Questions tagged [reference-request]
This tag is for requests for books, papers, and citations.
284 questions
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What does the k and l in top-k and bottom-l usually stand for?
I've seen a lot of papers with the terms top-k, bottom-l, avg-k, etc e.g. in this paper. Is there a usual meaning for the k and l that I'm unaware of? Maybe I didn't pay due attention during ...
- 103
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58
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More accurate ways to approximate a Finite Fourier Sine Transform?
I'm reading through this research paper, and from section 2, I have deduced that the Finite Fourier Sine Transform along $0\le x\le L_x$ is formulated as
$$F(m) = \frac{2}{L_x}\int_0^{L_x} f(x) \sin\...
- 145
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References on equality-constrained matrix-free inexact SQP
I want to implement an equality-constrained SQP method for a fairly large and sparse problem. As such I need to use iterative solvers where my matrix-vector products are matrix-free. Also I compute my ...
- 3,021
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Need advice for how to solve for potential flow on a sphere?
outsider to computational science here. This type of problem comes up in my field, however we focus on qualitative analysis, so I want advice for the computational side of things. This problem would ...
- 145
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Remeshing open source software for hexahedral elements?
I am looking for open source software recommendations for remeshing distorted hexehedral triangulations, arising e.g from large deformation hyperelasticity boundary value problems.
Easy interfacting ...
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140
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'Spurious convergence' for oscillatory integrals
I am reading the paper
J. N. L. Connor and P. R. Curtis. A method for the numerical evaluation of the oscillatory integrals associated with the cuspoid catastrophes: Application to Pearcey’s integral ...
- 906
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117
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Weak coupling nonlinear solvers in PDE solvers
I have two time-dependent PDE solvers that target the nonlinear equations:
\begin{align}
\partial_t u - L_1(u) u &= f(v), \\
\partial_t v - L_2(v) v &= g(u),
\end{align}
where $L_1$ and $L_2$ ...
- 136
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65
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How to approximate the Koopman operator of a non-autonomous system?
For an autonomous system, the Koopman operator can be approximated by using dynamic mode decomposition (DMD).
I am looking for references that show how to approximate the Koopman operator $K$ (or its ...
- 417
6
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1
answer
752
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Name this modification of Newton's method
To reduce the cost of the Newton-Raphson method for multivariate rootfinding, a common trick is keeping the Jacobian matrix fixed for several iterations. For instance, in pseudocode:
...
- 13.1k
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121
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Fitting with spline but adding soft shape constraint
I would like to fit some data points that I know look somehow like a deformed ellipse. I would like to fit them with a spline but also adding something like a soft constraint that it should also look ...
- 225
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164
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Coupling simulations with different time-steps
Suppose I have two fluid solvers which which operate on two spatial domains which share a common boundary. I want to run them separately, and couple them.
Do I need run them at the same time-step? Or, ...
- 898
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84
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constrained optimization and active constraints at solution: statistical measures
Suppose we want to minimize an objective function (fitting parameters of a PDE) and the parameters have box constraints and linear inequality constraints. Some of the constraints are active at the ...
3
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1
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189
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Any FEM book recommendations that focus on stability and proofs on error bounds?
Everything from descrete stability proofs for steady state and time dependent problems. energy stability, stability of mixed methods, nonlinear problems, vector valued problems in fluid/structural/EM, ...
- 536
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75
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Immersed Boundary FEM reference recommendation
I want to do some Fluid-Structure Interaction using the Immersed Boundary FEM.
Could you please recommend some books or lecture notes on it?
- 211
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81
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Solving systems of the form $y_i=UW x_i$ for $U,W$
I'm looking for pointers/examples of solving system of equations $y_i=f_W(f_U(x_i))$ for $W,U$ where
$f_M(x) \approx M x$
$U,W$ are updated simultaneously
$i\in (0, 10^{12})$
Simplest example is ...
- 2,779