Questions tagged [reference-request]
This tag is for requests for books, papers, and citations.
273
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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 ...
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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 ...
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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....
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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 ...
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FEM Python book
Is there any book or site available with Finite element Method for partial differential equations with python code apart from Fenics?
user37062
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2
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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, ...
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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
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1
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293
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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?
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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 ...
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167
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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 ...
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292
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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 ...
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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-...
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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 ...
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956
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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 ...
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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 ...
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2
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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 ...
- 560
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3
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527
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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 ...
- 1,271
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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 ...
- 19
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464
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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 ...
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130
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Methods to approximate obective function gradients from point cloud
Problem statement:
Assume that I have an objective function $f(x)$ which takes as input a $D$-dimensional vector $x\in\mathbb{R}^D$, and that $f(x)$ is sufficiently smooth. Assume further that I ...
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1
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125
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Truncated power series algebra implementation
1) I am looking for references for an efficient implementation and usage of TPSA. What sources exist besides Berz's 1989 original paper and the incomplete chapter in Dragt's book?
2) Are there ...
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0
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363
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What is the fastest algorithm for computing log determinant of a PSD matrix? (All possible PSD matrices)
I am diving into some literature to understand which is the best algorithm for computing the log-determinant of a PSD matrix. More generally, I am interested in a list of resources to read, which ...
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677
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Consumer hardware for scientific computing?
I'm interested in problems around probability, statistics, and statistical mechanics, and often I find it useful to perform simulations to get some sense of the underlying phenomena. Example ...
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77
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How to approach geographic data interpolation by distance?
let's say I have a set of geographic locations (lat, lng) resulting from a query. Those locations have some kind of internal ranking, my set is sorted by this number in a descending order.
Now I'm ...
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"Geometry of ill-conditioning" for least-squares problems
It is an idea that dates back to Demmel, 1987 that the condition number of a problem is often related to the distance to the closest ill-posed problems. In Section 3 of the above paper, the author ...
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Simulating advection - diffusion problem in a network of 1D pipe
I'm interested in solving the following advection-diffusion system in a 1D network of pipes.
$$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2} - v\frac{\partial C}{\partial x}$$
...
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Book Recommendation: Analysis and design of mechanistic models - such as pharmacokinetics or hydrology models
I have been looking at an interesting book "Pharmacokinetic-Pharmacodynamic Modeling and Simulation" by Peter Bonate on pharmacokinetic models: the models of how medical drugs work their way through ...
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Are there well-known methods for navigating on kd-trees?
When you have a mesh, there are many well-known methods to navigate it, as for example using a half-edge data structure, that allows easy circulation around faces and vertices.
Are there similar ...
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Reference request: Riks method (Nonlinear FEM)
I'm struggling to find a good detailed reference explaining the Arc-length method or, more generally, Riks method and its derivations. I looked for the classical books in nonlinear mechanics (the ones ...
user30551
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Classification of multiobjective optimization algorithms
I am looking for a good (canonical?) overview paper(s)/book(s) on the classification of multiobjective optimization algorithms. I am focused on obtaining a representative set of Pareto optimal ...
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Good reference on the implementation and limitations of SDIRK methods
For the solution of many PDE, implicit high-order time integration schemes are required. I am specifically interested in schemes that do not require a constant time step.
I am well acquainted with ...
- 1,147
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1
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Original paper on the augmented Lagrangian method in FEM
I am writing a paper in which I want to cite the earliest reference to the augmented Lagrangian method in FEM. For the pure Lagrangian method in FEM, the classical work of Babuška [1] is the original ...
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Null space for smoothed aggregation algebraic multigrid
I do not really get the point of null space usage for creating the prolongation operator for smoothed aggregation algebraic multigrid. I know what the null space is per definition and I know that the ...
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Is it Grid/Cluster/Cloud Computing? How are those terms defined?
There are three very connected and widely used terms:
Grid and grid computing
Cluster and cluster computing
Cloud and cloud computing
In many situations, it is not obvious which term to use, as I ...
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Reverse automatic differentiation and integration
In Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control and more Sanz Serna writes:
It is well known that the reverse mode of differentiation implies
...
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References for the nonlinear reaction-diffusion equation using Finite Element Methods
I want to study how to solve the following PDE
\begin{cases}
-\nabla \cdot(\ k(x,y) \ \nabla u \ ) + \beta(x,y)\ u^2 = f(x,y), \ (x,y) \in \Omega \subset \mathbb{R^2} \\
\hspace{0.5cm} u = ...
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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)?
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Time integration of wave equation
My question is: how come that certain formulations of the wave equation can be time integrated more efficiently then others?
Le me expand a bit on that. Consider the wave equation:
$$ \frac{d^2 p(t,...
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990
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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 ...
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Cardinal B-Splines with derivative information
Have Schoenberg's cardinal B-splines been extended to accept derivative information at each knot, similar to how Lagrange interpolation can be improved by Hermite interpolation?
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Is there an optimization scheme/algorithm that converges, for this non-convex scenario but with some special properties
I have a smooth function $f(x) = \frac{g(x)}{h(x)}$ that is the ratio of two smooth convex functions $g(x)$ and $h(x)$. It is known that $f(x)$ has a global minimum, achieved at the unique point $x_0$....
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Research articles on MultiObjective Non-Linear Programming (MONLP)
I'm looking for papers dealing with multi-objective non-linear programming which could help me implement an algorithm to solve my problem.
My problem is :
Maximize $f(x) = c \cdot x$, while ...
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Numerical integration of Fokker-Planck equation allowing for negative drift?
The Fokker-Planck equation (a.k.a Kolmogorov forward equation or Smoluchowski equation) describes the evolution of a probability density function and numerical integration of the FPE should conserve ...
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