Questions tagged [reference-request]

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

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11
votes
2answers
891 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 ...
1
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2answers
55 views

Two-dimensional ordering issue – alternate sort order ascending/descending to reduce fluctuations - trivial?

I have a solution in search of a problem that some of you could perhaps help me with. Let $L$ be a list of elements. Each element has two inherent properties/attributes ($a$, $b$) that can each be ...
1
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1answer
79 views

Discrete model of cell - cell communication

I am trying to understand how cell to cell communication is studied using a discrete modelling framework. Could someone please suggest suitable references or libraries which already have ...
3
votes
1answer
106 views

Adaptive Lagrangian-Eulerian methods and practical benchmark results

Does anyone know of any published study that talks about the practical aspects of running Adaptive Lagrangian-Eulerian techniques for solid and/or fluid mechanics problems? I'm looking for things ...
3
votes
3answers
518 views

Minimum number of elements (mesh size) for electromagnetic simulation

Does someone have a reference for the minimum number of elements (or maximum mesh size) for electromagnetic simulations where a mathematical or numerical explanation is given? I have found several ...
0
votes
1answer
315 views

Simple particle-in-cell examples

I am studying about the 1D EM-PIC (Electro Magnetics using particle-in-cell) simulation. I want to have a simultaneous time-integration of the electric/magnetic fields plus the motion of free charges ...
5
votes
2answers
186 views

Term for the typical "linear in the larger dimension, quadratic in the smaller" cost for linear algebra

Many dense linear algebra decompositions (QR, SVD...) on an $m\times n$ matrix have cost $$ O(\max(m,n)\min(m,n)^2) $$ when implemented in practice on a computer. Is there a colloquial name or a more ...
25
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3answers
16k views

Recommendation for Finite Difference Method in Scientific Python

For a project I am working on (in hyperbolic PDEs) I would like to get some rough handle on the behavior by looking at some numerics. I am, however, not a very good programmer. Can you recommend ...
1
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0answers
77 views

Finite Difference Approximation for the Laplacian in 2D that produces a nonsymmetric matrix

Consider the following PDE \begin{align} -\Delta u &= f \ \ \text{en} \ \ (0,1)\times (0,1) \label{P1} \\ u &= 0 \ \ \text{en} \ \partial ((0,1)\times (0,1)) \label{P2} \end{align} if we ...
1
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1answer
92 views

Finding the source of numerical instability in a electrostatic problem solved by conformal mapping

I'm using conformal mapping to solve a 2D electrostatic problem (calculating the potential $u(x,y)$ in the plane). Let $C_1$ and $C_2$ be two circles at an electric potential $U_1$ and $U_2$, ...
1
vote
1answer
126 views

Tensor product representation for the 9-point finite difference approximations for the Poisson equation

If we use 5-point finite difference approximations in a uniform rectangular grid to solve the Poisson PDE \begin{align} -\Delta u &= f \ \ \text{en} \ \ (0,1)\times (0,1) \label{P1} \\ u &= ...
10
votes
3answers
1k 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. ...
5
votes
4answers
900 views

How important is learning hardware/architecture for scientific computing?

Apologies if this is a bit of a soft, unclear, or opinion-based question. I'm a relatively new PhD student in a (computational) quantum chemistry group. My group develops and maintains a few software ...
2
votes
2answers
174 views

Scientific computing code development hands on introduction

I have a background in Computational Mechanics but my knowledge remains very user-oriented. What I mean by that is that I have a fairely good knowledge about how to use a commercial engineering ...
5
votes
1answer
656 views

4th order tensor rotation - sources to refer

I am trying to model a linear elastic material in Abaqus using a UMAT. For my application, I need to rotate the 6x6 compliance matrix for a given set of eigenvectors (or a rotation matrix). I came ...
0
votes
1answer
137 views

Help me choose a book on the numerical integration of PDEs

For ODEs I have these books: Griffiths, David, Higham, Desmond J., Numerical Methods for Ordinary Differential Equations, 2010 Alfio Quarteroni, Riccardo Sacco, Fausto Saleri, Numerical Mathematics, ...
0
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0answers
36 views

HLLC Riemann solver with shock test 2 - extension to low densities

I am currently using the HLLC solver to solve a 1-D system of Euler equations with very satisfactory results. However, there are cases where my solution produces low-density, high velocity states, ...
1
vote
1answer
58 views

What is the best cooling and flippling schedule in simulated annealing?

I've noticed that some heuristics for it on my problem which work surprisingly well. I guess it ought to be systematically studied although I cannot find guides or overviews for it.
2
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0answers
78 views

A priori error estimates - finite element method - mixed boundary conditions

Consider the problem $$ \left\{\begin{array} {rcl} -\Delta u & = 0 & \text{ in } \Omega \\ u & = 0 & \text{ on } \Gamma_D \\ \frac{\partial u}{\partial n} &= g &\text{ on } \...
2
votes
1answer
333 views

Reference request: C++ and numerical analysis book

I'm a master student with a good Numerical analysis background. I'm going to do a master thesis in the same subject, but I need to use C++ since my advisor loves it, and I also believe it's the best ...
1
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1answer
37 views

Introductory reference on bit-twiddling? [closed]

I'm looking for introductory resources--web pages, book chapters, articles--that introduce the C language with an immediate focus on bit-twiddling functions (e.g. bitwise XOR, AND, shifts), and of ...
3
votes
0answers
60 views

What is this QR-factorization-based preconditioning called?

I have recently started to delve into someone else's code, and there is a part in there I don't quite understand. The authors of the code use some form of pre-conditioning to speed up the optimization....
6
votes
2answers
764 views

When is it easy to invert a sparse matrix?

(Crossposted on cstheory.SE) When is it easy to invert a sparse matrix? Specifically, I'm wondering about the cases in which matrix inversion has similar cost to sparse matrix multiplication, hence ...
1
vote
2answers
75 views

Efficient ODE steppers with query of $f$ and $\nabla f$ is efficient

Assume we have an IVP $y'(t) = f(t,y)$, and that $\partial_t f$ and $\nabla f$ are cheap to compute. Assume further that more derivatives are not cheap to compute, or inaccessible for some reason, ...
4
votes
1answer
651 views

FEM Python book

Is there any book or site available with Finite element Method for partial differential equations with python code apart from Fenics?
1
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0answers
62 views

Book recommendation on numerical methods for solving Integro-Differential equations

I was wondering if anyone could recommend a good book or resource on numerical methods for solving integro-differential equations? Of course I am familiar with the methods for solving ODEs and PDEs ...
10
votes
1answer
357 views

Resources on mesh generation for finite element methods

I know that this is not really apart of the rules as this is a recommendation question and these don't really have an answer per say. But, like this forum posting: https://stackoverflow.com/questions/...
0
votes
0answers
49 views

Finding a CFD paper with extra degree of freedom variable in mass conservation

I am trying to find a paper that I saw about a year ago. I am not sure of the actual date of the paper. I believe it was a finite difference CFD paper. The interesting part of the paper was the ...
2
votes
1answer
161 views

Diagonalization of Hermitian matrices vs Unitary matrices

What are the general algorithms used for diagonalization of large Hermitian matrices and Unitary matrices? ($>5000 \times 5000$) LAPACK seems to diagonalize Hermitian matrices almost 20 times as ...
17
votes
4answers
695 views

What are some applications which require interval arithmetic?

I have a very basic notion about interval arithmetic (IA), but it seems to be a very interesting branch of computational science both theoretically and practically. It is clear that the obvious ...
3
votes
2answers
117 views

Good references for dual-weighted residual (DWR) method for goal-oriented adaptive mesh refinement (AMR)

Can anyone help me with good references (books or papers) where I can learn about dual-weighted residual (DWR) method for goal-oriented adaptive mesh refinement (AMR)?
17
votes
2answers
4k views

Drawbacks of Newton-Raphson approximation with approximate numerical derivative

Suppose I have some function $f$ and I want to find $x$ such that $f(x)\approx 0$. I might use the Newton-Raphson method. But this requires that I know the derivative function $f'(x)$. An analytic ...
1
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0answers
57 views

computing time scale and steady state concentration in microfluidic channels

I have been performing convection-diffusion transport studies on microfluidic channels like the following The inlet concentration is specific and I obtain the time-dependent concentration profiles of ...
28
votes
11answers
9k 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 ...
13
votes
4answers
3k 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 / ...
3
votes
1answer
351 views

The Formula of Explicit Runge-Kutta Fourteen order

I need an explicit Runge-Kutta 14th order formula. If you know about some reference that discusses at least 10th order (or higher, since I'm looking for the 14th) of Runge-Kutta and there is ...
1
vote
1answer
693 views

What is the state of the art in solving stiff initial value problems?

I'm looking for current references on solving stiff ODEs. Most of what I know (say, BDF methods) apparently date back to the 1980's, and I feel like a lot of progress should have been made in that ...
0
votes
1answer
147 views

Red flags for numerical computing?

I've learnt the hard way that you should avoid: computing small numbers as the difference of two large numbers evaluating chaotic functions with imprecise inputs. Are there any other red flags a ...
5
votes
0answers
39 views

Origin of phrase `computational microscope'

I have heard the term 'computational microscope' used to describe the practice of molecular simulation (in the context e.g. computational chemistry, materials science) and its use as a numerical tool ...
1
vote
3answers
241 views

Morley element implementation reference

I am looking for a detailed reference on the implementation of the Morley element for FEM, specifically for the biharmonic equation. By detailed, I mean that it should discuss the problems associated ...
1
vote
0answers
52 views

Assume $AX = C$. How to determine which entry of $BX - D$ is non-negative?

Let $A,B$ be $n \times n$ matrices and $C,D$ be $n \times 1$ matrices. Moreover, all entries of $A,B,C,D$ are non-negative. Assume that there is a unique matrix $X$ that solves $AX = C$. My goal is ...
27
votes
9answers
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
vote
1answer
120 views

Applications of Julia in Chemistry and Molecular Physics?

I was wondering if there are any Theoretical & Computational Chemistry (MM, QM) codes or publications out there that are based primarily on the Julia programming language?
1
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0answers
41 views

Advice for a topic in a seminar

I am a master student in Mathematics, and I have to prepare a seminar for a course in mathematical methods for applied sciences. I have a good background in numerical analysis for ODEs, PDEs and hence ...
0
votes
1answer
77 views

Avalability of SNOPT optimization solver

I'd like to know if SNOPT solver is available free of cost for academic research in any of the optimization software packages. I came across a few softwares that have SNOPT, but those require a ...
0
votes
0answers
63 views

How to solve odd-order differential equations in FEM? Petrov-Galerkin?

I've recently learned about using weighted residuals with the Galerkin method to numerically approximate even-order differential equations (for linear elements, I'm still a beginner). It seems for odd-...
2
votes
1answer
406 views

C++ book recommendation- Scientific computing and C++

I'm a master's student in Math interested in Numerical Analysis. I know there are lots of questions like that on this site, but I think this is the best place to ask. So, I'm looking for an ...
1
vote
1answer
145 views

Is C++ and Object-Oriented Numeric Computing for Scientists and Engineers by Daoqi Yang still relevant?

I'm looking to learn C++ primarily from a scientific computation perspective. The approach of the textbook seems ideal to me as it covers C++ from first principles with an emphasis on numerical ...
7
votes
5answers
737 views

Adjoint method for optimization problem

I am interested in the adjoint method for shape optimization problems. However, I couldn't find a helpful introduction. So I come here and look forward to some enlightening advices. Could you direct ...
1
vote
0answers
66 views

Can Representation Theory be studied computationally / numerically?

Can a subfield such as the representation theory of Lie algebras be studied computationally / numerically -- is there an interplay between the abstract and the concrete? I would be grateful for an ...

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