Questions tagged [reference-request]
This tag is for requests for books, papers, and citations.
267
questions
1
vote
0
answers
63
views
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 ...
- 131
1
vote
0
answers
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 ...
- 231
0
votes
0
answers
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 ...
- 607
3
votes
3
answers
201
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
$$J(u, \sigma) = \int_\Omega\left\{\frac{1}{2}A\sigma : \sigma + u\cdot\left(\nabla\...
- 9,168
1
vote
1
answer
114
views
Could you recommend some books on FEM that explain various data-structures in FEM?
I want to understand the data structure of elements, elements around elements, and so on, and various other data structures in FEM, could you please recommend some books?
- 8,572
6
votes
1
answer
207
views
Continuous vs discontinuous space-time FEM
What are some reasons for approximating a (e.g. parabolic) PDE using the space-time method, with continuous finite elements in time, vs discontinuous finite elements in time?
Are there e.g. ...
- 8,572
5
votes
0
answers
87
views
How to get an "optimal point" for refinement in FEM adaptive mesh refinement?
Consider the following 1D problem
\begin{align*}
\begin{cases}
\displaystyle
-\frac{d^2u}{dx^2} = f(x), \hspace{0.5cm} x\in (a,b) \\[4mm]
u(a) = u_{a}, \ \ u(b) = u_{b}
\end{cases}
\end{align*}
I ...
- 51
1
vote
1
answer
118
views
Non-Uniform Grids: Approximation Quality: First Order Finite Difference vs. First Order Finite Volume
Consider the advection/transport equation in 1D with constant velocity $a(x) \equiv 1$
$$u_t(t,x) + u_x(t,x) = 0$$
on a, say, periodic domain.
On uniform grids $$ \{x_i\}_{i = 1, \dots, N}, \quad x_{i ...
- 849
2
votes
1
answer
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 ...
- 8,572
3
votes
1
answer
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 ...
CommunityBot
- 1
7
votes
0
answers
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. ...
- 231
0
votes
0
answers
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 ...
- 2,085
0
votes
0
answers
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 ...
- 8,572
1
vote
1
answer
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,...
- 8,572
0
votes
0
answers
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
1
vote
2
answers
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 ...
- 16.4k
1
vote
1
answer
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 ...
- 519
7
votes
3
answers
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 ...
- 18.2k
4
votes
1
answer
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 ...
- 12.1k
0
votes
0
answers
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 ...
- 461
0
votes
2
answers
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 ...
- 1,305
5
votes
0
answers
181
views
Dense least-squares with millions of variables
Suppose $X$ is a dense $m\times n$ data matrix and we seek to find $w$ by approximately iterating least-squares filter equation:
$$w = w - \mu (X'X)^{-1}X'(Xw-b)$$
What are known approaches for $10^9&...
- 1,869
1
vote
1
answer
121
views
What are the prerequisites and resources to self-learn the Boundary Element Method for Contact Mechanics problems?
What are the prerequisites to learning BEM?
In which order is it advisable to learn BEM and FEM - either one before the other, or does it not matter?
What are some good resources to self-learn BEM?
P....
- 21
6
votes
1
answer
2k
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 ...
- 3
1
vote
1
answer
76
views
A priori estimates in finite elements for inhomogeneous heat equation
Consider the problem
$$\partial_t u-\Delta u = f\\
u(\Sigma_1)=f_D\\
\partial_\nu u (\Sigma_2)=f_N\\u(0)=u_0$$
where the sides of the space-time cylinder $\Sigma_i$ are disjoint (one of them could be ...
1
vote
0
answers
22
views
Unconstrained convex optimization: correlation between dimensionality and Lipschitz constant
The author of the SIAM News article "Optimization Theory and Perspectives on the Field of Machine Learning" mentions:
... For unconstrained convex optimization, GD (gradient descent) ...
- 8,572
3
votes
1
answer
114
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 ...
- 31
4
votes
1
answer
103
views
A priori FEM estimates without $H^2$ regularity
In basic lectures on finite elements theory, people always assume $H^2$ regularity of the solution in order to derive $O(h^k)$ a priori estimates in the norms $H^{2-k}$, $k=1,2$. For simplicity let's ...
0
votes
0
answers
63
views
Reference request for finite elements theory
Consider a domain $\Omega \subseteq \mathbb{R}^{2,3}$ which is non convex and with $C^2$ boundary. Could you recommend a good reference where it is explained how:
without needing isoparametric ...
- 131
7
votes
1
answer
2k
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?
...
- 8,572
3
votes
3
answers
2k
views
Scalar vs. vector potential for magnetostatics
When trying to solve a magneto-static boundary-value problem (BVP) ($\nabla \times \mathbf{H} = \mathbf{J}$ and $\nabla \cdot \mathbf{B} = 0$), one can use either the magnetic vector potential $\...
- 213
1
vote
0
answers
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, ...
- 171
1
vote
1
answer
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 ...
- 3,791
3
votes
1
answer
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 ...
- 8,572
1
vote
3
answers
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 ...
- 2,041
0
votes
1
answer
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 ...
6
votes
1
answer
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 ...
- 10.1k
1
vote
1
answer
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) ...
- 1,971
1
vote
1
answer
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 ...
- 8,207
10
votes
2
answers
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-...
- 906
2
votes
1
answer
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) ...
- 1,971
14
votes
4
answers
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 ...
- 1,023
12
votes
2
answers
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
2
answers
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 ...
- 23
1
vote
1
answer
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 ...
- 2,501
3
votes
2
answers
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 ...
5
votes
2
answers
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 ...
- 1,738
25
votes
3
answers
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
0
answers
115
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 ...
- 83
1
vote
1
answer
114
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 $U_2$, ...
- 2,240