# Questions tagged [reference-request]

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

197 questions
Filter by
Sorted by
Tagged with
4k 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....
7k views

### Robust algorithm for $2 \times 2$ SVD

What is a simple algorithm for computing the SVD of $2 \times 2$ matrices? Ideally, I'd like a numerically robust algorithm, but I'll like to see both simple and not-so-simple implementations. C code ...
3k views

### Modern C++ in scientific computing?

I am looking for books or articles, or blog-posts, or any published material in general, that address specifically the uses of C++ modern features (move semantics, the STL, iterators, lazy evaluation, ...
3k 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 ...
12k 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 ...
701 views

### Is it well known that some optimization problems are equivalent to time-stepping?

Given a desired state $y_0$ and a regularization parameter $\beta \in \mathbb R$, consider the problem of finding a state $y$ and a control $u$ to minimize a functional \begin{equation} \frac{1}{2} \...
3k 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 ...
590 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 ...
1k 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 ...
438 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 ...
340 views

### Citable references for software best practices

I'm currently writing up my PhD thesis. I spent a significant fraction of my PhD cleaning up and extending existing scientific code, applying software engineering best practices which were previously ...
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 ...
880 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 ...
355 views

### For noisy or fine-structured data, are there better quadratures than the midpoint rule?

Only the first two sections of this long question are essential. The others are just for illustration. Background Advanced quadratures such as higher-degree composite Newton–Cotes, Gauß–Legendre, ...
666 views

### Finite elements on manifold

I'd like to solve some PDEs on manifolds, say for example an elliptic equation on a sphere. Where do I start? I'd like to find something that use preexisting code/libraries in 2d , nothing so fancy (...
924 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: ...
2k views

1k 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 ...
295 views

### Good tutorials on how to use Butcher tables?

I tried to go to the primary sources in order to understand how to use Butcher tables to simplify the algebra I need to do when using Taylor series to find the order of accuracy of a scheme, for ...
438 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 ...
25k views

### Difference between Nodes and CPUs when running software on a cluster?

I'm looking into moving some computations of mine to a data center to get more computation power. In the context of this process, I am getting confused by the differentiation of a computation node and ...
534 views

### Introductory book on computational physics [duplicate]

I'm currently working on my MS in CS and have developed an interest in astrophysics. Luckily one of my professors is a astrophysicist and is currently doing research through computational physics and ...
245 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 ...
351 views

### How to directly compute the inverse of an ill-conditioned dense matrix

I know that it is generally a bad idea to compute the inverse matrix directly. However, if it is necessary to compute the inverse of an ill-conditioned invertible dense matrix, then what can I try? ...
88 views

### What good are hard-sphere event-driven molecular dynamics simulations in the face of chaos?

Simple hard-sphere dynamical systems can exhibit chaotic dynamics. Due to finite-precision arithmetic when implemented on a computer, the presence of chaos implies that for a given set of initial data,...
465 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 ...