7 votes

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 ...
F_B's user avatar
  • 111
5 votes

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 ...
Federico Poloni's user avatar
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 ...
Philip Roe's user avatar
  • 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, ...
Neil Lindquist's user avatar
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 ...
helloworld922's user avatar
1 vote

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 ...
Lutz Lehmann's user avatar
  • 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 ...
Sardine's user avatar
  • 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, ...
Orkolorj9's user avatar

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