# Questions tagged [reference-request]

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

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### 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....
353 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? ...
1k views

### Books on mathematical foundation of finite element methods

After reading three books about finite element method, with two of them covering also finite volume and grid generation, I found myself lost when I have to discuss these topics with library developers ...
377 views

### Introduction to computational science?

I'm a high school student interested in computational science, and I would like to learn more about it. This year I took AP Computer Science for that reason, but except for some very basic gambling ...
411 views

### Fourth order IMEX Runge-Kutta method

I am looking for the Butcher tableau of a fourth order accurate Runge-Kutta method with IMEX splitting. I have been reading the ''classical'' paper on the subject by Ascher, Ruuth and Spiteri as well ...
503 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, ...
3k views

### Introduction to Lattice Boltzmann methods [closed]

I am trying to learn the Lattice-Boltzmann method and was looking for some good beginner resources explaining the method. I have been looking at some codes online, but have been having trouble ...
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 ...
703 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} \...