7
votes
Accepted
Understanding the diffusion error of numerical schemes
Just figured it out. The solution diffuses BY A FACTOR OF $|G|^n$ after n time steps. So in my example, for the low frequency case, if let's say the original signal was a square wave advecting to the ...
- 111
5
votes
Accepted
The error propagation in calculating the inverse using a matrix decomposition
Irrespective of how you compute an approximate inverse $K\approx M^{-1}$, there is a limit to the (normwise) accuracy up to which $KM \approx I$ can hold: just because of the fact that $K$ and $M$ are ...
- 11.1k
3
votes
Understanding the diffusion error of numerical schemes
@FB, Apparently you are now sorted, but I just wanted to point out a source
of confusion you may not yet have considered. Many people call $|G|$ the
amplification factor, which I find much more ...
- 1,084
3
votes
Storing Raw Simulation Data or Truncated Data?
I would recommend keeping the computation in your original precision and reducing the accuracy just when you write, unless the computation is too slow. If you reduce the precision of the computation, ...
- 750
2
votes
Finite difference approximation error
Take the Taylor series and re-arrange it to be
$$
f'(x) - \frac{f(x+h)-f(x)}{h} = - f''(x) \frac{h}{2} - f'''(x) \frac{h^2}{3!} - f^{(4)}(x) \frac{h^3}{4!} + \ldots
$$
Assuming that $f^{(n)}(x)$ is ...
- 2,391
1
vote
Accepted
Reverse engineering phase shift and numerical damping
For an undampened harmonic oscillator $\ddot x+w^2x=0$ you can set the velocity component to $\dot x=wy$ and then $z=x+iy$ to get
$$
\dot z=wy-iwx=-iwz.
$$
The implicit Euler method can now be exactly ...
- 5,489
1
vote
Geometrically nonlinear finite element problem and mesh distortion
In FEA, the basis functions are defined over a reference element, here a unit square. This is a "function basis factory" of sorts, as you then write a global basis restricted to a given ...
- 368
1
vote
Error propagation through an FFT
In Higham's book there is throughout and easily understandable treatment of the error in the Cooley-Tuckey algorithm.
Unluckily the matrix pproach proposed by mathew gunther leds to overestimates, ...
- 21
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