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3
votes
1answer
58 views

spectral decomposition in Numpy, sign difference

I am trying to follow along with an example from a book, but I get seemingly different answers depending on which spectral decomposition function I use in Numpy. I am trying to transform the Matrix G, ...
2
votes
1answer
59 views

2d pseudo-spectral turbulence simulation with random initial velocities

I am trying to write a 2d pseudo-spectral DNS code with random initial velocities. This is kind of a classic simulation where the very tiny vortices group together forming larger and larger vortices ...
6
votes
2answers
144 views

Spectral Methods in time

I was reading up on Spectral Methods for PDEs. In all the descriptions I read, while the position component is approximated via a Fourier series or other methods, the time component is still ...
2
votes
1answer
172 views

Partial derivatives of a 3D array in Matlab

I'm interested in taking some partial derivatives of a 3 dimensional array in Matlab - say $A(i,j,k)$ approximates $f(x_i,y_j,z_k)$. I need to approximate things like $\partial_{xy}f$, ...
2
votes
0answers
84 views

Choosing good basis functions to approximate a Lipschitz function

Let $D = \left\{0, t_1, t_2, \ldots, t_n\right\} \times [0,1]$ and $$ f: D\to [0,1], $$ be a function of time and a one-dimensional space. There is no analytical formula for $f$, but $f(t_i, \cdot)$ ...
5
votes
3answers
200 views

Conforming mesh refinement for quads/hex elements

The context - I'm working with a spectral FE (higher order interpolation at GLL nodes) code on conforming hexahedral meshes, and our PI is interested in improving mesh quality, possibly with adaptive ...
0
votes
1answer
30 views

a question about kernelized locality preserving projections

kernel LPP is of form: $$\min_{\alpha} \ \alpha^{T}KLK\alpha \\ s.t. \ \alpha^{T}KDK\alpha = 1$$ and it eventually results in solving generalized eigenvalue problem below: $$KLK \alpha= \lambda KDK ...
6
votes
0answers
182 views

Stochastic Galerkin Projection Approach for using Generalized Polynomial Chaos Expansion (GPCE) in solving PDE

I am not sure if this is very general question but I want to know Is there any way that I can define the Test and trial function in the way that I want and dont use the default functions. so if I want ...
3
votes
1answer
191 views

Chebyshev spectral differentiation via FFT

I am using the Chebyshev spectral differentiation technique that is described concisely under "details" here. The idea is to take the initial data $v_0,v_1\,...,v_N$ and store it in union with itself ...
4
votes
2answers
200 views

Orthonormalized Bernstein polynomials using Gram-Schmidt

I was wondering, before trying to do that myself, has anyone attempted to do orthonormalization of Bernstein polynomials using Gram-Schmidt? I discussed this with several people and have been told ...