Questions tagged [reference-request]
This tag is for requests for books, papers, and citations.
200
questions
1
vote
0answers
54 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 ...
3
votes
1answer
311 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 ...
3
votes
0answers
50 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 ...
0
votes
0answers
25 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 ...
3
votes
0answers
96 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 ...
3
votes
1answer
145 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 ...
1
vote
0answers
65 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 ...
7
votes
0answers
99 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 ...
1
vote
1answer
93 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.
$$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2} - v\frac{\partial C}{\partial x}$$
...
1
vote
0answers
27 views
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 ...
4
votes
0answers
96 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 ...
3
votes
1answer
90 views
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 ...
2
votes
0answers
43 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 ...
3
votes
1answer
76 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 ...
2
votes
0answers
55 views
References to solve system of differential equations which describe the evolution of sandpile surface using the finite element method
I want to solve the following nonlinear system in 1D
\begin{cases}
\dot{R} + v \frac{\partial R }{\partial x} - \frac{\partial }{\partial x}\left( D \frac{\partial R }{\partial x} \right) -\Gamma =...
4
votes
1answer
101 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 ...
2
votes
1answer
86 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 ...
3
votes
0answers
43 views
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 ...
2
votes
0answers
52 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
...
3
votes
1answer
114 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 = ...
3
votes
2answers
69 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)?
3
votes
1answer
113 views
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,...
1
vote
1answer
433 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
0answers
30 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?
2
votes
1answer
86 views
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$....
1
vote
1answer
51 views
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 ...
2
votes
1answer
125 views
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 ...
3
votes
1answer
211 views
Derivation of backward differentiation formulas(BDF)
I have been reading upon numerical techniques that are used to solve stiff ordinary differential equations.
From the description given here, I could follow the steps till equation (5).
I am finding ...
3
votes
0answers
36 views
Guide for finite-difference schemes for Hamilton-Jacobi-Bellman Equations
I need to solve a simple, low-dimensional Hamilton-Jacobi-Bellman equation.
Is there a simple guide for doing this numerically using finite-difference schemes? I found a few research articles ...
2
votes
0answers
2k views
Good C++ optimization library for BFGS
To implement maximum likelihood estimators, I am looking for a good C++ optimization library that plays nicely with Eigen's matrix objects. Eigen has some capability of interfacing of its own but if ...
1
vote
0answers
54 views
Has there been a comparison bewteen SIMPLE/SIMPLER and JFNK for steady CFD?
I'm looking for a comparison between the Jacobian-Free Newton-Krylov (JFNK) method performance compared to the conventional CFD nonlinear solution methodologies like SIMPLE.
Does anyone know if such ...
2
votes
2answers
84 views
Elliptic equation with finite volume and unstructured high order geometry
I have found that in unstructured mesh, discretizing the laplacian operator with finite volumes requires special care, as given in An Introduction to Computational Fluid Dynamics: The Finite Volume ...
4
votes
2answers
101 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)
$$
when implemented in practice on a computer. Is there a colloquial name or a more ...
2
votes
0answers
40 views
Sensitivity Lagrangian solution general case
I have asked this question already on maths and mathoverflow.
Just a question about a literature reference. I am writing a paper for engineers.
Usually for the Lagrange multiplier problem
$$
\...
7
votes
2answers
90 views
What good are hard-sphere event-driven molecular dynamics simulations in the face of chaos?
Simple hard-sphere dynamical systems can exhibit chaotic dynamics. Due to finite-precision arithmetic when implemented on a computer, the presence of chaos implies that for a given set of initial data,...
12
votes
2answers
356 views
For noisy or fine-structured data, are there better quadratures than the midpoint rule?
Only the first two sections of this long question are essential. The others are just for illustration.
Background
Advanced quadratures such as higher-degree composite Newton–Cotes, Gauß–Legendre, ...
0
votes
1answer
77 views
References in Scientific Computation for a Computer Science Undergrad? [duplicate]
TLDR: What references and pre-requisites are necessary for a Computer Science Undergraduate to get ready for a Masters and Career in Scientific Computation / Computational X
For a Computer Science ...
1
vote
1answer
19 views
Implementation of a ratio with a well-defined limit
I'm implementing a function $f(x_1, x_2, \dots x_n)$ given by the ratio of two closed form equations.
$$ f(x_1, x_2, \dots, x_n) = \frac{g(x_1, x_2, \dots, x_n)}{h(x_1, x_2, \dots, x_n)} $$
...
1
vote
2answers
2k views
Physics Simulation in C++
OK, I know a bit of C++ (very basic syntax), and I want to do physics simulation in C++, like stuff like (also the things mentioned here):
Ripples and waves over a 2-d surface
Vibrating string/...
7
votes
1answer
366 views
How to directly compute the inverse of an ill-conditioned dense matrix
I know that it is generally a bad idea to compute the inverse matrix directly. However, if it is necessary to compute the inverse of an ill-conditioned invertible dense matrix, then what can I try?
...
3
votes
1answer
88 views
Computation of the heat kernel from Brownian motion
This question is rather simple but I have some difficulties to find code. Let us suppose that I wrote a routine, in a given language, that computes the evolution of a particle doing Brownian motion in ...
2
votes
0answers
152 views
Analysis and numerical methods for PDEs arising in industrial problems
Assume some basic knowledge of numerical methods for PDEs, acquired through A. Quarteroni's Numerical models for differential problems.
I'm looking for a reference to get started on the analysis of ...
3
votes
1answer
382 views
Radiation boundary condition (heat transfer)
I am looking for reference on how to implement nonlinear boundary conditions. Specifically, I am interested in implementing a radiation boundary condition for heat transfer with the FEM:
$-k \frac {\...
1
vote
0answers
123 views
Reference request: free/open source books on intro numerical PDE
I'm interested in finding a free online textbook that is an introductory textbook on numerical PDE for engineers. It should cover the basics of finite differences, finite elements, and Fourier series ...
0
votes
1answer
126 views
pde-constrained optimization
I'm trying to solve a problem where I have a initial and final distribution of tumor, and my goal is to find the best map of parameters (diffusion and reaction terms) for a reaction-diffusion equation,...
8
votes
1answer
245 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/...
1
vote
2answers
355 views
C++ template design pattern for groups (algebra)
Having both programmed my share of c++ and studied some beginners group theory some year ago, I got curious about this...
Is there any particularly popular template based (object oriented) design ...
6
votes
0answers
128 views
Do practice and theory differ substantially when implementing Neumann Boundary Conditions using a Mixed Method?
I have implemented a pretty straightforward finite element solver for the following Poisson equation. For the purposes of this question we can assume the source term and the Dirichlet data both ...
10
votes
1answer
492 views
First appearance of the phrase “inverse crime”
In research on inverse problems, it's common to construct a synthetic data set from a known set of parameters and then test whether the inversion technique can reconstruct those parameters. In doing ...
1
vote
0answers
38 views
Computing Direct Scattering Transform
I'm working on the Nonlinear Schrodinger equation (NLSE) in 1d:
$$i\psi _t (t,x)+ \psi _{xx} + |\psi|^2\psi = 0 \, ,$$ for $t\geq 0$ and $x\in \mathbb{R}$.
This equation is integrable, and so ...
