Questions tagged [reference-request]

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

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31
votes
9answers
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....
7
votes
1answer
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? ...
5
votes
3answers
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 ...
6
votes
2answers
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 ...
6
votes
1answer
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 ...
4
votes
3answers
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, ...
2
votes
1answer
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 ...
20
votes
3answers
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 ...
19
votes
3answers
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} \...
5
votes
5answers
4k views

Recommendation for an introductory level book in computational physics?

I'm a physics undergrad, looking for a good introductory book on computational science, and numerical methods. Mostly I'm looking for applied books. (Simply because... in a theoretical book, if I can'...
9
votes
1answer
384 views

$L^2$-convergence of finite element method when right hand side is only in $H^{-1}$ (Poisson eqn)

I know that the piecewise linear finite element approximation $u_h$ of $$ \Delta u(x)=f(x)\quad\text{in }U\\ u(x)=0\quad\text{on }\partial U $$ satisfies $$ \|u-u_h\|_{H^1_0(U)}\leq Ch\|f\|_{L^2(U)} $...
14
votes
3answers
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 ...
9
votes
2answers
719 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 ...
8
votes
3answers
239 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 ...
8
votes
1answer
239 views

Resources on mesh generation for finite element methods

I know that this is not really apart of the rules as this is a recommendation question and these don't really have an answer per say. But, like this forum posting: https://stackoverflow.com/questions/...
5
votes
5answers
823 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 ...
6
votes
2answers
513 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 ...
6
votes
0answers
126 views

Do practice and theory differ substantially when implementing Neumann Boundary Conditions using a Mixed Method?

I have implemented a pretty straightforward finite element solver for the following Poisson equation. For the purposes of this question we can assume the source term and the Dirichlet data both ...
6
votes
1answer
665 views

ENO/WENO component-wise vs characteristic-wise

Can someone give some references to understand what's the differences between a component-wise and a characteristic-wise ENO scheme? If I'm right, the characteristic variables come from the ...
2
votes
1answer
86 views

Is there an optimization scheme/algorithm that converges, for this non-convex scenario but with some special properties

I have a smooth function $f(x) = \frac{g(x)}{h(x)}$ that is the ratio of two smooth convex functions $g(x)$ and $h(x)$. It is known that $f(x)$ has a global minimum, achieved at the unique point $x_0$....
5
votes
3answers
174 views

Algorithms for radiation treatment planning

I have a medical physics problem - I want to maximise the dose absorbed by a brain tumour whilst minimising the dose in the rest of the brain, especially certain organs, such as the pituitary gland, ...
5
votes
0answers
84 views

Interface Formulation at Finite Volume Boundaries when using the Dual Mesh

When using the dual mesh (vertex-centered) for finite volume methods, you end up with a cell center at the boundaries between materials. It is possible that the equations being solved in each ...
4
votes
2answers
188 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 ...
2
votes
2answers
354 views

2d Euler manufactured solutions

Where can I find manufactured solutions for the 2d Euler equations, with the complete analytical terms, including the Jacobian of the source term ?
2
votes
2answers
144 views

Preconditioner for scalar laplacian system

Suppose that I have a large (on the order of 10^6 unknowns) 3D scalar Poisson system which I would like to precondition. The boundary conditions have been treated so that the system is SPD. I.e., $$\...