Questions tagged [reference-request]
This tag is for requests for books, papers, and citations.
54
questions with no upvoted or accepted answers
9
votes
0answers
443 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 ...
7
votes
0answers
122 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 ...
6
votes
0answers
298 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 ...
6
votes
0answers
134 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 ...
6
votes
0answers
99 views
Reference request for numerical variational method
I have a variational problem where the unknown function is a periodic path $\gamma:[0,1)\to\mathbb{R}^2$, and the functional is
$$ \int_0^1\left( \tfrac12\|\dot\gamma(s)\|^2 + \mathcal{F}[\gamma]\...
5
votes
0answers
38 views
Origin of phrase `computational microscope'
I have heard the term 'computational microscope' used to describe the practice of molecular simulation (in the context e.g. computational chemistry, materials science) and its use as a numerical tool ...
5
votes
0answers
3k views
Good C++ optimization library for BFGS
To implement maximum likelihood estimators, I am looking for a good C++ optimization library that plays nicely with Eigen's matrix objects. Eigen has some capability of interfacing of its own but if ...
5
votes
0answers
86 views
Interface Formulation at Finite Volume Boundaries when using the Dual Mesh
When using the dual mesh (vertex-centered) for finite volume methods, you end up with a cell center at the boundaries between materials. It is possible that the equations being solved in each ...
5
votes
0answers
187 views
Time-stepping for coupled nonlinear PDEs
What are good references for time-stepping of the coupled incompressible Navier-Stokes-heat equation (Boussinesq flow),
$$
\begin{cases}
\rho\left(\dot{\mathbf{u}} + \mathbf{u}\cdot\nabla \mathbf{u}\...
5
votes
0answers
118 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
0answers
52 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 ...
3
votes
0answers
49 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....
3
votes
1answer
78 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
0answers
56 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 ...
3
votes
0answers
136 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
0answers
38 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 ...
3
votes
0answers
197 views
Rhie--Chow interpolation on PDE level
The Rhie--Chow [1] interpolation seems to be a standard tool in the Finite-Volume discretization of incompressible flows.
It is commonly defined on the discrete level [2].
In the lecture notes [3] --...
3
votes
0answers
120 views
Floating-point arithmetic in scientific computations rules of thumb
I am looking for a nice reference (a review, tutorial, or maybe a book) that has tips and their explanations about general issues of floating-point arithmetic in scientific computations.
Some that I'...
3
votes
0answers
80 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, ...
2
votes
0answers
69 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 ...
2
votes
0answers
46 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 ...
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 =...
2
votes
0answers
60 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
...
2
votes
0answers
44 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
$$
\...
2
votes
0answers
156 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 ...
2
votes
0answers
52 views
A test suite of large systems of nonlinear equations
I am looking for a kind of modern test set of large nonlinear problems. The only option I managed to find so far is rather dated: http://folk.uib.no/ssu029/Pdf_file/Testproblems/testprobRheinboldt03....
2
votes
0answers
336 views
Numerical methods for calculating the inverse CDF when closed form approximation not available
I need to calculate the inverse CDF for a probability distribution, however there is no closed form approximation available in the literature.
The distribution I am working with is the Normal Inverse ...
2
votes
0answers
116 views
Resources for large-scale MILP optimization
With the advent of "big data" applications, different algorithms have to be used to efficiently solve optimization problems, even in the convex case (e.g. the recent success of stochastic gradient ...
2
votes
0answers
194 views
Good approximate solutions for a MILP problem
The company I work for has been developing an application for real-time control of sewer networks. Every 5 minutes, a MILP problem is built or updated, then solved using Gurobi.
For mid-sized cities, ...
2
votes
0answers
183 views
Texture analysis methods modern survey paper
I want to study the methods of analyzing textured images. So i searched google scholor but only found very old papers
statistical and structural approaches to texture 1979 haralick
Image Texture ...
1
vote
0answers
52 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 ...
1
vote
0answers
51 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 ...
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 ...
1
vote
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 ...
1
vote
0answers
60 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 ...
1
vote
0answers
44 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 ...
1
vote
0answers
70 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 ...
1
vote
0answers
63 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 ...
1
vote
0answers
126 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 ...
1
vote
0answers
41 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 \, ,$$ for $t\geq 0$ and $x\in \mathbb{R}$.
This equation is integrable, and so ...
1
vote
0answers
81 views
Discrete operator textbooks
This will be a vague question.
When I was writing a finite element matrix assembly routine, a colleague noticed that I had a bug in my code because the sparsity pattern of the one of the blocks didn'...
1
vote
0answers
92 views
Kahan Summation for Three-Term Recurrences
Kahan summation applies to summation problems, but not to three-term recurrence relations. However, a three-term recurrence shares many of the features of a summation-albeit with a rescaling step at ...
1
vote
0answers
14 views
Optimizing estimator of composed functions when function is known
Note: This was cross-posted from comp-sci, as I didn't know this community existed!
I have a problem which I'm looking to see if there is literature on:
Consider three types of actors, a Director, ...
1
vote
0answers
54 views
convergence of a method
I want to show convergence of a finite element method for a higher order equation.I have a coupled equations that solved together and gives two variables as answer $[u, v]$.
$$w+\Delta u=0$$
$$\...
1
vote
0answers
137 views
How to compute frank copula and its derivative accurately?
I need to fit a model using MLE with Frank copula by linking two discrete univate distribution function $u = F(x)$ and $v = F(y)$ together, and the joint distribution function is
$$
\Phi(x,y) = C(F(x)...
1
vote
0answers
106 views
Lattice Boltzmann Method
I have done Molecular Dynamics Simulation and now want to venture into Lattice Boltzmann Method. What would be the best reference book/lecture notes/videos for a beginner?
1
vote
0answers
37 views
Optimal partition - variable number of parts
Suppose I have a box $D \subset \Bbb{R}^2$ (compact set). Denote $\mathcal{P}= \{ (\Omega_1,...,\Omega_n) : \bigcup_{i=1}^n \Omega_i = D,\ \Omega_i \cap \Omega_j =\emptyset\}$ the family of partitions ...
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 ...
0
votes
0answers
34 views
Effect of Peclet number on concentration profiles
I have been performing convection-diffusion transport studies on microfluidic channels like the following
I came across an article that illustrates the effect fo Peclet number on concentration ...
0
votes
0answers
57 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-...
