Questions tagged [reference-request]
This tag is for requests for books, papers, and citations.
29
questions
33
votes
9
answers
6k
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....
- 1,689
7
votes
1
answer
2k
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?
...
- 173
29
votes
11
answers
10k
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 ...
- 956
7
votes
1
answer
620
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 ...
- 1,238
6
votes
3
answers
3k
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 ...
- 157
6
votes
2
answers
444
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 ...
- 61
4
votes
3
answers
790
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,
...
- 11.9k
2
votes
2
answers
506
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 ?
- 23
2
votes
2
answers
217
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.,
$$\...
- 642
2
votes
1
answer
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 ...
- 29
25
votes
3
answers
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 ...
- 677
19
votes
3
answers
1k
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} \...
- 677
15
votes
3
answers
383
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 ...
- 273
12
votes
2
answers
1k
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 ...
- 3,580
10
votes
2
answers
581
views
FEM for vector valued problems: reference request
I'm a PhD working in a computational mechanics lab. I come from a Math department, and I have a good background for what concerns the basics of finite elements, like inf-sup conditions, DG, non-...
- 67
10
votes
1
answer
494
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/...
- 489
10
votes
1
answer
1k
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)}
$...
- 777
8
votes
3
answers
280
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 ...
- 3,344
7
votes
2
answers
658
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 ...
- 1,916
6
votes
0
answers
152
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 ...
- 1,000
6
votes
1
answer
896
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 ...
- 1,019
5
votes
5
answers
1k
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 ...
- 3,580
5
votes
0
answers
99
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 ...
- 4,587
5
votes
2
answers
363
views
Term for the typical "linear in the larger dimension, quadratic in the smaller" cost for linear algebra
Many dense linear algebra decompositions (QR, SVD...) on an $m\times n$ matrix have cost
$$
O(\max(m,n)\min(m,n)^2)
$$
when implemented in practice on a computer. Is there a colloquial name or a more ...
- 10.1k
5
votes
5
answers
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'...
user121
5
votes
3
answers
184
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
2
answers
252
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 ...
- 1,916
2
votes
1
answer
132
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 $x_0$....
- 141
1
vote
3
answers
462
views
Morley element implementation reference
I am looking for a detailed reference on the implementation of the Morley element for FEM, specifically for the biharmonic equation. By detailed, I mean that it should discuss the problems associated ...
- 621