# Questions tagged [numerics]

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### Courant Friedrichs Lewy condition - how to get it?

I am interested, how can we get CFL condition for every type of PDE? It's known that for 1st order linear equation $$\frac{\partial u}{\partial t}+a\frac{\partial u}{\partial x}=0$$ CFL is get from ...
0answers
129 views

### Algorithms to compute largest gap between smallest nonzero eigenvalues of sparse symmetric matrix

I am looking mainly for c/c++ implementations but also for theoretical algorithms to compute gaps between smallest positive eigenvalues of symmetric, singular matrix or real numbers. To be precise, I ...
0answers
257 views

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### Computing linear combinations of sines and cosines (phasors)

I have a finite series that looks like this: $f(t) = \sum^n_{i=0} A_i cos(\Theta_i + \omega_i t) + B_i sin(\Theta_i + \omega_i t)$ That is, a finite series of pairs of phasors. What's the state of ...
3answers
6k views

### Efficient computation of the matrix square root inverse

A common problem in statistics is computing the square root inverse of a symmetric positive definite matrix. What would be the most efficient way of computing this? I came across some literature (...
0answers
638 views

### how to visualize velocity from Lagrangian particle tracking method

I have few particle's position and velocity information as a function of time. Particle is following a trajectory path, while doing so, one particle may disappear, other particle may appear. Particle ...
1answer
525 views

### Pde problem with robin boundary condition

I have my pde 2D problem with robin condition (form: du/dn +ku=g) to solve with matlab. i have the exact function u and I want to find the function g in robin condition. How can i do it? thanks for ...
1answer
554 views

### Second derivative of the Associated Legendre functions

I would like to compute, as part of the solution of the Laplace equation using the Fast Multipole Method, the second derivative of the associated legendre functions of the first kind . Specifically, I ...
1answer
969 views

1answer
112 views

### Efficient computation of tangent of fraction of angle

I want to compute $a = \tan(f \theta)$ for $f\in [0,1]$, given $g = \tan\theta$. Obviously, I can compute $a = \tan(f\tan^{-1}g)$, but I'm wondering if there's a more efficient way that avoids having ...
0answers
222 views

1answer
199 views

### How can exponential fitting be used with the finite element method?

Restricted to one dimensional problem, is it possible to dynamically adapt the finite element method (FEM) discretisation based on the local value of the Péclet number ($P_e$) for advection-diffusion ...
1answer
88 views

### numerical inaccuracy ellipsoid-ellipsoid collision

I am trying to implement ellipsoid-ellipsoid collision in my C++ code. Briefly this task can described as next: Let's assume that we have two arbitrarily oriented ellipses in the in space and this ...
2answers
2k views

### Does the finite element method impose any restrictions on the Peclet number for numerical stability?

Background on finite volume method When discretising the flux with a central difference stencil of the the advection-diffusion equation restriction $\frac{ah}{d} < 2$ must be observed for the ...
1answer
1k views

1answer
138 views

### Simulating the motion of a elastic body under gravity [closed]

I am doing a numerical simulation of a elasticity problem. It is very simple. A cuboid elastic body with the right end fixed on the wall, under the gravity(but here I set it to be 1 along the z-axis ...
1answer
465 views

### Are these coefficients correctly calculated?

I'm solving a problem (page 16 is in English) in numerical analysis and this is the solution: ...
2answers
187 views

### Continuation procedure to solve for a 2D curve that satisfies f(x,y) = 0

I have some function of $R^2$, that must be numerically computed. For instance, I might be interested in a real-valued contour integral that begins from (x,y) = 0.  f(x,y) = \Re\left[\int_0^{x + iy}...
3answers
549 views

### A problem in 1D linear finite element method

When applying Galerkin method, we have two conventions, i.e. multiply the test function $v$ at left/right, $(v,u)/(u,v)$. Both ways won't matter for a simple problem like Poisson's equation, since the ...