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2
votes
1answer
35 views

Zero-k mode in Pseudo-spectral solution of Stokes Flow

I'm trying to solve a Stokes flow problem with a pseudo-spectral method in periodic boundary conditions. The equations of interest are $-\nabla^2 \bf{v} + \nabla p = \bf{f} \\ \nabla \cdot \bf{v} = ...
1
vote
1answer
72 views

Solve steady state reaction-diffusion/Helmholtz equation numerically

I am solving a problem of the form: $\frac{\partial u(x,y,t)}{\partial t} = \nabla^2 u(x,y,t) - f(x,y,t)u(x,y,t) - \kappa(x,y,t)$ At the moment, I am solving this at each time step by assuming a ...
1
vote
3answers
100 views

Solve diffusion equation with linear source term

I would like to solve numerically the diffusion equation, where the sink term depends linearly on the field, and there is field-independent sink: $\frac{\partial^2 u(x)}{\partial x^2} =f(x)u(x) - ...
-2
votes
1answer
94 views

explain the difference between 1D Poisson solvers

I compared 2 methods for 1 dimensional Poisson equation solution. One is finite-difference method, "Successive Overrelaxation" from http://www.cs.berkeley.edu/~demmel/cs267/lecture24/lecture24.html; ...
2
votes
1answer
61 views

Trignometric/Fourier spectral collocation with zero Dirichlet BC in 2D

I am concerned with numerical solution to the following problem on $[0,1]\times[0,1]$. $\dfrac{\partial\theta}{\partial t}+u(x,t).\nabla \theta(x,t)=\kappa \nabla^2\theta(t,x)$ with Dirichlet ...
2
votes
1answer
86 views

Boundary conditions Chebyshev differentiation

I was wondering if anyone has any experience dealing with boundaries when implementing chebyshev differentiation. I am currently trying to implement a no slip boundary condition to solve the ...
3
votes
1answer
57 views

Two approaches to solving diffusion equation in Fourier space

I want to numerically solve the diffusion equation $\partial_t u = D \partial_x^2 u$ in Fourier space, and can think of multiple ways to do it. Setup Option 1 Differentiating $u$ twice in Fourier ...
2
votes
0answers
110 views

Integration of nonlinear PIDE via spectral methods

At the mean-field level, the dynamics of a polariton condensate can be described by a type of nonlinear Schrodinger equation (Gross-Pitaevskii-type), for a classical (complex-number) wavefunction ...
2
votes
3answers
171 views

Solving Stokes flow with walls using Oseen tensor

Introduction I've developed a code to solve for generalised, incompressible 2D Stokes flow $\eta \nabla^2 \mathbf{v} - \nabla p + \mathbf{S} = 0$ $\nabla . \mathbf{v} = 0$ where $\mathbf{S}$ can ...
1
vote
2answers
204 views

Computing Kolmogorov/Energy spectrum for turbulent boundary layer

Previously, I have calculated energy spectrum for 3D DNS data obtained for isotropic turbulence which is equally spaced in all three directions and then to compute the energy spectrum, one performs ...
3
votes
1answer
162 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
130 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
168 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
293 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
106 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 $f(t_i, \cdot)$ ...
6
votes
3answers
266 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
32 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 ...
5
votes
0answers
245 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 ...
4
votes
1answer
287 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
259 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 ...