1
vote
0answers
7 views

Correctly orthogonalizing and normalizing eigenvectors of a non-hermitian problem

I have some non-hermitian matrix $A$, that I have the left and right eigenvectors. (Calculated using SLEPc, by finding the eigenvectors of $A$ and $A^H$). I'm not sure how to orthogonalize them ...
2
votes
0answers
27 views

Level 3 BLAS accelerated solver for banded linear systems.

At the moment I consider the following problem. I have a huge dense banded matrix $A$ which I want to factorize and use to solve linear systems $Ax=b$. $b$ has around more than 100 columns. At the ...
3
votes
0answers
40 views

Why is Matlab's SVD faster on think matrices than on wide matrices?

I noticed something odd today. I have a matrix X that is very skinny (20800 x 200), double precision real numbers, not sparse, ...
1
vote
2answers
60 views

Incremental SVD implementation in MATLAB

Is there any library/toolbox which has implementation of incremental SVD in MATLAB. I have implemented this paper, it is fast but does not work well. I tried this but in this also error propagates ...
0
votes
0answers
48 views

Looking for open source numercial solver

I am trying to solve an optimization problem $min f(x)$ subject to $Ax\leq b$ with both $x \in R^{\sim 10000}$ and $b \in R^{\sim 10000}$. $A$ is somewhat sparse (usually less than 5% populated) and ...
0
votes
0answers
37 views

parallel computatioan of a PDE in MATLAB

I want to solve a 1-D PDE $(\partial_{tt} + \alpha\partial_t)u(x,t)=\partial_{xx}u(x,t)-\sin(u(x,t))+f$, using method of lines and for this I defined a spatial grid of about n~1000 points. Since my ...
6
votes
1answer
85 views

How to project a vector into the H(div) space (in the context of finite elements)?

Say I have a simple elliptic PDE: $$ -\nabla\cdot(K\nabla p) = f \;\;\;\text{in}\;\Omega $$ with the appropriate boundary conditions. I solve for $p$ using a FEM (a discontinuous Galerkin method to ...
0
votes
0answers
16 views

wilcoxon signed rank test [on hold]

Is it correct to test a data set of as low as 5 for a wilcoxon signed rank test for a significance value of 7%? Currently I'm using MATLAB for this test and I am getting a p=0.0625. Can I be assure ...
0
votes
0answers
10 views

Fit model to transfer function using different frequency resolutions

I am not certain if I should post this here or maybe on another stackexchange site such as signal processing, however because this is about fitting a model on to a transfer function and not on how to ...
0
votes
0answers
67 views

Penalty Formulation for elliptic PDE [on hold]

Penalty methods are applied to elliptic PDEs with complex/irregular domain. Given a Dirichlet problem of the form: find $u\in{H^1}(\Omega)$ so that $$-\Delta{u}+u=f\;\;\mbox{in}\;\Omega$$ ...
1
vote
1answer
48 views

beta in Nesterov's first method for piece wise linear convex optimization problem

I am trying to implement Nesterov's first method to solve convex piece-wise linear optimization problem, from this website: ...
0
votes
0answers
19 views

Abaqus changing the orientation [closed]

in Abaqus, *ORIENTATION,NAME=RECT,SYSTEM=RECTANGULAR 1.0, 0.0, 0.0, 1.0, 1.0, 0.0,0.0,0.0,0.0 **** i would like to change the orientation of the composite ...
3
votes
2answers
843 views

How can calculations cause an arithmetic overflow even if the final value fits?

I am reading Algorithm Design Manual by Skiena, which says in Chapter 8, Section 8.1.4 when talking about the calculation of binomial coefficients: Intermediate calculations can easily cause ...
6
votes
1answer
92 views

Compute eigenvectors of a matrix with known eigenvalue spectrum

If I have already accurately known the eigenvalue spectrum (i.e. all eigenvalues) of a matrix, is there any efficient numerical algorithm to compute all the eigenvectors corresponding to these ...
0
votes
1answer
66 views

Already exist? parallel computing [closed]

Parallel computing allow us to compute tasks in parallel. And if there was a system like torrent that unlike sharing files, it share computing power? For example I have a gpu and I use only 25% of its ...
0
votes
0answers
30 views

Cross platform GPU computation for real time ray tracing rendering engine! [closed]

As optix - https://developer.nvidia.com/optix is real time ray tracing rendering engine but it only works on CUDA, I want to implement real time ray tracing engine for games like which will work on ...
1
vote
1answer
46 views

Accurate way for computing a ratio coming from Monte Carlo simulation

I am seeking recommendations on how to compute the Binder ratio numerically accurate when doing Monte Carlo simulation on spin models. Binder ratio is defined as: $$ B = \frac{\langle ...
1
vote
2answers
74 views

How to solve ODEs with constraints using BVP4C?

I am using BVP4C to solve a system of ODEs which is as follows. \begin{equation} \left\{ \begin{aligned} \frac{\partial f(x,y)}{\partial x} &- ...
3
votes
1answer
104 views

Software for triangulating a point set (with restrictions)

I want to triangulate a point-set like the one below. I would like the triangulation of the point-set to have the following properties The triangles must have as vertices the black and orange ...
1
vote
0answers
33 views

Determining Youngs Modulus of defined material in FEA (ABAQUS)

I am quite new to FEA but need to determine if I am performing my simulations correctly. I have a cube of material with defined elastic properties (Youngs Modulus and poison ratio). I perform a ...
1
vote
2answers
117 views

Integrating radial Schrodinger equation with Lennard-Jones potential using Runge-Kutta with adaptive step size ends up with a step-size of zero

I'm currently taking a course in computational physics. I'm new to computational physics and programming in general. I'm using numerical recipes to try and integrate the radial Schrodinger equation ...
7
votes
1answer
167 views

Danger of complex arithmetics in scientific computing

The complex inner product $\langle u,v\rangle$ has two different definitions decided by conventions: $\bar{u}^Tv$ or $u^T\bar{v}$. In BLAS, I found the routines cdotu, zdotu, and cdotc, zdotc. The ...
1
vote
1answer
75 views

Can Gauss-Seidel/SOR (preconditioned?) be apllied to all zero diagonal system?

After applying finite difference method to a Laplace/Poisson problem always arises a diagonal dominant system of equations that can be solved with Gauss-Seidel or SOR methods. If the original PDE does ...
2
votes
1answer
63 views

communication penalty when using wide stencils in parallel computations

When reading about discontinuous Galerkin methods one finds the argument that these methods allow higher-order accuracy while maintaining a compact stencil (a cell only communicates with its direct ...
0
votes
0answers
32 views

Parallel black box optimization with NOMAD utilizing n GPU codes [closed]

I am using NOMAD in batch mode on UNIX for black box optimization. I have 4 Tesla GPU cards at my disposal and I want to utilize that capacity by running 4 points in parallel using MPI. The blackbox ...
3
votes
0answers
49 views

Computing accuracy of my finite difference scheme for uniform grid on a non-uniform grid

I have a ADI finite difference scheme for the 2D Navier-Stokes equations that uses a second order accurate (central) approximation for the advective terms. I am ignoring the diffusive terms for now. I ...
0
votes
0answers
25 views

Linearization of a controller: necessary?

let's say I have a generic system with the transfer function $G(s)$. The plant is non linear but time invariant. For the controller I want to implement a controller with the transfer function $N(s)$ ...
0
votes
0answers
47 views

Matlab backslash command slow on diagonal matrix

So I'm solving the system Ax=b for a random 2000x1 b. Using the tic-toc commands I timed how long A\b would take for a random diagonal A.(A=diag(rand(2000,1));) Then I perturbed the 1,2 entry of A ...
0
votes
1answer
56 views

MATLAB: Backslash operator using symbolic variables with an overdetermined system

I have an overdetermined system (too many equations), expressed as Ax=b, in MATLAB. When I try to solve it using A\b, I receive the error: ...
1
vote
0answers
27 views

CFD: Doubt with time convergence in advection fully implicit upwind scheme

I'm trying to solve an advection - convection problem using an implicit upwind scheme - you can see here the finite difference discretization used. I start the model (built from scratch on Scilab) ...
1
vote
3answers
201 views

2D Stokes equation Code

Does anyone know where could I find a code (in Matlab or Mathematica, for example) for he Stokes equation in 2D? It has been solved numerically by so many people and referenced in so many paper that I ...
4
votes
3answers
224 views

Propagating Schrodinger equation

My task is to simulate quantum evolution. To do that I need to perform this operation $$w = e^{-itH}v$$ where $H$ is a sparse matrix and $v$ is the initial column vector. I am wondering if there is ...
3
votes
0answers
51 views

Is there any numerical application whose performance heavily depends on the division operation?

I am an undergraduate student majoring in computer science. Recently, I am interested in the division operation, which is not directly supported by some architectures. While some architectures ...
4
votes
1answer
83 views

How to avoid negative values of numerical solution of transport equation using FEM scheme?

The transport equation is actually an advection-diffussion-reaction equation, which has the form as $$\frac{\partial C}{\partial t} + v_1 \frac{\partial C}{\partial x} + v_2 \frac{\partial ...
0
votes
0answers
22 views

Solving the Wilberforce pendulum using Runge-Kutta method [duplicate]

I'm writing a program in C++ (almost from scratch) for solving the coupled equations that rise from the Wilberforce pendulum: $m\ddot{z}+kz+\frac{1}{2}\epsilon \theta = 0$ $I\ddot{\theta}+\delta ...
1
vote
0answers
29 views

Iteration methods for solving rectangular or singular linear system of equations

I want to solve consistent system of linear equations $Ax = b$, where matrix $A$ is rectangular or singular square matrix. I am interested to know what are the available iteration methods to solve ...
0
votes
0answers
29 views

state of art non smooth convex optimization [duplicate]

Basically, I am trying to implement non-smooth convex optimization in c++. I am wondering what is the state of art condition of non-smooth convex optimization. For example, what's the best method ...
0
votes
1answer
42 views

fast gradient method for convex piecewise linear function

What is the state of art gradient based algorithms in convex optimization solving non-smooth piece-wise linear functions? Thank you. EDIT: It is different from one of my previous post in the sense ...
0
votes
0answers
38 views

FFT parallel processing in MPI

I am working now in Beowulf Cluster and parallel processing, I want code for Fast Fourier transfer functions written in any language, e.g., C/C++. Without using FFTW library based on message passing ...
0
votes
0answers
25 views

Book recommendation on simulation of linear and nonlinear electronic circuits

I am looking for a book on electronic circuit simulation explaining the numerical modeling using transient and frequency based methods from a computational point of view. It should also have an ...
8
votes
1answer
117 views

Can the method of lines be used to discretize all PDEs?

I have found that the method of lines is a very natural way to think about the discretization of PDE's. Therefore I always default to that mindset when presented with a new set of equations. I have ...
3
votes
0answers
81 views

Rounding errors in images of Julia sets

One typically computes Julia sets by iterating a complex function, such as a polynomial or rational function. How do rounding errors affect the results? I'm looking for references on this issue, ...
0
votes
1answer
41 views

What are some tips on developing a problem-specific ODE solver?

I have a small system of stiff ODEs describing a chemical reaction. The right-hand side is quite complicated, as well as the Jacobian. This equation will be solved many times with different initial ...
2
votes
0answers
59 views

1 D Diffusion equation FDM with different layers

I'm trying to solve this particular equation $\frac{\partial u}{\partial t} = \frac{\partial}{\partial x} \big[D_{i}(x)\frac{\partial u}{\partial x} \big] + S(x,t)$ where the $i$ index denotes ...
1
vote
1answer
46 views

Reaction-Diffusion problem A->B, solving for B

I need to solve a Reaction-Diffusion using Finite Elements, piecewise linear elements. In this problem, a reaction $A \rightarrow B$, with rate law $ r_A = - k_A \cdot u_A $, takes part, where $u_i$ ...
0
votes
0answers
15 views

Measure Performance of Distributed computing system

Assume you have a distributed computing network of 3 PCs with GFLOPS of 30, 20 and 10. How would you measure the performance of the distributed network as a whole? assuming you know the flops of ...
2
votes
0answers
26 views

Iteratively finding both left and right eigenvectors for non-symmetric complex matrix

I have a complex, non-Hermitian matrix $\mathbf{A}$, for which I need to find a few eigenvalues and eigenvectors in the generalised eigenvalue problem: $$\mathbf{A}\cdot \mathbf{x} = \lambda ...
1
vote
1answer
60 views

eigenvalues of a general complex matrix in C++

Is there a free C or C++ library including a routine for the eigenvalues of a general complex matrix? I checked a number of linear algebra packages like Eigen, but there does not seem to be support ...
0
votes
0answers
25 views

Find out the expression for angular speed in terms of time

The orbit of a small mass orbiting to a much larger mass (e.g. a small planet relative to a fixed star) is described by $$ u=\dfrac{1+e\cos{\theta}}{l} $$ where $u = 1/r$, $r$ and $\theta$ are the ...
2
votes
1answer
73 views

L2-Projection using quadratic basis functions

I am trying to understand 1D $L^2$-projections using quadratic basis functions. Using 3 data points, and the Lagrange polynomial it is easy enough to see how to write out 3 basis functions. With the ...

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