Questions tagged [reference-request]

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

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2
votes
1answer
99 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
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3answers
298 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 ...
27
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11answers
8k 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 ...
7
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4answers
632 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
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4answers
388 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. ...
8
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1answer
145 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)=...
-1
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1answer
842 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 ...
5
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0answers
187 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 \mathbf{u}\...
2
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0answers
194 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, ...
3
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1answer
109 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 ...
0
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0answers
85 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 ...
2
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2answers
142 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
68 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
442 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 ...
5
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1answer
320 views

A question about GMRES

We know that if the matrix $A$ is symmetric positive definite, the FOM (full orthogonalization method) and the GMRES are theoretically equivalent to the CG (conjugate gradient) and the CR (conjugate ...
11
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3answers
2k 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 ...
6
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2answers
150 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.
2
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1answer
98 views

Scalable, effective and mesh quality assuring local dynamic tetrahedral mesh refinement algorithm

I have been reading about Tetrahedral Mesh Refinement algorithms, but the literature covering this is very wide. My work involves implementation of different 3D computational geometry algorithms, and ...
10
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4answers
4k views

Memory efficient implementations of partial Singular Value Decompositions (SVD)

For model reduction, I want to compute the left singular vectors associated to the - say 20 - largest singular values of a matrix $A \in \mathbb R^{N,k}$, where $N\approx 10^6$ and $k\approx 10^3$. ...
9
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3answers
30k views

Difference between Nodes and CPUs when running software on a cluster?

I'm looking into moving some computations of mine to a data center to get more computation power. In the context of this process, I am getting confused by the differentiation of a computation node and ...
5
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4answers
841 views

What methods exist to solve for the fluid flow past a cylinder using finite differences on a Cartesian grid?

I'm interested in finite-difference approaches to the incompressible Navier-Stokes equations that can handle complex geometry without the use of an unstructured mesh or a non-Cartesian grid. To be ...
1
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1answer
1k views

What is a “wake” in the context of CFD?

I am getting into computational fluid dynamics (CFD). One of my professors mentioned that a cylindrical wake would be a good starting point to learn about turbulence modelling when using CFD software. ...
4
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1answer
146 views

Early work on inverse problems

Long time ago I came across with a paper that covered early theoretical work (first half of 20th century) in the field of inverse problems. I remember there was a reference to a paper which proved ...
3
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1answer
87 views

Progression of molecular dynamics simulation sizes

I'm looking for literature on the progression (year on year, or more fine-grained if possible) of Molecular Dynamics simulation sizes. By simulation size I mean number of atoms, time step, total ...
4
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1answer
297 views

Where can I find a proof that the numerical sign problem is NP-hard?

I've reading up on the numerical sign problem, and how a general solution is NP-Hard. I can't seem to find a proof of this, though. Does anyone know where I can find a proof that the numerical sign ...
6
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2answers
404 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 ...
0
votes
1answer
189 views

Where do I find engineering problems to practice solving computationally?

I'm an engineer and I'm planning to get a bigger toolbox than Excel to solve difficult problems. I started learning Python (as that seems the script language to go for math intense jobs, and runs in ...
9
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4answers
401 views

Reference request: Rigorous analysis of algorithms for PDE and ODE

I'm interested in suggestions for book references on the subject of numerical PDE and ODE, in particular, a rigorous analysis of such methods in a manner written for professional mathematicians. It ...
5
votes
1answer
173 views

Modern alternatives to DRESOL Riccati solver

I am looking for a modern version or an alternative to the DRESOL package for differential matrix Riccati equations. The main issue that the original package uses single-precision type ...
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'...
1
vote
1answer
1k views

software request for solving acoustic wave equation

I am searching some libraries or toolboxes (preferred MATLAB) for solving acoustic wave equation in heterogeneous media with time varying source term, i.e. $$\nabla^2 \psi(\vec{r},t) - \frac{1}{c(\vec{...
5
votes
1answer
131 views

Use Butterworth and Chebychev filters

I need to calculate frequency response, phase response and apply to signals the Butterworth, Chebychev1 and Chebychev2 band-pass filters. I'm developing in C++ with Qt, and I'm looking for algorithms ...
5
votes
2answers
190 views

Is computational science recommended as part of the typical undergraduate curriculum every computer science department should teach?

Computational science remains uncommon in many computer science departments, particularly in universities without an engineering school. Is it not considered part of the standard computer science ...
3
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0answers
80 views

Conservative field mapping between two topologically disconnected surface meshes

Some background: the Front-Tracking method uses a triangular surface mesh to describe the boundary between two immiscible fluids. To deal with the breakup and coalescence of the fluid interface, ...
6
votes
3answers
376 views

Computing an orthogonal matrix subject to linear constraints

I am looking for a method to solve the matrix equation $$ DXa = Xb $$ where $D\in \mathbb{R}^{n\times n}$ is diagonal, $a, b\in \mathbb{R}^{n}$ and $X$ is the unknown orthogonal $n\times n$ matrix ...
6
votes
2answers
1k views

How to find all complex roots of an equation in a domain

I am facing a problem where I want to find the complex roots of $f(z)=z-sin(z)=0$ numerically. There are infinitely many roots of the function, but I am only interested in the $N$ closest to the ...
5
votes
2answers
154 views

What is the algorithm for computing block reflectors in xDLARFB

The theory behind computing a single Householder reflector to zero out part of a column of a matrix is pretty well described in Matrix Computations by Golub and Van Loan. However, the blocked ...
2
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3answers
2k views

Scalar vs. vector potential for magnetostatics

When trying to solve a magneto-static boundary-value problem (BVP) ($\nabla \times \mathbf{H} = \mathbf{J}$ and $\nabla \cdot \mathbf{B} = 0$), one can use either the magnetic vector potential $\...
8
votes
2answers
600 views

Helmholtz and Biharmonic equation examples with exact solution

I'm looking for examples of Helmholtz and Biharmonic equations in Cartesian co-ordinates with exact solutions, in order to compare my numerical solutions with it. I was able to find quite a few ...
2
votes
2answers
152 views

What are good examples of problems which are stiff due to very long interval of integration?

There is a class of stiff initial value problems for ODEs that have small Lipschitz constants, slowly-changing solutions, but very long interval of integration. The only practical example of such a ...
9
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0answers
443 views

What's a good numerical/optimization software package for solving the 2-D optimal stopping problem?

I am looking for a numerical software package to help me solve the 2-dimensional "free boundary" PDEs that arise in optimal stopping problems. In one dimension a standard optimal stopping problem in ...
10
votes
2answers
756 views

Finite difference scheme for “wave equation”, method of characteristics

Consider the following problem $$ W_{uv} = F $$ where the forcing term can depend on $u,v$ (see Edit 1 below for the formulation), and $W$ and its first derivatives. This is a 1+1 dimensional wave ...
6
votes
1answer
950 views

What is the scaling or order of molecular dynamics (MD) simulations?

Often in computational science, we talk about the scaling or order of a particular method ($\mathcal{O}(N)$, $\mathcal{O}(N^2)$, $\mathcal{O}(N \log N)$, etc.). I am having a really difficult time ...
9
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2answers
802 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 ...
9
votes
2answers
845 views

Initially Bracketing Minimum for Line Search

Leafing through a few textbooks, I've noticed that the problem of initially bracketing a minimum during a line search tends be an afterthought (at least in my undergraduate texts). Are there well-...
3
votes
1answer
151 views

What is a good introduction to mixed quantum-classical modelling

Currently, I have some experience with classical molecular dynamics simulations, and I've had undergraduate course in quantum mechanics (the course was "analytical" one, no approaches to computer ...
6
votes
2answers
574 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 ...
5
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2answers
205 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 ...
5
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0answers
118 views

How to choose a stable PML for pseudo-spectral method with strongly varying velocity

My friend was working on this, and he asked me about the stability of PML while applying on pseudo-spectral method, I believe his concern was how to choose the difference(if the difference should be ...
4
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3answers
1k views

Applications of Moore - Penrose generalized inverse of a matrix and associated projection?

I am seeking applications in the industry for the Moore-Penrose generalized inverse $A^\dagger$ of a matrix $A$. The Moore-Penrose Inverse of $A\in \mathbb{C}^{m\times n}$, denoted by $A^\dagger$, ...