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

learn more… | top users | synonyms

9
votes
2answers
146 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} ...
2
votes
3answers
142 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 ...
0
votes
0answers
30 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
143 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
votes
0answers
76 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 ...
0
votes
0answers
10 views

Large Poset with Macaulay 2

I want to use Macaulay 2 to study a family $(\mathcal{P}_n)$ of subposets of $\mathcal{P}=\mathbb{N}_{/0}\times\mathbb{N}_{/0}\times D_4$ where ...
1
vote
0answers
35 views

reverse engineering excel files [closed]

I have to understand a number of 20 excel files, highly related and complex. Do you know about a software tool which can help me in understanding how the cells relate and the excel files reports are ...
2
votes
0answers
35 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
vote
0answers
23 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
181 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.
7
votes
2answers
150 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 ...
12
votes
3answers
240 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
81 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
64 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
140 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
3answers
205 views

Introductory book on computational physics

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
337 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
113 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 ...
0
votes
0answers
215 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
100 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
vote
0answers
69 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
votes
1answer
62 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 ...
1
vote
0answers
68 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 ...
1
vote
2answers
108 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
votes
1answer
60 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 ...
10
votes
1answer
216 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
votes
3answers
448 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
votes
2answers
75 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
votes
1answer
65 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 ...
9
votes
4answers
512 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 $k\approx 10^3$. ...
4
votes
3answers
1k 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 ...
2
votes
1answer
191 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
vote
1answer
89 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
votes
1answer
96 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 ...
2
votes
1answer
59 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 ...
3
votes
1answer
152 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 ...
4
votes
2answers
203 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
153 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 ...
8
votes
4answers
243 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
89 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 ...
1
vote
4answers
468 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 ...
1
vote
1answer
421 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) - ...
5
votes
1answer
98 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
129 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
votes
0answers
55 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, ...
3
votes
2answers
137 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 ...
5
votes
2answers
334 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
95 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
votes
3answers
585 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 ...
6
votes
2answers
312 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 ...