This tag is for requests for books, papers, and citations.
1
vote
0answers
58 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
44 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. ...
3
votes
1answer
77 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
44 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
106 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
168 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
139 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 ...
6
votes
4answers
171 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 ...
3
votes
1answer
50 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
3answers
162 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 ...
0
votes
0answers
40 views
boundary condition impact on the Fourier stability analysis
I am looking for some reference on the stability analysis of the finite difference scheme for the linear constant coefficient pde. I have a few books and I see how the Fourier analysis is used but ...
0
votes
1answer
124 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. $$\nabla^2 \psi(\vec{r},t) - ...
5
votes
1answer
66 views
Use Butterworth and Chebychev filters
I need to calculate frequency response, phase response and apply to signals the Butterworth, Chebychev1 and Chebychev2 band-pass filters.
I'm developing in C++ with Qt, and I'm looking for algorithms ...
5
votes
2answers
115 views
Is computational science recommended as part of the typical undergraduate curriculum every computer science department should teach?
Computational science remains uncommon in many computer science departments, particularly in universities without an engineering school. Is it not considered part of the standard computer science ...
2
votes
0answers
44 views
Conservative field mapping between two topologically disconnected surface meshes
Some background: the Front-Tracking method uses a triangular surface mesh to describe the boundary between two immiscible fluids. To deal with the breakup and coalescence of the fluid interface, ...
3
votes
2answers
108 views
Computing an orthogonal matrix subject to linear constraints
I am looking for a method to solve the matrix equation
$$ 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
147 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 ...
4
votes
2answers
65 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
254 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 ...
-2
votes
1answer
90 views
Reference-request: Computational science and physics [closed]
I'm interested in the following question:
Is Nature computable at it's most fundamental level?
Can anyone suggest any works (books, papers / articles, reviews) related to the above question?
...
2
votes
2answers
98 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 ...
6
votes
0answers
185 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 ...
8
votes
2answers
272 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 ...
5
votes
1answer
106 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 ...
4
votes
2answers
163 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 ...
7
votes
2answers
141 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 ...
3
votes
1answer
114 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 ...
5
votes
2answers
258 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 ...
0
votes
0answers
27 views
Where can I find a detailed description of the AABBtree data structure implementation?
googling does not return much results on this. Are there any good descriptions in some book/article somewhere?
I require a fast collision detection algorithm between two sets of unordered Axis ...
0
votes
0answers
33 views
Good Introductory text for Matrix Structural Analysis and Finite-Element Methods [duplicate]
Possible Duplicate:
Modern resources for learning FEM
This question is semi-related to ...
2
votes
2answers
53 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 ...
4
votes
0answers
57 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
votes
3answers
202 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$, ...
5
votes
1answer
261 views
What are the strategies for local Adaptive Mesh Refinement (local AMR) on unstructured meshes?
I am interested in local AMR on unstructured meshes. Currently, I'm working with the OpenFOAM library - it supports completely unstructured local AMR:
cell refinement criteria determine a list of ...
12
votes
1answer
208 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 ...
6
votes
3answers
184 views
Wanting to learn about matrix solvers
Edit: I was advised to replace the question with a more specific one.
Coming from a very theoretical background, I'm pretty ignorant about what practical matrix solvers exist. (I have been, and will ...
4
votes
2answers
243 views
How to quickly implement and test a turbulence model?
What is the best software for quickly implement and test a Reynolds Averaged Navier-Stokes turbulence model ?
10
votes
3answers
1k 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 ...
9
votes
3answers
509 views
Blaze linear algebra library?
The paper "Expression Templates Revisited: A Performance Analysis of Current Methodologies" in SIAM Journal of Scientific Computing references the "Blaze" linear algebra library. I haven't heard of it ...
11
votes
3answers
336 views
Book reference for Numerical Analysis
I've had a glimpse of Numerical Analysis (majorly, Numerical Methods like root finding, quadratic equations and other preliminary stuff) in my Calculus class but now, I find myself wanting more ...
6
votes
3answers
192 views
Construction of $C^1$/$H^2$-conforming finite element basis for triangular or tetrahedral mesh
In the paper Hierarchical Conforming Finite Element Methods for the Biharmonic Equation, P. Oswald claimed Clough-Tocher type elements has $C^1$-continuity while being a cubic polynomial on each ...
4
votes
3answers
181 views
Quality Measures for Various Pseudo-Random Number Generators
According to this paper,
Ideally, a pseudorandom number generator would produce a stream of
numbers that:
are uniformly distributed,
are uncorrelated,
never repeats itself,
...
5
votes
3answers
146 views
Reference Request for Profiling High Performance Computing Codes
I write codes in Fortran and C for various matrix algorithms. However, when I profile my codes using VTune, I usually run into some terminology that I cannot fully appreciate. Is there a good resource ...
2
votes
1answer
101 views
High-resolution finite volume schemes for two phase flow (fields with jumps) literature sources
what other recent sources of literature on this topic would you recommend?
This is where I'm starting from:
Leveque's article: HRIC scheme
But the related articles seem to be a bit dated (some up ...
6
votes
2answers
201 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 ...
7
votes
1answer
311 views
weighted SVD problem?
Given two matrices $A$ and $B$, I'd like to find vectors $x$ and $y$, such that,
$$ \min \sum_{ij} (A_{ij} - x_i y_j B_{ij})^2. $$
In matrix form, I'm trying to minimize the Frobenius norm of $A - ...
5
votes
4answers
258 views
Some good reading on polygon algorithms
What are some good resources (books, articles, sites) about polygon intersection and union algorithms?
7
votes
1answer
71 views
Numerically stable algorithms for computing remainder of polynomials
Let $f, g \in \mathbb{R}[x]$ and $\deg f > \deg g$. I am looking for asymptotically fast and numerically stable algorithms for computing $f \bmod g$. In the applications intended, both $f, g$ are ...
15
votes
6answers
560 views
Modern resources for learning FEM
I need to get started using Finite Element Methods. I am about to start reading Numerical solutions of partial differential equations by the finite element method by Claes Johnson, but it's dated ...
5
votes
1answer
97 views
Question about the smoothing operators in multigrid methods for nonlinear PDEs
Suppose we are dealing with a nonlinear problem, say
$$
A u := L u + G(u) = f
$$
the nonlinearity of the operator $A$ is the polynomial type, ie, $L$ is a linear operator, and $G(u) = u^k$, or ...
