Questions tagged [reference-request]
This tag is for requests for books, papers, and citations.
240
questions
5
votes
1answer
76 views
Fast way of computing the action of a matrix power on a vector
For integer $k>0$, it is well-known that one can use binary exponentiation to evaluate the matrix power $\mathbf A^k$, where $\mathbf A$ is an $n\times n$ matrix.
However, it is not clear to me if ...
1
vote
1answer
58 views
How to Impose nonhomogeneous Neumann Boundary Condition in the DG Formulation
Consider the following partial differential equation
\begin{align}
\frac{\partial u}{\partial t}+\frac{\partial f}{\partial x} &= g(x,t), \ \ x\in \Omega = [x_{L},x_{R}] \\
u(x,0) &= u_{0}(x) ...
10
votes
2answers
439 views
FEM for vector valued problems: reference request
I'm a PhD working in a computational mechanics lab. I come from a Math department, and I have a good background for what concerns the basics of finite elements, like inf-sup conditions, DG, non-...
2
votes
1answer
99 views
DG method for solving Hyperbolic Partial Differential Equation with Dirichlet Boundary Conditions
Consider the following partial differential equation
\begin{align}
\frac{\partial u}{\partial t}+\frac{\partial f}{\partial x} &= g(x,t), \ \ x\in \Omega = [x_{L},x_{R}] \\
u(x,0) &= u_{0}(x) ...
0
votes
2answers
128 views
Searching for recent code source for "Parallel scientific computing in C++ and MPI "
I am learning C++ scientific computing with "Parallel scientific computing in C++ and MPI A Seamless Approach to Parallel Algorithms and their Implementation" since it kept coming up a lot ...
1
vote
1answer
82 views
Discrete model of cell - cell communication
I am trying to understand how cell to cell communication is studied using a discrete modelling framework. Could someone please suggest suitable references or libraries which already have ...
1
vote
2answers
58 views
Two-dimensional ordering issue – alternate sort order ascending/descending to reduce fluctuations - trivial?
I have a solution in search of a problem that some of you could perhaps help me with.
Let $L$ be a list of elements. Each element has two inherent properties/attributes ($a$, $b$) that can each be ...
1
vote
0answers
85 views
Finite Difference Approximation for the Laplacian in 2D that produces a nonsymmetric matrix
Consider the following PDE
\begin{align}
-\Delta u &= f \ \ \text{en} \ \ (0,1)\times (0,1) \label{P1} \\
u &= 0 \ \ \text{en} \ \partial ((0,1)\times (0,1)) \label{P2}
\end{align}
if we ...
1
vote
1answer
99 views
Finding the source of numerical instability in a electrostatic problem solved by conformal mapping
I'm using conformal mapping to solve a 2D electrostatic problem (calculating the potential $u(x,y)$ in the plane). Let $C_1$ and $C_2$ be two circles at an electric potential $U_1$ and $U_2$, ...
1
vote
1answer
181 views
Tensor product representation for the 9-point finite difference approximations for the Poisson equation
If we use 5-point finite difference approximations in a uniform rectangular grid to solve the Poisson PDE
\begin{align}
-\Delta u &= f \ \ \text{en} \ \ (0,1)\times (0,1) \label{P1} \\
u &= ...
1
vote
3answers
144 views
Stable finite elements for the mixed form of the elasticity equations
The mixed form of the elasticity equations is to find the unique critical point of the Hellinger-Reissner functional
$$J(u, \sigma) = \int_\Omega\left(\frac{1}{2}A\sigma : \sigma - (\nabla\cdot\sigma)\...
2
votes
2answers
185 views
Scientific computing code development hands on introduction
I have a background in Computational Mechanics but my knowledge remains very user-oriented. What I mean by that is that I have a fairely good knowledge about how to use a commercial engineering ...
6
votes
4answers
919 views
How important is learning hardware/architecture for scientific computing?
Apologies if this is a bit of a soft, unclear, or opinion-based question. I'm a relatively new PhD student in a (computational) quantum chemistry group. My group develops and maintains a few software ...
0
votes
1answer
141 views
Help me choose a book on the numerical integration of PDEs
For ODEs I have these books:
Griffiths, David, Higham, Desmond J., Numerical Methods for Ordinary Differential Equations, 2010
Alfio Quarteroni, Riccardo Sacco, Fausto Saleri, Numerical Mathematics, ...
0
votes
0answers
37 views
HLLC Riemann solver with shock test 2 - extension to low densities
I am currently using the HLLC solver to solve a 1-D system of Euler equations with very satisfactory results.
However, there are cases where my solution produces low-density, high velocity states, ...
1
vote
1answer
58 views
What is the best cooling and flippling schedule in simulated annealing?
I've noticed that some heuristics for it on my problem which work surprisingly well. I guess it ought to be systematically studied although I cannot find guides or overviews for it.
2
votes
0answers
89 views
A priori error estimates - finite element method - mixed boundary conditions
Consider the problem
$$ \left\{\begin{array} {rcl}
-\Delta u & = 0 & \text{ in } \Omega \\
u & = 0 & \text{ on } \Gamma_D \\
\frac{\partial u}{\partial n} &= g &\text{ on } \...
2
votes
1answer
370 views
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 ...
1
vote
1answer
42 views
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 ...
3
votes
0answers
67 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....
1
vote
0answers
64 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 ...
4
votes
1answer
817 views
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
2answers
75 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, ...
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 ...
2
votes
1answer
180 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 ...
6
votes
2answers
1k 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 ...
1
vote
0answers
60 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 ...
5
votes
1answer
873 views
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 ...
0
votes
1answer
147 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 ...
5
votes
0answers
42 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 ...
1
vote
0answers
57 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 ...
2
votes
1answer
138 views
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?
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 ...
3
votes
1answer
106 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 ...
0
votes
1answer
94 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 ...
0
votes
0answers
66 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-...
1
vote
1answer
406 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 ...
2
votes
1answer
490 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 ...
1
vote
1answer
163 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 ...
3
votes
2answers
564 views
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 ...
1
vote
3answers
247 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
vote
0answers
72 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
359 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
100 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 ...
1
vote
0answers
52 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
196 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 ...
6
votes
1answer
492 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
76 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
131 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
160 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.
$$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2} - v\frac{\partial C}{\partial x}$$
...