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1500 questions
7
votes
2 answers
Enforcing non-negative constraint in fourier-spectral method
I have a PDE optimization problem, and a scalar field (which I am optimizing over) is supposed to be nonnegative everywhere in the domain. Since I am working in Fourier space for solving this problem numerically, I need to convert this non-negative…
user16835
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7
votes
1 answer
Why does std::complex<> initialize its value to 0 upon default construction?
Doing so strikes me as a waste of time. Consider
std::complex *a = new std::complex[1<<28];
This could be near-instantaneous and only grab pages once they're used, except it isn't.
It appears I'm not the only one bothered by…
Andreas Klöckner
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7
votes
1 answer
Forced viscous damping in elastodynamics
I have an 2D elastodynamics problem, that is a problem which is driven by the Cauchy equation:
$$\rho\ddot u-\mathrm{div}\sigma=\rho f$$
where $u$ is the displacement, $\sigma$ the Cauchy stress tensor, $f$ the density of volumetric forces, and…
Benjamin
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7
votes
2 answers
What exactly causes mesh locking in thin plate bending problems?
In thin plate bending problems, it would be very nice if we could model a thin rectangular plate with a mesh of many elements in the transverse directions, but only a single element in the longitudinal direction. However, when try to model a plate…
Paul
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7
votes
4 answers
Fluid-structure interaction solver for cardiovascular applications
I would like to start running FSI simulations for cardiovascular applications.
More precisely, I'm interested in the behaviour of aortic valve under
physiological flow conditions in which the interaction of fluid and structure
must taken into…
user117893
- 71
- 3
7
votes
1 answer
Python trust region optimization code that allows ellipsoid-shaped trust regions
Are there any high quality trust region optimization implementations that
allow nonspherical ellipsoid trust regions, and
are written in Python, or are easy to call from python?
By nonspherical ellipsoid trust regions, I mean that each Newton…
Nick Alger
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7
votes
2 answers
Comparing various implementations/software packages for large-scale finite element simulations
I currently use FEniCS and Deal.II to solve various FEM problems. I am also writing my own implementation of these problems by directly implementing the data structures, routines, and solvers within PETSc. What kind of comparisons can I draw between…
Justin
- 791
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7
votes
3 answers
Given large $x \in \mathbb{R}$, How to determine if $2^x$ is an integer?
Given large $x \in \mathbb{R}$, I want to know whether or not $2^x$ is an integer. Is there any fast way to answer the question for $x>2^{500}$?
I have also asked a slightly different form of this question on math.se: How many significant figures…
Must
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7
votes
1 answer
Eikonal Equation solver with different grid densities
The Fast Marching Method, Fast Iterative Method, and Fast Sweeping Method are three ways of solving the Eikonal Equation on a discrete grid, essentially just a wavefront spreading out from initial points, e.g.:
The idea is that we want to compute…
Phylliida
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7
votes
2 answers
Initializing implicit linear multistep methods
A sixth order backward differentiation formula (BDF) need six (five plus initial value) previous solutions to get started. How I can get these previous solutions? I need a method accurate to sixth order capable of handling stiff problems.
user3368561
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7
votes
2 answers
applications of computational geometry in fields such as CFD?
Out of curiosity, I was recently trying to search what skills are required to be successful as developer in scientific computing field (e.g. CFD or similar). And to do so, I was going to through various job postings to understand what industries…
Pranav
- 309
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7
votes
1 answer
How to avoid negative values of numerical solution of transport equation using FEM scheme?
The transport equation is actually an advection-diffussion-reaction equation, which has the form as
$$\frac{\partial C}{\partial t} + v_1 \frac{\partial C}{\partial x} + v_2 \frac{\partial C}{\partial x} = D \left(\frac{\partial^2C}{\partial…
winterfly
- 81
- 2
7
votes
3 answers
Strong coupling of a non-linear multiphysic problem: failure with Newton Raphson method
I am trying to solve a multiphysic problem using finite elements and a Newton Raphson solution scheme. I have two non-linear subsystems that are coupled bi-directionally.
The first subsystem includes an equation that I solve for $p_f$:
$\nabla u -…
Johann
- 71
- 2
7
votes
3 answers
Converting from planar polynomial domain to planar polygon
Let's assume we have a planar domain whose boundary can be described with a polynomial curve (like Bezier curves).
Now assume that you want to produce a discretization of the boundary, i.e. you want to produce a polygon by sampling the polynomial…
JuanPi
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7
votes
1 answer
Why are functional representations of systems important in numerical applications?
I tried asking a similar question in SE.Physics, and I got some information regarding the abstract side of this, but I figured I should post here to get more complete information about the numerical benefits of variational formalisms.
Assuming I am…
Ron
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