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

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1answer
28 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. ...
16
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6answers
675 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, ...
3
votes
2answers
60 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
vote
3answers
96 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 be curved edges as shown in the figure: I ...
5
votes
1answer
54 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 ...
1
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0answers
32 views

Monotonic convergence of Newton's method for boundary value problems

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. ...
1
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1answer
39 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 ...
0
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0answers
12 views

Resonant interactions, instability of nonlinear waves- which numerical method:HOSE or FNPT-based?

I am studying non linear interactions for water waves. Resonant interations type problems or instability of waveforms are the kinds of problems of interest. Resonant interactions and related ...
1
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0answers
29 views

Recommend route for research in numerical backward stochastic differential equation

I am a first year master student. My supervisor assigned numerical backward SDE as my master thesis topic and let me read a thesis from his former PHD student. After finishing reading the thesis, I ...
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3answers
70 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 ...
2
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1answer
52 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 ...
3
votes
1answer
94 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 ...
4
votes
1answer
87 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 ...
1
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2answers
95 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, ...
1
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0answers
31 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 ...
2
votes
0answers
31 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 ...
9
votes
3answers
187 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 ...
3
votes
3answers
152 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
1answer
72 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 ...
7
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1answer
151 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 ...
5
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0answers
69 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 + ...
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0answers
46 views

Agent-Based Modeling

I am interested in learning about and learning how to use agent-based modeling. Specifically, I want to use agent-based modeling for economics research. Can anyone suggest resources appropriate for ...
5
votes
1answer
158 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
votes
1answer
49 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 ...
0
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2answers
262 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 ...
9
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4answers
198 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 ...
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0answers
56 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) = ...
2
votes
2answers
22 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 = ...
1
vote
1answer
105 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 ...
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2answers
126 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 ...
3
votes
2answers
346 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 / ...
11
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3answers
320 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} ...
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3answers
315 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 ...
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0answers
51 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?
4
votes
3answers
173 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 ...
3
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0answers
99 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 ...
4
votes
0answers
66 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 ...
1
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0answers
30 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 ...
3
votes
1answer
533 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.
8
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2answers
199 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 ...
13
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3answers
302 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 ...
2
votes
1answer
85 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.
2
votes
1answer
70 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, ...
5
votes
3answers
171 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 ...
7
votes
4answers
315 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 ...
1
vote
4answers
361 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 ...
7
votes
1answer
116 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 ...
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0answers
312 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 ...
3
votes
0answers
126 views

Time-stepping for coupled nonlinear PDEs

What are good references for time-stepping of the coupled incompressible Navier-Stokes-heat equation (Boussinesq flow), $$ \begin{cases} \rho\left(\dot{\mathbf{u}} + \mathbf{u}\cdot\nabla ...
1
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0answers
92 views

Good approximate solutions for a MILP problem

The company I work for has been developing an application for real-time control of sewer networks. Every 5 minutes, a MILP problem is built or updated, then solved using Gurobi. For mid-sized cities, ...