Questions tagged [reference-request]
This tag is for requests for books, papers, and citations.
273
questions
17
votes
2
answers
4k
views
Drawbacks of Newton-Raphson approximation with approximate numerical derivative
Suppose I have some function $f$ and I want to find $x$ such that $f(x)\approx 0$. I might use the Newton-Raphson method. But this requires that I know the derivative function $f'(x)$. An analytic ...
- 273
7
votes
3
answers
265
views
Wanting to learn about matrix solvers
Edit: I was advised to replace the question with a more specific one.
Coming from a very theoretical background, I'm pretty ignorant about what practical matrix solvers exist. (I have been, and will ...
- 173
6
votes
3
answers
1k
views
How to quickly implement and test a turbulence model?
What is the best software for quickly implement and test a Reynolds Averaged Navier-Stokes turbulence model ?
- 419
25
votes
3
answers
16k
views
Recommendation for Finite Difference Method in Scientific Python
For a project I am working on (in hyperbolic PDEs) I would like to get some rough handle on the behavior by looking at some numerics. I am, however, not a very good programmer.
Can you recommend ...
- 677
13
votes
3
answers
1k
views
Blaze linear algebra library?
The paper "Expression Templates Revisited: A Performance Analysis of Current Methodologies" in SIAM Journal of Scientific Computing references the "Blaze" linear algebra library. I haven't heard of it ...
- 805
16
votes
4
answers
2k
views
Book reference for Numerical Analysis
I've had a glimpse of Numerical Analysis (majorly, Numerical Methods like root finding, quadratic equations and other preliminary stuff) in my Calculus class but now, I find myself wanting more ...
- 3,344
9
votes
3
answers
1k
views
Construction of $C^1$/$H^2$-conforming finite element basis for triangular or tetrahedral mesh
In the paper Hierarchical Conforming Finite Element Methods for the Biharmonic Equation, P. Oswald claimed Clough-Tocher type elements has $C^1$-continuity while being a cubic polynomial on each ...
- 2,542
4
votes
3
answers
843
views
Quality Measures for Various Pseudo-Random Number Generators
According to this paper,
Ideally, a pseudorandom number generator would produce a stream of
numbers that:
are uniformly distributed,
are uncorrelated,
never repeats itself,
...
- 12k
8
votes
3
answers
282
views
Reference Request for Profiling High Performance Computing Codes
I write codes in Fortran and C for various matrix algorithms. However, when I profile my codes using VTune, I usually run into some terminology that I cannot fully appreciate. Is there a good resource ...
- 3,344
3
votes
1
answer
199
views
High-resolution finite volume schemes for two phase flow (fields with jumps) literature sources
what other recent sources of literature on this topic would you recommend?
This is where I'm starting from:
Leveque's article: HRIC scheme
But the related articles seem to be a bit dated (some up ...
- 1,916
7
votes
5
answers
887
views
Adjoint method for optimization problem
I am interested in the adjoint method for shape optimization problems.
However, I couldn't find a helpful introduction. So I come here and look forward to some enlightening advices.
Could you direct ...
- 249
11
votes
1
answer
4k
views
weighted SVD problem?
Given two matrices $A$ and $B$, I'd like to find vectors $x$ and $y$, such that,
$$ \min \sum_{ij} (A_{ij} - x_i y_j B_{ij})^2. $$
In matrix form, I'm trying to minimize the Frobenius norm of $A - \...
- 870
8
votes
5
answers
1k
views
Some good reading on polygon algorithms
What are some good resources (books, articles, sites) about polygon intersection and union algorithms?
- 81
9
votes
1
answer
163
views
Numerically stable algorithms for computing remainder of polynomials
Let $f, g \in \mathbb{R}[x]$ and $\deg f > \deg g$. I am looking for asymptotically fast and numerically stable algorithms for computing $f \bmod g$. In the applications intended, both $f, g$ are ...
user182
33
votes
9
answers
6k
views
Modern resources for learning FEM
I need to get started using Finite Element Methods. I am about to start reading Numerical solutions of partial differential equations by the finite element method by Claes Johnson, but it's dated 1987....
- 1,729
6
votes
1
answer
316
views
Question about the smoothing operators in multigrid methods for nonlinear PDEs
Suppose we are dealing with a nonlinear problem, say
$$
A u := L u + G(u) = f
$$
the nonlinearity of the operator $A$ is the polynomial type, ie, $L$ is a linear operator, and $G(u) = u^k$, or ...
- 2,542
11
votes
3
answers
1k
views
Which linear algebra texts should I read before learning numerical linear algebra?
Assuming one wishes to study numerical linear algebra in depth (and follow journals on numerical linear algebra and matrix theory), which would be a better course/better book to take up at first:
...
- 3,344
24
votes
4
answers
5k
views
When do orthogonal transformations outperform Gaussian elimination?
As we know, orthogonal transformations methods (Givens rotations and Housholder reflections) for systems of linear equations are more expensive than Gaussian elimination, but theoretically have nicer ...
- 1,832
16
votes
1
answer
538
views
How effective is the 'tendrils of knowledge' approach to Comp. Sci?
I was reading this on Math SE. The basic question is :
Assume that someone wishes to study something advanced; one way to do this would be to start off from basics and build up. But the "bigger ...
- 3,344
17
votes
4
answers
745
views
What are some applications which require interval arithmetic?
I have a very basic notion about interval arithmetic (IA), but it seems to be a very interesting branch of computational science both theoretically and practically. It is clear that the obvious ...
- 1,832
2
votes
0
answers
188
views
Texture analysis methods modern survey paper
I want to study the methods of analyzing textured images. So i searched google scholor but only found very old papers
statistical and structural approaches to texture 1979 haralick
Image Texture ...
- 121
13
votes
2
answers
919
views
Automatic generation of integration points and weights for triangles and tetrahedra
Usually one would consult a paper or book to find integration points and weights for unit triangle and tetrahedra. I am looking for a method to automatically compute such points and weights. The ...
user530
5
votes
5
answers
1k
views
Introductions to hp-FEM
do you know good introductions into or surveys $hp$-adaptive finite elements?
In particular I do not know how the heuristics for choosing spatial refinement or increased polynomial degree are ...
- 3,600