# All Questions

8,469 questions
Filter by
Sorted by
Tagged with
21 views

### How to extract connected components from persistence diagram?

From the given point cloud (Fig. 1), I use Scipy-TDA to extract persistence diagram (Fig. 2). What I'm interested in is to extract 3 circles. For example, I'd like to know 3 center points and labels ...
43 views

### Testing the time dependent Schrodinger Equation with an analytical solution?

I am numerically solving the Schrodinger Equation in 1D first and in higher dimension later, but I want to know the convergence rate of my numerical solver in different grid size and numerical methods....
7 views

### Error at boundary due to fixed b.c in 3rd order pde

I have a 3rd order in space and first-order in time PDE to solve, as an initial value problem, using the finite element method under fixed boundary condition at endpoints. My endpoints in space are <...
103 views

### (FEM) Efficient CRS vectors evaluation using elements connectivities

What is an efficient way of evaluating the column (col_ind) and the row (row_ptr) vectors for the CRS (Compressed Row Storage) storage format using the Connectivity Array? The Connectivity Array is a ...
62 views

### How to solve for f(A)x=b without GMRES?

How to solve for $f(A)x=b$? For GMRES, an answer is given in this book chapter: http://link.springer.com/chapter/10.1007%2F978-3-642-58333-9_2. Ungated version: https://www.researchgate.net/profile/...
108 views

### GMRES : incomplete Krylov-subspace

At each iteration $i$ of the GMRES method, is calculated a single new orthonormal vector of the existing Krylov subspace. If the norm of that vector is 0 (or close to 0), then the subspace is "...
196 views

### Solve a very large linear system (question about a library linear algebra to do this)

I need to solve a very large linear system (coming from finite element method). I'm currently using the Intel MKL library, but the system has been delayed more than 20 hours. The matrix of the system ...
280 views

Quadrature-free DG method using nodal Lagrangian basis are computationally very efficient. I have seen many papers using this method for linear PDE but almost no literature for non-linear PDE like ...
8k views

### scipy odeint - Excess work done on this call

I'm newbie both in calculus and Python/Scipy so I apologize if this question is too dumb. I'm trying to model flow between two pressure vessels. Let's say we have two points and a link between them ...
43 views

### Global to local transformation matrix in 2D frame structures

In section 3.2 of this paper [1], where 2D planar frame structures are being analyzed, the authors mentioned a transformation matrix to be used in extracting the element displacement vector from the ...
61 views

### Bareiss algorithm vs. LU-decomposition

I at the moment try to fully understand the Bareiss algorithm for calculating determinants. One question that came to my mind is the following: Why is LU-decomposition much more often used than the ...
26 views

### Code for computing the Partial Fréchet Distance [closed]

I am looking for a code (Python, Matlab, R) to compute the partial Frechet distance. That is a similarity measure for curves that takes into account partial matchings. References Buchin, K., Buchin,...
729 views

### How is the divergence and curl approximated in Smoothed Particle Hydrodynamics?

I was reading through Monaghan, SPH, 1992 paper and he states that any quantity $A$ at $r_b$ can be approximated by $A(r) = \sum_b m_b \frac{A_b}{\rho_b}W(r-r_b,h)$ and so the gradient of that ...
110 views

### Mesh with constraints

Is it possible to construct a constrained tetrahedral mesh of a domain using Tetgen or similar software? What I mean by constrained is that there are some nodes or edges that are not free but are ...
158 views

### Is there a simple way to avoid carbuncles for FD WENO methods?

I have implemented finite-difference WENO scheme for Euler equations (with some variants - WENO-JS, WENO-Z, WENO-M, different flux splitting). It works well, but have problem with so-called carbuncles ...
33 views

### Moreau Yosida approximation [closed]

Definition: Let $(X,d$) be a metric space and let $f:X\to\mathbb{R}$ be a bounded function. (that is, there is some $M>0$ such that $|f(x)|\leq M$ for all $x\in X$). Then the lower and upper ...
46 views

### Compute distances from a vector to a matrix of vectors

Let $\vec{a} \in \mathbb{R}^\alpha$, and let $H$ be a rank 3 tensor with dimensions $M_{[i \in \mathbb{N}]} \times N_{[j \in \mathbb{N}]} \times \alpha_{[k \in \mathbb{N}]}$ (where the subscript are ...
31 views

### Evaluating integral $F(r_2) = \frac{1}{r_2^n} \int_0^{r_2} r_1^n f(r_1)\ \mathrm{d}r_1$ without growing instability

I have the following expression to be numerically integrated in a vector-based library (e.g. numpy, MATLAB, etc), $$F(r_2) = \frac{1}{r_2^n} \int_0^{r_2} r_1^n f(r_1)\ \mathrm{d}r_1,$$ where $n$ is ...
4k views

### Algorithm for high quality 1/f noise?

How can I generate arbitrarily high quality $1/f$ noise, for use in a model? My model involves a lot of feedback, over a large number of iterations, with a very high bandwidth, so I'd like the $1/f$ ...
32 views

### Matrix requirements for cusparse*csrgemm2

I would like to perform a matrix multiplication like: $C=A*B*A'$ using cusparse library function cusparseDcsrgemm2. To do this I split it into two matrix-matrix multiplications where all matrices ...
24 views

141 views

### Fast algorithm for computing cofactor matrix

I wonder if there is a fast algorithm, say ($\mathcal O(n^3)$) for computing the cofactor matrix (or conjugate matrix) of an $N\times N$ square matrix. And yes, one could first compute its determinant ...
419 views

### fastest linear system solve for small square matrices (10x10)

I am very interested in optimizing the hell out of linear system solving for small matrices (10x10), sometimes called tiny matrices. Is there a ready solution for this? The matrix can be assumed ...
46 views

### Dealing neighbor list in NVT Monte Carlo (MC) simulation

I'm making a NVT Monte Carlo (MC) simulation code with only short range interaction. I found many MC tutorial codes (usually Lennard-Jones system) in online. However, most of them are doing energy ...
70 views

### Singular vectors of s1 for tiny dense matrices

I have a function whose main bottleneck is finding a(ny) singular vector pair in the space of the largest singular value, along with the singular value itself. This is done a huge number of times. ...
46 views

### Showing N = NP on-line [closed]

I have a theorem that proposes a method to build algorithms. All the algorithms produced by this method are in P ... they never go up to more than $6(n^{12})$ operations. Following that, I have ...
67 views

### Big Theta Complexity of Gaussian Elimination using Complete Pivoting

I already know the Big O for partial pivoting is $O(n^3)$ and remain the same for complete pivoting. I also know the big theta complexity for partial pivoting is $2/3 n^3$ I would like to know the ...
79 views

### Calculate cofactor-matrix efficiently [duplicate]

I've implemented an algorithm that can calculate the cofactor-matrix of a matrix in $\mathcal{O}(n^5)$. The algorithm just step-by-step iterates over the whole matrix ($\mathcal{O}(n^2)$) and for ...
55 views

### Arnoldi Decomposition Algorithm

I try to get into GMRES via Arnoldi-Decomposition. For my understanding, I Implemented the Arnoldi-Decomposition in python. ...
3k views

### Parallel Scientific Computation Software Development Language?

I want to develop a parallel scientific computation software from scratch. I want some thoughts on which language to start. The program involves reading/writing data to txt files and doing heavy ...
612 views