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Results tagged with laplacian
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user 41748
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Applying spectral method to a damped, driven 2D bending-mode wave equation on an irregular d...
To clarify, consider an example in 1D:
In the interior, the discrete Laplacian is $\{1,-2,1\}$
At an e.g. right edge for Dirichlet boundary conditions, the discrete Laplacian is $\{1,-2,0\}$
For Neumann … boundary conditions, the discrete Laplacian at this boundary is $\{1,-1,0\}$. …
- 153
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Applying spectral method to a damped, driven 2D bending-mode wave equation on an irregular d...
These 16 components represent the top 16 eigenmodes of the Laplacian operator $\nabla^2$ with Dirichlet boundary conditions set to zero. … boldsymbol w}_{\boldsymbol x,t}} -d \dot {\boldsymbol w}_{\boldsymbol x,t} + {\boldsymbol u}_{\boldsymbol x} {\boldsymbol u}_t.
$$
Take the Fourier transform in time , and change to the eigenbasis of the Laplacian …
- 153