Questions tagged [reference-request]
This tag is for requests for books, papers, and citations.
267
questions
2
votes
1
answer
105
views
Strategies for controlling number of new elements in adaptive mesh refinement
I am working on adaptive techniques for solving some elliptic equations.
The technique is based on residual on elements. My problem is that when I use a predefined tolerance for refining elements, the ...
- 523
10
votes
3
answers
2k
views
Benchmarks for Gröbner bases and polynomial system solution
In the recent question Solving system of 7 nonlinear algebraic equations symbolically, Brian Borchers experimentally confirmed that Maple can solve a polynomial system that Matlab/Mupad cannot handle. ...
- 10.1k
8
votes
3
answers
1k
views
Good introduction to numerical methods for magnetohydrodynamics (MHD)
I very recently started to read up about magnetohydrodynamics (MHD). While I have experience in the fluid part (both theory and numerics), my knowledge about the magneto part is very limited.
At the ...
- 1,238
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
0
votes
1
answer
44
views
Reference Material
I am starting to get into scientific computing with a library called Deal.II and I was wondering what the community recommends as good source material that I can learn about scientific material.
...
- 1
28
votes
9
answers
4k
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, ...
- 1,689
3
votes
2
answers
362
views
Looking for reference on Streamline Upwind Petrov Galerkin finite elements for incompressible unsteady Navier-Stokes
I am looking for a relatively simple book/paper that explains the basic Streamline Upwind Petrov Galerkin (SUPG) method for solving the incompressible unsteady Navier-Stokes equations. Most of the ...
- 1,859
4
votes
3
answers
387
views
Point inside curved finite element
I like to create interpolation functions for second order finite element meshes. For elements with straight edges all is good, but some of my elements may have curved edges as shown in the figure:
I ...
- 382
5
votes
1
answer
102
views
Reference request: theory regarding time evolution of closed loop 2D elastic shapes?
I am interested in approximating the time evolution of 2D curves. Here's an illustration:
An issue that arises when naively making this approximation as illustrated above, is that as one increases ...
- 669
1
vote
0
answers
103
views
Monotonic convergence of Newton's method for boundary value problems [closed]
I’m interested in solving nonlinear elliptic boundary value problems of the type
$$
-a\Delta u + f(u) = 0,
$$
$$
u|_\Gamma = u_0
$$
by Newton’s method when its convergence is global and monotonic.
...
- 281
1
vote
1
answer
50
views
Resources exploring the problem of "volume exclusion"?
Consider the following situation:
There are two boundaries -- one is denoted using grey lines, and the other is denoted using black lines. The boundaries are numerically represented using "vertices", ...
- 669
1
vote
3
answers
174
views
Reference Suggestions for MPI
I'm learning MPI in order to use MPI with a model written in Fortran. What are some good resources (books, websites, etc.)? Introductory/beginner material, and detailed references would both be ...
- 275
3
votes
1
answer
86
views
Resource recommendations for numerical methods involved in dynamical systems analysis
I am interested in learning numerical methods that specifically have to do with analyzing dynamical systems. In particular:
drawing phase plane diagrams
drawing phase portraits
analyzing bifurcations ...
- 669
3
votes
1
answer
134
views
Numerical computation of $\log \int_a ^b f(x) \mathrm{d}x$ from $\log f(x)$?
I want a numerical method to evaluate:
$$\log \int_a ^b f(x) \mathrm{d}x$$
when what I have is a numerical routine to evaluate $\log f(x)$. The problem is that if $f(x)$ takes very large or very ...
- 1,689
5
votes
1
answer
181
views
Need a good reference for numerical transport phenomena
I'm a chemical engineering undergraduate and I'm currently starting to work in a theoretical transport phenomena/colloid science group.
While my group has a nice code base for larger scale ...
- 163
2
votes
2
answers
310
views
Looking for references on this adaptive Runge–Kutta method (GSL’s rk2)
Background
For a study that is beyond the scope of this question, I applied all of GSL’s adaptive Runge–Kutta methods to a certain problem. This includes a Runge–Kutta method of 2nd and 3rd order, ...
- 2,002
2
votes
0
answers
125
views
Resources for large-scale MILP optimization
With the advent of "big data" applications, different algorithms have to be used to efficiently solve optimization problems, even in the convex case (e.g. the recent success of stochastic gradient ...
- 197
2
votes
2
answers
117
views
Adaptive plotting of two-variable functions $z=f(x,y)$ algorithm pseudocode?
I am looking for explanations of algorithms to adaptively sample a function of two variables $f(x,y)$, in a given domain $x_0\le x \le x_1$, $y_0\le y \le y_1$. Intuitively, I want to sample more ...
- 1,689
13
votes
3
answers
1k
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 (...
- 133
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, ...
3
votes
1
answer
83
views
How to Check a Hyper-Cube for Defects
I would greatly appreciate some help/references on solving the following problem:
You are in charge of searching through a n-dimensional hyper-cube $[0,1]^n$ to make sure that it does not contain ...
- 31
8
votes
1
answer
477
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 ...
- 669
6
votes
0
answers
106
views
Reference request for numerical variational method
I have a variational problem where the unknown function is a periodic path $\gamma:[0,1)\to\mathbb{R}^2$, and the functional is
$$ \int_0^1\left( \tfrac12\|\dot\gamma(s)\|^2 + \mathcal{F}[\gamma]\...
- 11.4k
6
votes
1
answer
896
views
ENO/WENO component-wise vs characteristic-wise
Can someone give some references to understand what's the differences between a component-wise and a characteristic-wise ENO scheme?
If I'm right, the characteristic variables come from the ...
- 1,019
-1
votes
1
answer
157
views
Can you give some information for rothe method [closed]
I want to learn a numerical method for PDEs other than finite difference method. After some research on internet i have found Rothe method and it looks interesting to me. Unfortunately, i couldn't ...
- 101
2
votes
3
answers
2k
views
Applying the method of lines to parabolic PDEs: references and software
Could you please advise some literature about the numerical method of lines (MOL) for parabolic PDEs? It is a method of solving PDEs with discretizing only by space but not by time. A system of ODEs ...
- 281
9
votes
4
answers
399
views
Fast explicit solution for $\mathbf{A}\mathbf{x} = \mathbf{b}$, $ \mathbf{b} \in \mathbf{R}^3$, low condition number
I am looking for a fast (dare I say optimal?) explicit solution the 3x3 linear real problem, $\mathbf{A}\mathbf{x} = \mathbf{b}$, $\mathbf{A} \in \mathbf{R}^{3 \times 3}, \mathbf{b} \in \mathbf{R}^{3}$...
- 762
1
vote
0
answers
172
views
How to compute frank copula and its derivative accurately?
I need to fit a model using MLE with Frank copula by linking two discrete univate distribution function $u = F(x)$ and $v = F(y)$ together, and the joint distribution function is
$$
\Phi(x,y) = C(F(x)...
- 183
2
votes
2
answers
32
views
Runge-Kutta with all nodes at n+1 or zero weights otherwise
So, lets say for the family of the explicit Runge-Kutta methods:
$$y_{n+1} = y_n + \sum_{i=1}^s b_i k_i$$
where,
$$k_1 = hf(t_n, y_n)$$
$$k_2 = hf(t_n+c_2h, y_n+a_{21}k_1)$$
$$\vdots$$
$$k_s = hf(t_n+...
runge_kutta_question
2
votes
1
answer
171
views
Buckling reference using the FEM
I want to analyze buckling in a composite using the FEM. So far I have studied this references
Zdenek P Bazant, Luigi Cedolin. Stability of Structures: Elastic, Inelastic, Fracture and Damage ...
- 8,207
1
vote
2
answers
161
views
Reference for approximation errors in 2D and 3D by using FEM
I'm currently searching for an elaborate referece that covers most of the approximation errors for elliptic second order problems (like, for the laplacian dirichlet problem) by using finite element ...
- 107
14
votes
4
answers
4k
views
Looking for Runge-Kutta 8th order in C/C++
I would like to use Runge-Kutta 8th order method (89) in a celestial mechanics / astrodynamics application, written in C++, using a Windows machine. Therefore I wonder if anyone knows a good library / ...
- 277
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
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
1
vote
0
answers
131
views
Lattice Boltzmann Method
I have done Molecular Dynamics Simulation and now want to venture into Lattice Boltzmann Method. What would be the best reference book/lecture notes/videos for a beginner?
- 201
4
votes
3
answers
242
views
vector PDEs on manifolds
What are the subtleties involved in solving vector PDEs on manifolds? Can someone suggest a reference summarizing the problems involved?
Specifically I want to solve a vector Helmholtz equation with ...
- 176
4
votes
0
answers
129
views
Floating-point arithmetic in scientific computations rules of thumb
I am looking for a nice reference (a review, tutorial, or maybe a book) that has tips and their explanations about general issues of floating-point arithmetic in scientific computations.
Some that I'...
- 1,689
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
1
vote
0
answers
40
views
Optimal partition - variable number of parts
Suppose I have a box $D \subset \Bbb{R}^2$ (compact set). Denote $\mathcal{P}= \{ (\Omega_1,...,\Omega_n) : \bigcup_{i=1}^n \Omega_i = D,\ \Omega_i \cap \Omega_j =\emptyset\}$ the family of partitions ...
- 965
3
votes
1
answer
2k
views
Crouzeix-Raviart Finite Element
Can anybody recommend me a good introduction to Crouzeix-Raviart Finite Elements? Their motivation is not obvious and the body of literature is hard to overlook.
- 3,580
8
votes
2
answers
421
views
The effect of decoupling a coupled system of PDEs
I asked a somewhat similar question previously but perhaps it might have been too specific for anyone to really answer. Here is a bit more general of a question that I am struggling with. Consider the ...
- 937
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
2
votes
1
answer
113
views
Optimal algoritm of gcd with complexity
I want to know the best optimal algoritm of gcd with its complexity if you have a any useful source I will be glad to have a look at it.
- 21
2
votes
1
answer
103
views
Methods to solve this equation on finite fields?
Is there any analytical (exact, closed-form solution) or numerical method to solve an equation such as
$p(x) = r^x$
where $p(x)$ is a polynomial whose coefficients are drawn from a finite field, ...
- 153
5
votes
3
answers
411
views
Machine epsilon does not limit relative rounding error for denormals. Is this a problem?
As we know, machine epsilon limits relative rounding error in the range of normalized floating point numbers. But it is easy to check that this is not true for denormalized numbers.
My question is ...
- 1,842
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
4
answers
774
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 ...
- 115
1
vote
4
answers
403
views
How to produce visually unexpected results?
Below is a totally made up example.
So let's say on the left we have a weird black-white image or, in other words, a matrix of zeros and ones. We then apply a specific algorithm to the given matrix. ...
- 191
8
votes
1
answer
158
views
F(x) = 0 vs. ||F(x)||^2->min
In many areas of application, one needs to solve a nonlinear system of equations
$$
F(x) = 0.
$$
Sometimes, the formulation
$$
\|F(x)\|^2 \to\min
$$
is used. Clearly, every solution $\hat{x}$ of $F(x)=...
- 3,108
-1
votes
1
answer
864
views
Any note on Immersed boundary finite difference method?
For parts of a talk, I need a note on "Immersed boundary finite difference method", mainly about the reason of appearing this branch in the finite difference methods, considering mathematical ...
