# Questions tagged [reference-request]

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

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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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1 vote
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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 ...
• 121
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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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1 vote
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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?
1 vote
76 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, ...
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51 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 ...
293 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 ...
4k 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 ...
• 2,273
1 vote
93 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 ...
• 421
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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 ...
162 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 ...
46 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 ...
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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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1 vote
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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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### 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 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 ...
• 421
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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-...
1 vote
750 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 ...
1 vote
956 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 ...
• 153
1 vote
221 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 ...
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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
1 vote
527 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 ...
• 1,271
1 vote
87 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 ...
464 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 ...
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130 views

### 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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125 views

### 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 ...
363 views

### 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 views

### 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 ...
• 105
1 vote
77 views

### 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 ...
• 11
167 views

### "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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1 vote
198 views

### 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. $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2} - v\frac{\partial C}{\partial x}$$ ...
• 421
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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 ...
• 287
698 views

### 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 ...
• 607
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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 ...
47 views

### 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 ...
• 8,602
232 views

### 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
139 views

### 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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388 views

### 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 ...
• 8,602
79 views

### 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 ...
153 views

### 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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1 vote
990 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 ...
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52 views

### 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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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 ...