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4 votes

"Cleanest, most professional" approach to implement a finite differences scheme in dimension greater than two

Finite differences are implemented by fitting a (multivariate) interpolating polynomial through a set of points and taking the derivatives of said interpolating polynomial. Contrary to popular belief (...
lightxbulb's user avatar
  • 2,162
4 votes

How to refine $h$ and $\Delta t$ for convergence tests on evolution PDE

Here are a few solutions that you could explore to determine the orders in space and time. 1) Separate study of time error You can use a given spatial mesh, and perform multiple simulations with finer ...
Laurent90's user avatar
  • 1,943
2 votes

How to derive excitation equation used in Finite-Element-Method waveport-driven simulation?

The second term arises from imposing an impedance/absorbing boundary condition, $\hat n \times \nabla \times \vec E = -jk_0\cdot \hat n \times \hat n \times \vec E$, after applying integration by ...
rchilton1980's user avatar
  • 4,896
1 vote

Formulation of K for tetrahedral elements for the Finite Element Method

You have applied constraints at only a single node so your global stiffness matrix is singular. (Your linear equation solver should have reported this.) To prevent rigid body motion of your cube of ...
Bill Greene's user avatar
  • 6,074
1 vote

How to ensure solution evolves forward in Modified Riks Method by Crisfield?

You are correct that you cannot control the direction of the continuation in general just from looking at the loads and residuals. There has to be some sort of notion of direction inherent to the ...
whpowell96's user avatar
  • 2,478

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