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1500 questions
6
votes
1 answer
Calculate large and small frequency separation for the Sun
I want to determine the big and small frequency seperation from timeseries data for the sun. An excerpt of the data (timeseries and power series) is plotted below.
The power series is calculated in MATLAB like this:
n = length(t_obs);
dt =…
user4452
6
votes
0 answers
Stochastic Galerkin projection approach for using generalized polynomial chaos expansion (GPCE) in solving PDE
I want to know if there is any way to define the test and trial function in the way that I want instead of using the default functions. So if I want define the polynomial and basis and coefficient, how can I do it in Fenics? Here is the concept in…
Bahram
- 111
- 3
6
votes
1 answer
Boundary value method for equation $u_{tt} = u_{xxx}$
I have this funny equation
$$
\frac{\partial^2 u}{\partial t^2} = \frac{\partial^3 u}{\partial x^3}, \qquad x \in [0,1], \qquad t \in (0,T]
$$
with initial conditions $u(x,0) = \sin(2\pi x)$, $\frac{\partial u}{\partial t}(x,0) = 0$ and periodic…
Uroš
- 263
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- 7
6
votes
0 answers
What is the best OpenFOAM RAS turbulence model for a motorbike/vespa problem?
I am learning OpenFOAM as a hobby and using my Vespa racing as the topic to apply it to. The objective is to produce modifications that improve the top speed (as well as getting some values such as lift). I am basing my simulation on the motorbike…
internetscooter
- 447
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- 6
6
votes
1 answer
FEniCS: how to access coordinates when writing an equation for a trial function
I need to solve the following equation in FEniCS:
$$
\boldsymbol{\nabla} \cdot \begin{pmatrix}
f(y)\frac{\partial u}{\partial x} - g(x,y)\frac{\partial u}{\partial y} \\
- g(x,y)\frac{\partial u}{\partial x}+f(x)\frac{\partial u}{\partial y}
…
facetus
- 358
- 2
- 8
6
votes
1 answer
Reference BLAS/LAPACK from NETLIB is twice as fast as MKL for complex numbers
I'm solving the Helmholtz equation using PETSc. I found with the PETSc configure option --download-f-blas-lapack my program runs twice as fast over running it with MKL. Is this a common trend or are there other factors at play? I'm using gcc and…
Hui Zhang
- 1,319
- 7
- 16
6
votes
0 answers
Benchmarks or generic configurations for optimal flow control
I am about to test my algorithms for solving optimal control problems of type:
Find an input $u$, such that for a time interval $(0,T]$ the cost functional
$$J(v,u) = \mathcal M(v(T)) + \int_0^T\mathcal K(v(t),u(t)) dt, $$
becomes minimal, where…
Jan
- 3,418
- 22
- 37
6
votes
1 answer
Compute spatial second derivatives in Isogeometric analysis
Motivation:
In isogeometric analysis, state variables(e.g. displacement) are defined in the parametric domain, which can be mapped to the physical domain by $\boldsymbol{\xi}\mapsto \boldsymbol{x}$ as shown beneath. However the quantity related to…
newbie
- 249
- 1
- 3
6
votes
1 answer
generalized eigenvalue problem
I need to solve a real generalized eigenvalue problem
$Ax= \lambda Bx(*)$
A and B are calculated from equations…
ZeyuHu
- 317
- 2
- 7
6
votes
1 answer
Trouble implementing Neumann boundary conditions because the ghost points cannot be eliminated
Neumann boundary conditions are implemented by introducing ghost points outside the domain and then using the boundary conditions to eliminate the ghost points. For example, see this question.
I have a set of three equations in variables $(u,v,w)$…
boyfarrell
- 5,409
- 3
- 35
- 67
6
votes
1 answer
SVD and Lanczos method
I have been given the task of implementing SVD using the Lanczos method.
As I understand it only helps to find eigenvalues using a sequence of tridiagonal matrices, but i don't know how to apply this to actually computing the SVD.
Do I need to…
John Smith
- 63
- 1
- 3
6
votes
1 answer
How to perform multigrid technique when relaxation methods don't converge?
It is well known that, when a system of linear equations is obtained from discretization of partial differential equation, the solution process can be accelerate significantly by multigrid technique. In the smoothing step of a multigrid cycle,…
Hanyu Ye
- 191
- 5
6
votes
2 answers
Which libraries have good implementations of Basis splines?
I'm looking to use the finite element method with B-splines as my function basis. Which C/C++ libraries have good B-spline support?
Specifically, I'm looking for an implementation of a stable algorithm, even if it's slow. I plan to precompute a lot…
Dan
- 3,355
- 3
- 21
- 47
6
votes
2 answers
Are there any specialized methods available for solving structurally symmetric sparse linear systems?
When solving $Ax=b$, prior knowledge about $A$'s structure can help in designing an efficient solver which exploits this information (e.g conjugate gradient method is to be used when $A$ is symmetric and is preferable to GMRES when we know $A$ is…
smilingbuddha
- 645
- 5
- 10
6
votes
0 answers
How does GAMG in OpenFOAM really work?
I use OpenFOAM for CFD simulations. A very popular preconditioner is GAMG which needs a low number of iterations per a time step in SIMPLE or PISO solvers that are used to simulate the fluid flow.
I would like to understand how GAMG prepares the…
luksmir