# Questions tagged [numerical-modelling]

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### Calculation of the EFIE integral

I need help computing the following integral: $$\int_{}\frac{(1+jk|\vec{r}-\vec{r}^\prime|)e^{-jk|\vec{r}-\vec{r}^\prime|}}{|\vec{r}-\vec{r}^\prime|}d\vec{r}^\prime$$ in this integral $\vec{r}$ ...
• 21
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### Discrete wave simulation - absorbing boundaries?

I wrote a simple 2D wave simulation using the following equations: $$\frac{\partial^2 u}{\partial t^2}=c^2\nabla^2u$$ Where $\nabla^2$ is the discrete laplace operator using a Von Neumann neighborhood ...
• 171
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### How to set up the differential equation system to speed up computation?

I've set up a system of differential equations, obtained after discretizing pde, in the following way ...
• 421
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### A simple PDE solution question

I need to ask a question about partial derivatives. I want to solve this equation (steady state, one dimensional continuity equation): $$\frac{\partial (\rho u)}{\partial z}=0$$ which is equivalent to:...
• 71
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• 71
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### Solving differential equation by specifying jacobian pattern

This is a follow up to my previous question posted here I'm trying to construct the sparsity pattern of the jacobian matrix to speed up the computation of a large system of odes. The following is the ...
• 421
given the following ODE: $$\frac{d^{4}w}{dx^{4}} + B\frac{d^{2}w}{dx^{2}} = 1$$ with boundary conditions $w(0) =0 , w(1) = 0,w'(0) = 0,w'(1) = 0$ its possible to solve analytically but I am attempting ...
### Implementing routine for $-\nabla\cdot (k(x,y) \nabla u)=f$ in Matlab
I am solving the Poisson Equation for 2D given by the following expression: $$-\nabla\cdot (k(x,y) \nabla u)=f$$ in a rectangle with Dirichlet conditions on the boundary using Matlab. In principle I ...