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

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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 ...
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0answers
27 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
66 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 ...
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1answer
49 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
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1answer
91 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 ...
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1answer
81 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 ...
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2answers
88 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, ...
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0answers
25 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 ...
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0answers
29 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
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3answers
172 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
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1answer
71 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 ...
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1answer
148 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 ...
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0answers
66 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
44 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
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1answer
132 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
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1answer
44 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 ...
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2answers
240 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
186 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
52 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) = ...
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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 = ...
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1answer
99 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
122 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
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2answers
313 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 / ...
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3answers
299 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
286 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
47 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
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3answers
169 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 ...
2
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0answers
92 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 ...
2
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0answers
46 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 ...
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0answers
29 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
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1answer
496 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.
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2answers
193 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 ...
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3answers
295 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
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1answer
82 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
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1answer
68 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, ...
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3answers
169 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 ...
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4answers
308 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 ...
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4answers
352 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
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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
298 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
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0answers
121 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 ...
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0answers
88 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, ...
2
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1answer
69 views

Equal Area Sampling on Curved Surface:

I have a quantity $\beta(\mathbf{x}) \in \mathbb{R}$ that I wish to compute on a curved, smooth surface defined by $\{\mathbf{x}: \Gamma(\mathbf{x})=0\} \subset \mathbb{R}^{3}$. (This surface is ...
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0answers
71 views

References on the topic of DEM and XDEM

DEM: discrete element method. XDEM: extended discrete element method. For my current project of furnace simulation with granular materials, I am interested in the methods mentioned above. I have not ...
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2answers
113 views

General Linear Algebra Wrapper Library

I am currently mulling over the idea of taking a code I currently work with and rebuilding it from the ground up to allow for the use of more efficient programming and numerical techniques. In the ...
3
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1answer
63 views

Suitable algorithm for superposing variable scalar distributions in 2D area with constraints

I'm trying to place multiple light sources on a 2D plane, in a fashion that satisfies multiple constraints. The 2D scalar distributions are the irradiance distributions of each light source that are ...
9
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1answer
255 views

Is there some good mailing list for `Computational Science`?

I am wondering whether there is some very good mailing list or google groups for Computational Science, where we can discuss questions instead of only asking and replying questions. In fact, I am ...
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3answers
973 views

Volume of 3D convex hull of small point sets all on the hull

I have a question that is similar to this one asked before except in 3D, and I only need the volume, not the actual shape of the hull. More precisely, I'm given a small set of points (say, 10-15) in ...
4
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2answers
80 views

Books/Resources on Sparse Optimization?

I'm looking to learn more about Sparse Optimization and apply it to machine learning problems. Could you please recommend some books/resources on this topic? Both theoretical and applied are fine.