0
votes
0answers
42 views

Open Source Linear Algebra Library

I am making a code in C that requires the equivalent of Matlab's '\' command for a linear system of the form AX=B where A is an NxN matrix and X, B are Nx1 vectors- i.e a code that performs X=A\B that ...
3
votes
0answers
25 views

Stability analysis for a hyperbolic PDE on staggered grid

I am trying to understand the stability of a finite difference equation on the staggered grid. I could understand the Von Neumann stability analysis for the collocated grid for a simple acoustic ...
1
vote
0answers
41 views

Python environments for AMG and Gauss Seidel as solvers instead of preconditioners

I am working on block preconditioning and seemingly it is common to write customised Krylov solvers for them. Within each solver, the individual block linear system with preconditioners are ...
0
votes
1answer
47 views

Exact distribution of random walk after 10 or 100 steps

(Variant of Stats Exercise to Protect the Innocent). Starting for $x = 0$ I can do one of two operations $\pm 1$ or $\pm 4$. Let $T$ be one iteration of this step. What is the mean and standard ...
5
votes
1answer
74 views

What is the difference between Computational Science and Data Science?

Background: My PhD was in 'Computational Science'. My dissertation was on the analysis of X-Ray Diffraction Data and analysis of thermally perturbed nuclei in the overall dynamic analysis of the ...
0
votes
0answers
22 views

CVX problem formulation

Hello, I have a trouble formulating the statement for cvx Matlab package. Here x is a state variable, alpha, c1,c2 - contstants. Ai, Bi, di are matrices depending on Ai-1, Bi-1, di-1. One of the ...
6
votes
3answers
56 views

Approximating rotation matrix of arbitrary objective function

I want to approximate the rotation in SO(3) (ie. 3D rotation) that minimizes some objective function. I'm looking for a SO(3) rotation representation that lends itself to energy minimization. I'm ...
0
votes
0answers
20 views

How to flash AMD BIOS chip on automated catheter production machine in factory? [on hold]

this is my first question I hope I make it clear enough and posted in the right section. The automated catheter production machine at the factory I'm doing my internship is down. When turned on there ...
1
vote
0answers
15 views

Gauss Seidel moving mesh AMR hamilton Jacobi

I was trying to implement a moving mesh algorithm using Gauss Seidel, so: I have a pde like this (Hamilton - Jacobi eq) $\begin{cases}\phi_t+H(\phi_x)=0 & [-1,1]\times [0,T]\\\phi(x,0)=\phi_0 &...
1
vote
1answer
29 views

Produce large displacement under small displacement approximation?

I have managed to make my model converge fairly well and achieve large displacements and deformations. It exhibits stress and strain good continuity by solving it under small displacement and ...
0
votes
1answer
60 views

Open source FEM implementation for Windows

I am wondering is there any robust, well-tested, accurate open source FEM solver package for Windows? I would like to use to power the engine of my structural engineering application. The FEM package ...
0
votes
0answers
17 views

Square error estimate for adaptive mesh refinement

In a particular implementation(Finite volume advection using upwind) of adaptive mesh refinement the error square estimate for a cell C is given as $$ \sum_{i = x,y,z} vol * \frac{1}{12} * h^{2} * (\...
1
vote
0answers
28 views

Time integration for elastodynamics

I'd like to solve the elastodynamics equation for a problem with fast scales from an impact (although no shocks). $\rho\ddot{\mathbf{u}} - \nabla \cdot \sigma(\mathbf{u}) = \mathbf{f}$ In structural ...
1
vote
0answers
22 views

Relaxation Parameters for Steady Navier-Stokes

I am working on a project involving steady solutions for the Navier-Stokes Equations. In the past I've only worked with the unsteady Navier-Stokes, so some of this is new to me. In particular, at ...
-4
votes
0answers
22 views

matlab code for solving 2d unsteady heat conduction and advection

help me solve this problem please. i have been trying since long but didn't get any hint to even start.if any one can please provide me mat lab code for it? City University School of Engineering and ...
3
votes
0answers
61 views

Eigenvalue decomposition of the sum: $AA^T$ + diag($u$)

Suppose $A\in\mathbb{R}^{n\times c}$,$u\in\mathbb{R}^n$,$n\gg c$. The time complexity of eigenvalue decomposing directly for matrix $AA^T+\text{diag}(u)$ is $O(n^3)$. And it is easy to avoid $O(n^3)$ ...
6
votes
1answer
65 views

Best practice for dealing with Dirichlet boundary conditions in finite-difference schemes: add artificial unknowns?

I know of at least two ways of dealing with Dirichlet boundary conditions in finite-difference schemes (and, to a lesser extent, finite-element schemes). Here I'm thinking of solving Poisson's ...
1
vote
1answer
20 views

Finding common roots of two multivariate equations

I am trying to find points of a surface whose normal is parallel with the 3 dimensional axes (i.e. local maxima, minima and saddle points in x, y and z dimensions). The function of the surface is ...
1
vote
0answers
41 views

Basis over edges of a mesh

In 2D, the hat functions are the usual function basis for the finite dimentional space $\{v\in \mathcal{C}:v|_T\in P_1(T)\,\forall T\}$: set of continuously functions that are polynomials less than or ...
1
vote
0answers
83 views

4th Order Runge Kutta: Integration of Differential Equations for Planetary Orbit

I'm supposed to integrate differential equations for $r$ and $\theta$ in order to simulate orbital motion. The differential equation I used for $r$ is second order and $\theta$ is first order. The end ...
9
votes
3answers
284 views

Is providing approximate gradients to a gradient based optimizer useless?

Is it pointless to use gradient based optimization algorithms if you can only provide a numerical gradient? If not, why provide a numerical gradient in the first place if it is trivial to perform ...
0
votes
0answers
21 views

One domain subdivided in many subdomains to be refined independently

I have a domain divided in several subdomains (for example: 10000 subdomains), and solve an independent problem on each subdomain through some finite element method (then I assemble each solution on a ...
6
votes
0answers
55 views

Methods to Estimate Optimal Distance Measure for Multidimensional Data Set

My problem at hand pertains to choosing a distance measure for use in locally weighted regression. In my particular problem, I have a data set that is upwards of 10 dimensions, where the variables ...
4
votes
1answer
44 views

Vectorize a part of a huge matrix in C++

I have a large matrix, side-length is about $n\geq 1000$. I need to do element-wise multiplication of this matrix with another matrix many, many times. I make this process by: Vectorizing (through ...
-6
votes
0answers
29 views

CHOOSE BEST SOFTWARE [closed]

I want to simulate combustion, flow over body (not complex shapes) and another general work.I don't want to use open source.I think commercial softwares are stronger. Please help me to choose best ...
3
votes
1answer
50 views

How do I form the Chebyshev differentiation matrix in MATLAB?

I have some code that does exactly this, but I do not like to use things I do not understand. Here is the code ...
1
vote
0answers
7 views

RCWA for Non-Periodic Structure?

I have a quick question regarding Rigorous Coupled Wave Analysis (RCWA) for numerically solving problems (in optics). I am trying to simulate a device which is non-periodic in x, y directions (but is ...
-4
votes
0answers
70 views

Start CFD software [closed]

I want to start computational fluid dynamics (CFD) but I don't know which software is the best for it.For example : ansys (fluent) , autodesk (cfd) , Fluent 6.3 & etc. I want to simulate ...
1
vote
0answers
49 views

linearly interpolate and determine gradients for data on non-uniform grid

I have measurements of a quantity on a 3d grid. My measurements are distributed on four x-y planes similar to what is shown in the image below. The measurements roughly follow a Cartesian grid but ...
1
vote
0answers
45 views

Can I model laminar incompressible fluid flow and heat transfer in MATLAB's PDE toolbox?

I have a system of PDEs in cylindrical coordinates that needs to be solved: 1. Continuity equation 2. Incompressible Navier stokes ( in r & z coordinates) 3. Heat transfer equation with both ...
1
vote
1answer
73 views

Vectorizing list of different functions for Gradient Descent

I am new to machine learning and statistical analysis and am having trouble figuring how I should go about a problem I have. I believe that I understand the gradient descent algorithm and how it ...
9
votes
1answer
124 views

Adaptive gradient descent step size when you can't do a line search

I have an objective function $E$ dependent on a value $\phi(x, t = 1.0)$, where $\phi(x, t)$ is the solution to a PDE. I am optimizing $E$ by gradient descent on the initial condition of the PDE: $\...
1
vote
0answers
23 views

Difference between Chebyshev first and second degree iterative methods

Consider linear equation $Au = f$. We want to solve it with iterative method (assuming $A$ is good). First order iterative method is: $$ u^{k+1} = u^k - \alpha_{k+1}(Au^k - f), $$ The second degree ...
1
vote
0answers
17 views

List of Tersoff potentials?

I would like to know some GNU libraries or lists of downloadable Tersoff potentials. I couldn't find that many of them, and I also would like to know if there is a reason as to why this is the case.
1
vote
0answers
18 views

Computing 3-term Connection Coefficients for Wavelets

I am trying to calculate the three-term connection coefficients $$ Λ_{l,m}^{d_1,d_2,d_3} = ∫_{-∞}^∞ φ^{(d_1)}(x) φ^{(d_2)}_l(x) φ^{(d_3)}_m(x) dx $$ for Daubechies wavelets numerically using Python. ...
0
votes
0answers
36 views

Mesh partitioner with user-defined overlap

I am looking for a mesh partitioner, where I can specify overlap, for example h = 3. I have looked into metis, but I wasn't able to find such a functionality. Is there any other package which ...
0
votes
2answers
78 views

How does rigid body rotation affect resuts in a simulation?

I have been running a finite-element simulation where, for the sake of convergence, I chose to stay in small deformation hypothesis (in comsol, include non-linear geometry box not checked for who that ...
6
votes
0answers
96 views

What is some of the best software design you've seen in a numerical code? [closed]

I don't think I've ever seen any scientific computational software that I would consider "good" in terms of software design. I don't mean in terms of functionality, but in terms of good high-level ...
-1
votes
0answers
23 views

nonlinear coupled pde by finite difference

I want to solve nonlinear coupled PDE by finite difference method. I have done the discretization. the number of variables and number of equations are not same. How to deal with this situation?
0
votes
0answers
45 views

Numerical improper triple integration [duplicate]

I would like to calculate a triple integral with infinite limits: $$f(x,y,z) = \frac{e^{x^2 + y^2 + z^2}}{(1 + e^{x^2 + y^2 + z^2})^2}$$ with limits: $x: (0,\infty), y: (-\infty,\infty), z: (-\infty,...
1
vote
2answers
70 views

Finding an enclosing parabola for a set of points

I am looking for an algorithm that fits a parabola to a set of data points. However, no data point may be below the parabola. All points must be above the parabola. Is there an standard algorithm for ...
-2
votes
2answers
98 views

Array initialization in C

In this bit of code, the X and Y arrays should be identical but for some reason, that I CANNOT figure out for the life of me, X[0] is always 1 rather than 0. I have tried initializing the whole array ...
1
vote
0answers
42 views

Oscillations in Chorin's method due to the BC

I am pretty new to the CFD and I wanted to start with Chorin's projection. The starting problem is just a free jet flowing in the investigated area. I got terrible oscillations almost immediately and ...
1
vote
1answer
82 views

Fastest method forfinding a solution to x*log(x)

more specifically, $C x \log_2(x)- K = 0$, where $C$ and $K$ are constants ($\log_2$ means log base 2). I was solving a topcoder problem, SortEstimate, which requires us to solve the aforementioned ...
3
votes
1answer
35 views

Lanczos algorithms for Hermitian system with toeplitz kernel

Basically I am trying to compute the SVD of a large hermian matrix H using Lanczos iteration, while H consists if a toeplitz kernel K, which should be able to help speed up the matrix-vector ...
2
votes
1answer
49 views

Interpreting convergence study results, fixed CFL

I am trying to determine the order of my numerical method for resolving a fluid-structure interaction problem using the immersed boundary method. I am using Crank-Nicolson to resolve the fluid ...
10
votes
3answers
167 views

Small, unpredictable results in runs of a deterministic model

I have a sizable model (~5000 lines) written in C. It is a serial program, with no random number generation anywhere. It makes use of the FFTW library for functions using FFT - I do not know the ...
2
votes
1answer
73 views

Coupling Boundary Condition of one PDE with source term of another PDE

We have a system of equations, wherein the BC of one PDE is coupled with the source term of another PDE. We have a regular 2D unit grid in x and y. There are two PDEs to be solved The first PDE (...
0
votes
0answers
27 views

Parallel SVD via one side Jacobi for distributed memory

I want to build a code executing a parallel SVD via the one sided Jacobi method within a distributed memory approach (MPI). The only possibility therefore seems to be a block method. Sofar it looks ...
2
votes
1answer
62 views

Library for polygon processing in 3D

I need to process some polygons in 3D. They are typically loaded from an OFF or STL file. Then I need to do some transformations (rotation, move, resize), I'd like to check whether points are inside ...

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