Questions tagged [reference-request]
This tag is for requests for books, papers, and citations.
234
questions
9
votes
0answers
443 views
What's a good numerical/optimization software package for solving the 2-D optimal stopping problem?
I am looking for a numerical software package to help me solve the 2-dimensional "free boundary" PDEs that arise in optimal stopping problems. In one dimension a standard optimal stopping problem in ...
10
votes
2answers
770 views
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 ...
6
votes
1answer
1k views
What is the scaling or order of molecular dynamics (MD) simulations?
Often in computational science, we talk about the scaling or order of a particular method ($\mathcal{O}(N)$, $\mathcal{O}(N^2)$, $\mathcal{O}(N \log N)$, etc.).
I am having a really difficult time ...
9
votes
2answers
854 views
Higher precision floating-point arithmetic in numerical PDE
I have the impression, from very different resources and talks with researches, that there is a growing demand for high precision computations in numerical partial differential equations. Here, high ...
9
votes
2answers
879 views
Initially Bracketing Minimum for Line Search
Leafing through a few textbooks, I've noticed that the problem of initially bracketing a minimum during a line search tends be an afterthought (at least in my undergraduate texts). Are there well-...
3
votes
1answer
152 views
What is a good introduction to mixed quantum-classical modelling
Currently, I have some experience with classical molecular dynamics simulations, and I've had undergraduate course in quantum mechanics (the course was "analytical" one, no approaches to computer ...
7
votes
2answers
612 views
Recommendations for a usable, fast GPL-compatible derivative-free numerical optimization library that can be interfaced to C++
I am dealing with optimization of functions for which I do not have derivatives available, and the optimization is not constrained. I am searching for a high quality GNU Public License-compatible ...
5
votes
2answers
226 views
Is there a special algorithm for computing the convex hull ordering when the candidate points are on the hull?
I'm dealing with a set of points which are already placed on the 2D hull boundary: a convex polygon. I know this for sure. However, the point set is not ordered, and I need the polygon points to be ...
5
votes
0answers
118 views
How to choose a stable PML for pseudo-spectral method with strongly varying velocity
My friend was working on this, and he asked me about the stability of PML while applying on pseudo-spectral method, I believe his concern was how to choose the difference(if the difference should be ...
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
256 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 ?
25
votes
3answers
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 ...
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
616 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
266 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
192 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
718 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
3k 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
968 views
Some good reading on polygon algorithms
What are some good resources (books, articles, sites) about polygon intersection and union algorithms?
9
votes
1answer
131 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
297 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
511 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
691 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
187 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
909 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
961 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 ...