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1500 questions
10
votes
1 answer
Is it possible to express an arbitrary tensor contraction in terms of BLAS routines?
I noticed that libraries like numpy and pytorch are able to perform arbitrary tensor contractions at speeds similar to comparably sized matrix multiplications. This leads me to believe that underneath they somehow express these operations in terms…
ilya
- 111
- 4
10
votes
2 answers
FEM for vector valued problems: reference request
I'm a PhD working in a computational mechanics lab. I come from a Math department, and I have a good background for what concerns the basics of finite elements, like inf-sup conditions, DG, non-conforming FEs. I also did some basic codes, like…
bob_bill
- 67
- 10
10
votes
1 answer
Generalization of eigendecomposition problem
Let $A\in \mathbb{R}^{n\times n}$ and $v \in \mathbb{R}^n$. We recognize $Av=\lambda v$ for some scalar $\lambda$ as an eigendecomposition problem. Suppose $\mu \in \mathbb{R}^n$, and let $\odot$ denotes the Hadamard product. Does this system $Av =…
waic
- 173
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10
votes
1 answer
Sensitivity of $y$ w.r.t. to $x$ in $y=f(x)$ where f is a routine
Given a model $f$ as a programming routine, such that we are able to compute $y=f(x)$ for any $x \in \mathcal{D}$, I am interested in the sensitivity (or let us say derivative) of $y$ with respect to $x$.
The important thing is that $f$ could be any…
outlaw
- 264
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10
votes
1 answer
How to document math formulations in scientific computing codes?
I am writing the code relate to math.
There is some complicated math formulation in the project.
Directly writing the calculation code leads to hard understanding; thus I want to comment on the formulation.
I want the comment can be readable, and…
Xu Hui
- 323
- 1
- 9
10
votes
5 answers
Fourier pseudo-spectral method and numerical dissipation
Performing a direct numerical simulation of isotropic turbulence with Fourier pseudo-spectral method (Orzag & Patterson, PRL, 1972) using FFT.
For a background of the method, which is widely used in turbulence community, you can see this course:…
ucsky
- 419
- 3
- 10
10
votes
3 answers
Maximizing unknown noisy function
I'm interested in maximizing a function $f(\mathbf \theta)$, where $\theta \in \mathbb R^p$.
The problem is that I don't know the analytic form of the function, or of its derivatives. The only thing that I can do is to evaluate the function…
Jugurtha
- 707
- 4
- 12
10
votes
3 answers
Linear algebraic research direction that's not to do with differential equations and physics?
So I've found some interesting linear algebraic research areas that's both pure-ish, with a numerical bent to it, too -- e.g. inverse eigenvalue problems have both interesting theoretical and computational aspects, spectral graph theory seems pretty…
Samantha
- 101
- 2
10
votes
1 answer
Is using std::valarray considered good practice?
C++ has had the std::valarray class since the C++98 standard. It is meant to facilitate numerical computations, providing the sort of operations one would expect of a class implementing the mathematical concept of a vector space (with minor oddities…
Wolfgang Bangerth
- 55,373
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10
votes
4 answers
Fast and accurate double precision implementation of incomplete gamma function
What is the state of the art way of implementing double precision special functions? I need the following integral:
$$
F_m(t) = \int_0^1 u^{2m} e^{-tu^2} d u
= {\gamma(m+{1\over 2}, t)\over 2 t^{m+{1\over 2}}}
$$
for $m=0, 1, 2, ...$ and…
Ondřej Čertík
- 2,930
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- 40
10
votes
1 answer
Are there testing frameworks for numerical software development
I found that a lot of my computational science programming has testing requirements that are not covered by standard test frameworks:
Computation time testing
To make sure that algorithms don't get slower. I could do something…
Bananach
- 799
- 3
- 13
10
votes
2 answers
Task-based shared-memory parallel libraries in Scientific Computing
In recent years, several libraries/software projects have appeared that offer some form or another of general-purpose data-driven shared-memory parallelism.
The main idea is that instead of writing an explicitly threaded code, programmers implement…
Pedro
- 9,573
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10
votes
1 answer
Is there any explicit symplectic Runge-Kutta method?
As far as I know, all the symplectic Runge-Kutta methods are implicit which need to solve non-linear equations during the calculation. Is there any explicit method? If not, why?
Joseph Li
- 103
- 4
10
votes
3 answers
Ways of visualizing event data in search of performance issues
I'm trying to optimize an MPI application with a highly asynchronous communication pattern. Each rank has a list of things to compute, and sends messages as necessary if the inputs or outputs reside on a different rank. In addition, each rank is…
Geoffrey Irving
- 3,969
- 18
- 41
10
votes
2 answers
Finite difference scheme for "wave equation", method of characteristics
Consider the following problem
$$ W_{uv} = F $$
where the forcing term can depend on $u,v$ (see Edit 1 below for the formulation), and $W$ and its first derivatives. This is a 1+1 dimensional wave equation. We have initial data prescribed at $\{u+v…
Willie Wong
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