All Questions

Filter by
Sorted by
Tagged with
0
votes
1answer
106 views

seminorm of solutions of Laplace equation

If $u_1$ and $u_2$ are solutions of (weak-form) Laplace equation on a connected domain $\Omega$, with Dirichlet boundary values $u_{\partial\Omega, 1}$ and $u_{\partial\Omega, 2}$, respectively. If $$...
0
votes
1answer
139 views

Converting ROOT Tree to HDF5

I have a TTree in ROOT with 1000 events and 15 variables associated to each of them. I would like to convert this in its entirety to an hdf5 dataset. How do I organise my data in HDF5 Groups such that ...
1
vote
2answers
124 views

How to simulate over 1 billion particles?

I want to simulate human erythrocytes in capillaries. I calculated, that for a 1 meter long and 1 mm in diameter capillary there are about 3 billion blood cells. Erythrocytes are actually discs, but ...
3
votes
0answers
52 views

Calculation of Mean Square Displacement for Brownian dynamics system with Lennard Jones interactions in python3

I have a problem getting a sensible result for the Mean Square Displacement (MSD) for a simulation of $N$ particles under Brownian dynamics with Lennard-Jones interaction between them with or without ...
1
vote
1answer
30 views
4
votes
2answers
199 views

Motivation behind Collocation Method

In the previous question "Motivation behind Galerkin method", Paul gives a good and easy-to-understand explanation indicating that the Galerkin method is a kind of projection method. Can anyone ...
1
vote
1answer
24 views

How to choose between compact finite differences and spectral methods

For a project in my advanced numerical method class I have to solve the 1D Kuramoto-Sivashinsky equation. $$ u_t + u u_x + \lambda u_{xx} + \eta u_{xxxx} = 0. $$ As explained here I will solve it ...
1
vote
1answer
27 views

Type of Rosenbrock method by its coefficients

A Fortran code that solves stiff PDE systems contains the following arrays of Rosenbrock-Wanner method coefficients: ...
2
votes
0answers
31 views

evaluating $\coth(x) - 1/x$ for real x, on 2 “pieces”

The function $\coth(x) - 1/x$ has a removable singularity at 0. Its Taylor series is: $$ \coth(x) - 1/x = \frac{x}{3} - \frac{x^3}{45} + \frac{2x^5}{945} + \ldots $$ I would like to evaluate the ...
0
votes
0answers
14 views

How to implement the gmres method using Householder transformation instead of the Gram-Schmidt?

For Generalized Minimal Residual method GMRES, we usually use the Modified Gram-Schmidt MGS to generate an orthonormal basis of ...
2
votes
1answer
60 views

Inverting really big symmetric block matrix

I have a really big symmetric 7.000.000 X 7.000.000 matrix that i would like to invert. The matrix is extremely sparse and it can be rearranged as to become a block matrix. The biggest blocks are ...
1
vote
2answers
75 views

Is the similar subdivision of a delaunay mesh still delaunay?

I have a delaunay triangulation for a 2d box with say an airfoil inside. If I uniformly refine this mesh by subdividing each triangle in the mesh into 4 triangles by halving each edge, is the ...
1
vote
2answers
43 views

Why Householder transformation can not be chosen to be an identity matrix?

For Householder transformation, we know that $H = I-uu^T$, where $\|u\|_2=\sqrt{2}$. When it acts on any vector $x$, $Hx$ and $x$ is symmetric with respect to $span(u)^T$. But I have read a ...
2
votes
1answer
88 views

Givens rotation vs 2x2 Householder reflection

The usual story of Givens rotations vs Householder reflections is that Householder reflections are better if you want to map a long vector to $e_1$, while Givens is better if you want to map a 2-...
1
vote
1answer
48 views

Using adolc for the sign function in c++

Here is an implementation of the sign function in C++ using Adolc librairy for automatic differentiation. ...
0
votes
0answers
37 views

HSS preconditioner with gmres [closed]

I have a question about HSS preconditioner with GMRES method. For implementing the HSS preconditioner with GMRES, we need to solve the linear system of the form (I + H)(I + S)z =r, for a given r at ...
1
vote
1answer
39 views

Initial condition for Kuramoto-Sivashinsky

For a project in my advanced numerical method class I have to solve the 1D Kuramoto-Sivashinsky equation of which I know little. I just know that it was derived the equation to model the diffusive ...
2
votes
1answer
93 views

Efficient ways to numerically evaluate matrix exponentials

What are some computationally efficient ways to solve matrix exponentials, i.e. functions of the form : f(X)=$e^{X}$, where X is a square matrix ? So far I have been able to diagonalise some ...
3
votes
0answers
35 views

Solving saddle point problem having non-invertible top-left block with a PETSc nested matrix

My system is a symmetric FE problem with lagrange multipliers: $Z=\begin{pmatrix}A & C^T \\ C & 0\end{pmatrix}$ The matrix $A$ is positive semi-definite, non-invertible. The whole matrix is ...
3
votes
0answers
28 views

Hit-n-Run Monte Carlo on convex polytope

So, I'm currently trying to implement a MCMC to uniformly sampling hyper-points from the polytope defined as $\mathbb{K}=\{x\in\mathbb{R}^{n}\;\;\text{s.t.}\;\; A\,x=b \}$ in the specific case where, ...
4
votes
1answer
107 views

Computation of triple nested loops as a convolution product?

I'm trying to compute efficiently the following \begin{equation} A_j = \sum_{l'=1}^{\infty}\sum_{k= 0}^{K-1} L_{l'}T_ke^{2\pi i \frac{k}{K}j}\epsilon_{l',k} \end{equation} for $j = 0,1, \ldots, K-2,K-...
1
vote
1answer
30 views

Determinant of a matrix after removing or adding lines and columns

In quantum mechanics, the wavefunction of N electrons is given by a determinant. I am working on a Monte Carlo algorithm. At each Monte Carlo step, I need to add or remove an electron, which means ...
3
votes
0answers
47 views

Levinson Recursion for Non Square Toeplitz Matrices

Given a rectangular Toeplitz Matrix $ H $, how could one solve: $$ y = H x $$ For instance, $ H $ can be Linear Convolution Matrix of the filter $ h $: $$ H = \begin{bmatrix} {h}_{1} & 0 & ...
1
vote
1answer
372 views

What is the difference between Abaqus and Calculix contact input?

I would like to say first that am new at using Calculix. I'm using Abaqus/CAE to create a cup deep drawing simulation and everything worked perfectly but my objective is to run the same exact ...
2
votes
1answer
46 views

pdepe or Crank-Nicolson? How much is pdepe good?

I am beginner in MATLAB and similar. I sow and discussed with my professors doing simulations some times: they wrote down a lot of calculus, most of them using Crank-Nicolson Method and so implement ...
-1
votes
0answers
28 views

How to compute the gradient of T with Armadillo library [closed]

I am using the Armadillo library to solve a 3d heat conduction problem on 3d unstructured grid system,the gradient of the T field is determined by the least square method. I have created a matrix ...
4
votes
0answers
40 views

Why the two Gram-Schmidt algorithms produce different results for qr factorization?

For the qr factorization using classic Gram-Schmidt algorithm, I found the 2 different implementations below. The first one uses the for loop to compute the upper ...
4
votes
1answer
56 views

Why the solid FEM problem can not be solved after constraining 3 degrees of freedom?

I write a simple MATLAB code for solving solid FEM problem. The problem looks like that (1) (2) x-------x | / | | / | | / | x-------x (3) (4) ...
30
votes
2answers
11k views

why is A*v+B*v faster than (A+B)*v?

$A$ and $B$ are $n \times n$ matrices and $v$ is a vector with $n$ elements. $Av$ has $\approx 2n^2$ flops and $A+B$ has $n^2$ flops. Following this logic, $(A+B)v$ should be faster than $Av+Bv$. Yet,...
12
votes
4answers
666 views

Example where autodiff works but symbolic differentiation will not?

According to the survey paper on autodiff (linked) Autodiff works on inputs that cannot be specified in closed form but can be described by a sequence of code, each component of which is ...
-1
votes
0answers
56 views

Simulating an object in orbit

This question is more oriented around suggestions for simulation tools and how to approach simulating an object in orbit. So high level I am trying to simulate the concept of a Sky Hook. What are the ...
9
votes
2answers
7k views

Use of machine learning in computational fluid dynamics

Background: I have only built one working numeric solution to 2d Navier-Stokes, for a course. It was a solution for lid-driven cavity flow. The course, however, discussed a number of schemas for ...
0
votes
0answers
48 views

Is it possble to do this complex symbolic calculation with Matlab?

Sorry it's bit abrupt, but recently I am caught up in some symbolic calcualtion which is tedious and almost impossible with mere human hands, so just wondering is it possible to solve the double ...
5
votes
1answer
2k views

Eigen - store sparse matrix as binary

I need to store large sparse matrices in Eigen. I cannot find anything in the library except the function below, in Eigen/Unsupported. The problem with saveMarket is, that it saves in text format. Due ...
-1
votes
0answers
5 views

Change value of dependent sweep varietals

I am using Comsol to model a really hard problem. I am using the sweep for one variable (width), and as the problem state (Length=2*width). When I use the sweep the value of Length does not update. ...
10
votes
2answers
531 views

How to sample points in hyperbolic space?

Hyperbolic space in the Poincaré upper half space model looks like ordinary $\Bbb R^n$ but with the notion of angle and distance distorted in a relatively simple way. In Euclidean space I can sample a ...
1
vote
0answers
52 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 ...
2
votes
1answer
52 views

Solution method of nonlinear heat transfer analysis

The governing equation of transient heat transfer analysis is described as follows: $$C \frac{dT}{dt}+K T = Q$$ When using backward difference scheme for the discretization of the time we get the ...
1
vote
2answers
156 views

How to vectorize 2 nested for loop with one complex condition in the inner loop?

Octave calculations is too slow specially when you deal with scientific calculations that can span a very very large matrix, even just iterating. I have to vectorize it to speed up the calculation. ...
5
votes
1answer
139 views

Complex differentiation of linear solvers

I have a linear system $$Ax=b$$ which I'm solving approximately, and I need to take the frechet derivative of x with respect to z. Were I solving the problem exactly (either analytically or to machine ...
1
vote
1answer
75 views

Is this a valid way to implement Neumann BCs in finite differences?

I'm trying to solve the 1D heat equation with Neumann boundry conditions numerically using finite differences: $$u_t = \alpha u_{xx}$$ $$u_{x}(0, t) = u_{x}(L, t) = k$$ $$u(x, 0) = u_0(x)$$ The main ...
4
votes
0answers
82 views

Trying to understand splitting-based iterative method for 2D Laplace problem

I am trying to understand the theory behind a splitting based iterative method which uses the incomplete Cholesky factorization. Before giving the specific details, let me first give the problem ...
0
votes
2answers
39 views

contour plot of cloud of points

I have a cloud of points scattered in a rectangle and some data in this points, a bit like this $$ x(:)=[x(1), x(2), ..., x(N)] \\ y(:)=[y(1), y(2), ..., y(N)] \\ u(:)=[u(1), u(2), ..., u(N)] $$ ...
8
votes
1answer
149 views

When training a neural network, why choose Adam over L-BGFS for the optimizer?

More specifically, when training a neural network, what reasons are there for choosing an optimizer from the family consisting of stochastic gradient descent (SGD) and its extensions (RMSProp, Adam, ...
6
votes
1answer
2k views

Computational methods for finding the energy eigenvalues of the time-independent Schrodinger equation with arbitrary potential

I have seen in some papers that the energy levels in some arbitrary potential are specified. How can one find the energy levels in such arbitrary potentials. For example, $V(x)=\sin^2(x/2)$ with $x\in[...
9
votes
1answer
3k views

Solving linear systems by fft

I read in a paper and also at wiki that we can solve the system $$Ax=B$$ by Fast Fourier Transform, where $A$ is a circulant matrix. The solution is $$x=\mathtt{ifft}(\mathtt{fft}(B)/\mathtt{fft}(a))$...
2
votes
0answers
35 views

Avoid matrix multiplication in algebraic multigrid method

Currently when I try to solve a linear algebra system of the form of $A x =b$ I use the algebraic multigrid method. The algebraic multigrid method uses a Galerkin product to form the coarse grid ...
1
vote
2answers
62 views

Solving a 1D diffusion equation with linear and nonlinear source terms

I would like to numerically solve the following equation: $$\frac{\partial \rho (z,t)}{\partial t} = B(N_D \rho (z,t) + \rho(z,t)^2) + D \frac{\partial^2 \rho (z,t)}{\partial z^2}$$ with the boundary ...
3
votes
1answer
81 views

Can one publish a new model and simulation without physical experiments?

When I read strong papers from, say, the Journal of Fluid Mechanics, a simple model, simulations and physical experimental results are given, showing good agreement. Can one publish a new model and ...
0
votes
1answer
40 views

How to improve the efficiency of periodicity detection for long time based lined and gapped datasets

Our data set has $10^4$ data points, but has a long baseline and many gaps. As the histogram shows, the horizontal-axis is time and most of the time, there are no data. The vertical-axis is data ...

15 30 50 per page