Questions tagged [reference-request]
This tag is for requests for books, papers, and citations.
225
questions
4
votes
3answers
1k views
Applications of Moore - Penrose generalized inverse of a matrix and associated projection?
I am seeking applications in the industry for the Moore-Penrose generalized inverse $A^\dagger$ of a matrix $A$.
The Moore-Penrose Inverse of $A\in \mathbb{C}^{m\times n}$, denoted
by $A^\dagger$, ...
9
votes
1answer
2k views
What are the strategies for local Adaptive Mesh Refinement (local AMR) on unstructured meshes?
I am interested in local AMR on unstructured meshes. Currently, I'm working with the OpenFOAM library - it supports completely unstructured local AMR:
cell refinement criteria determine a list of ...
17
votes
2answers
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 ...
7
votes
3answers
248 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 ...
6
votes
3answers
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 ?
22
votes
3answers
15k 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 ...
12
votes
3answers
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 ...
16
votes
4answers
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 ...
9
votes
3answers
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 ...
4
votes
3answers
563 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,
...
8
votes
3answers
256 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
votes
1answer
188 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 ...
7
votes
5answers
659 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 ...
12
votes
1answer
2k 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 - \...
8
votes
5answers
879 views
Some good reading on polygon algorithms
What are some good resources (books, articles, sites) about polygon intersection and union algorithms?
9
votes
1answer
127 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 ...
31
votes
9answers
5k 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....
6
votes
1answer
289 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 ...
11
votes
3answers
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:
...
24
votes
4answers
4k 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 ...
15
votes
1answer
486 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 ...
17
votes
4answers
680 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 ...
2
votes
0answers
183 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 ...
12
votes
2answers
904 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 ...
5
votes
5answers
917 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 ...
