# Questions tagged [reference-request]

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

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1 vote
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### Has the arithmetic for exotic (unsigned float with positive exponent) number format been solved?

The data type is a doubly unsigned float. This is where the value and exponent are both strictly positive. The range of this number should include $0$ and $[1, ~2^{\text{exponent}})$, skipping all ...
1 vote
75 views

### Resource to learn assembly code

I'm a PhD student in mechanical engineering and I have to perform a lot of simulations for my project. In my lab we use several well-known libraries, from FEM to machine learning. As we're doing ...
38 views

### Efficient cutting of mesh edges

I am looking for efficient algorithms to cut a mesh along edges. I have a (half-edge) mesh and a list of inner edges that I want to cut, such that both are new boundary edges. At each vertex there can ...
201 views

3k views

### Introduction to Lattice Boltzmann methods [closed]

I am trying to learn the Lattice-Boltzmann method and was looking for some good beginner resources explaining the method. I have been looking at some codes online, but have been having trouble ...
167 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 ...
218 views

### Matrix-free FEM references

I've seen that many people are using matrix-free fem codes in my community (mechanical engineering). I have to admit that I googled a bit and I didn't manage to find a good reference for the subject. ...
65 views

### Solving L1 minimization problems in Eigen

I have an $m\times n$ dense matrix $\mathbf{M}$ and wish to solve $\mathbf{M}\mathbf{x} = \mathbf{b}$ via any of the "L1" methods using Eigen. By this I mean I'm happy with using basis ...
74 views

### Book recommendation on multiphysics

I want to learn multiphysics such as fluid-structure interaction where the simulation is performed for heat transfer, fluid dynamics, and electrodynamics. Could you please recommend some books about ...
1 vote
92 views

### Automatic Differentiation using foward mode on matrices

Whilst googling I see reverse mode automatic differentiation (AD) tends to be used when optimising neural networks. Would it not be better to use forward mode and treat your input as a single variable,...
11 views

### Non-Temporal Weighted Graph Datasets

I am searching for datasets to evaluate an algorithm designed for tasks such as node-classification (edge-prediction, etc.) on weighted and potentially directed graphs. The Stanford Network Analysis ...
1 vote
112 views

### Nonlinear Hyperbolic PDEs: Known solutions

I would like to collect some test-problems for nonlinear hyperbolic PDEs (Euler Equations, Shallow Water Equations, Ideal MHD, Acoustic Perturbation, ...) for which analytical solutions are known. A ...
1 vote
88 views

### Kolmogorov n-width

Could someone please point me to an understandable definition of the Kolmogorov n-width? I'm having a hard time figuring out what is the output of the definition - is it an integer? Edit: I realize ...
166 views

### Reference request: Philosophy of Computational Science

Do you suggest any references (papers, monographs, books) about the philosophy of computational science? Recently, I found out about the following two: Winsberg, E. (2009). Computer simulation and ...
98 views

### Stabilized Many Stage Runge-Kutta methods instead of Local/Multirate Time Stepping

Locally refined meshes are often inevitable for accurate, yet feasible computations. In the context of time-dependent PDEs, however, this comes at the cost that (due to the CFL condition) reducing the ...
54 views

### Finding optimal values from multiple parameter estimation runs

I've performed a parameter estimation repeat (i.e. 1000 parallel runs with the same initial values of parameters). I am trying to estimate ~20 parameters using measurements from experiments. After ...
325 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 ...
181 views

1 vote
73 views

### Implementation of integration schemes for ordinary differential equations in Python and peformance comparison

I look for a book/manual where I can find implementations of different integration schemes for ordinary differential equations (like 4-th order Runge-Kutta) in Python with Numba. To be more specific, ...
1 vote
148 views

### About using SOCP solvers to solve QCQP

I have noticed that some commercial solvers transform QCQPs into SOCPs and use SOCP algorithms to solve the resulting problem. I am wondering if there is a benefit to this approach over using a pure ...
68 views

### Requesting for Finite Difference Methods reference in Portuguese or English

Crossposted on Mathematics SE I have been assigned a group project for an introductory Linear Algebra subject on Finite Difference Methods and sparse matrices. Our professor advised we use Gilbert ...
1 vote
462 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 ...
150 views

### Mesh refinement in the Finite Element Method

I need some good references on how to implement programmatically the hp-refinement of meshes in the Finite Element Method in two/three-dimension. I've searched the web a lot and read many articles and ...
159 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
82 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) ...
1 vote
678 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 ...
581 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-...
155 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) ...
34k views

### Difference between Nodes and CPUs when running software on a cluster?

I'm looking into moving some computations of mine to a data center to get more computation power. In the context of this process, I am getting confused by the differentiation of a computation node and ...
1k views

### Higher precision floating-point arithmetic in numerical PDE

I have the impression, from very different resources and talks with researches, that there is a growing demand for high precision computations in numerical partial differential equations. Here, high ...
1 vote
59 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
88 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 ...
902 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 ...
363 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 ...
16k views

### Recommendation for Finite Difference Method in Scientific Python

For a project I am working on (in hyperbolic PDEs) I would like to get some rough handle on the behavior by looking at some numerics. I am, however, not a very good programmer. Can you recommend ...
1 vote
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 $U_2$, ...