Questions tagged [reference-request]

This tag is for requests for books, papers, and citations.

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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 ...

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