solution for lid-driven cavity flow. The course, however, discussed a number of schemas for ...