0
votes
2answers
43 views

Are there any possible applications of real-time Finite Element Analysis?

FEA when applied to solid mechanics / structural engineering result in the solution to the equation $$ F = K\cdot x $$ $F$ being the forces, $K$ the stiffness of the system and $x$ represents the ...
2
votes
0answers
15 views

Numerically solving a system of partial integro-differential equations in Matlab

Given the following system of partial integro-differential equations $$ \frac{dX(t)}{dt}=\Lambda-\mu X(t)-\beta X(t)Z(t),\\ \frac{\partial Y(t,\omega)}{\partial t}+\frac{\partial Y(t,\omega)}{\partial ...
2
votes
2answers
52 views

9-point stencil finite difference Laplacian with variable diffusion coefficients

So I'm trying to implement a 9-point stencil discretization to the 2D difussion equation. The stencil is here. However, most of the literature deals with a Laplacian that has a constant diffusion ...
5
votes
1answer
36 views

Classification of observations depending on its trajectory

I'm afraid the title is terrible, but I don't know how to summarize this problem in a few words. Using an instrument, we are monitoring the trajectory of several objects during a period of time. We ...
0
votes
0answers
20 views

Injection Vs Full Restriction in Dirichlet-Neumann 3-D Multigrid

I have implemented the Multigrid method for a Mixed Dirichlet-Neumann boundary value problem where $\nabla^{2}{u}=0$, $u = 1+x+y+z$ for Dirichlet and $\frac{\partial e}{\partial n} = 1$ for Neumann ...
0
votes
0answers
28 views

How to convert MPIAIJ to SEQAIJ matrix in petsc/petsc4py?

I am curious, if there is a function to convert MPIAIJ (distributed matrices in AIJ format) to a SEQAIJ matrix that lie on a single processor. It is possible to do such an operation for PETSc vectors ...
-2
votes
0answers
30 views

Best software for simulating fluid waves [on hold]

Hi I'm going to simulate the waves which caused by thermal fluctuation and I don't know what kind of software do I need!do you have any suggestions?I've tried COMSOL a little bit but I couldn't find ...
4
votes
2answers
251 views

What is the purpose of the test function in Finite Element Analysis?

In the wave equation: $$c^2 \nabla \cdot \nabla u(x,t) - \frac{\partial^2 u(x,t)}{\partial t^2} = f(x,t)$$ Why do we first multiply by a test function $v(x,t)$ before integrating?
3
votes
0answers
71 views

Finite Difference Beam Propagation Method problem

I am trying to implement the finite difference beam propagation method to study the propagation of a TE light signal through a waveguide. However, my solutions are exponentially growing, and display ...
1
vote
1answer
32 views

Convex Optimization problem with sum of absolute value constraints

How to solve the optimization problem written below? $$\begin{align} &\operatorname{argmax}\limits_{a}\; a^T b - \frac{1}{2} a^T X a\\ &\text{subject to } \sum_i |a_i|=4,\; \sum_i a_i = 0 ...
-7
votes
0answers
27 views

Anyone need expert help/consulting with advanced programming languages? [on hold]

Code Genius was started at MIT to connect programmers in the scientific community to experts of advanced languages for efficient and cost effective support. Our platform helps programmers find the ...
0
votes
0answers
23 views

Min/Max Depth of a binary tree [on hold]

Is the Min Depth of this tree 2, because of the distance of leaf node "9"? Is the Max Depth if this tree 4, because of the distance of leaf node "2"?
4
votes
2answers
63 views

Dissipative time-stepping scheme for first order in time system

When solving semi-discrete equations (originating from finite element models, for example), which are second-order in time of the form \begin{equation} M\ddot d + C\dot d + Kd = F, \end{equation} ...
6
votes
1answer
67 views

Generating random numbers for long molecular dynamics simulations

I've written a basic 2D Langevin dynamics simulator in C++, for a particle in a potential, solving the equation: $$M\ddot{X} = - \nabla U(X) - \gamma M \dot{X} + \sqrt{2 \gamma k_B T M} R(t)$$ This ...
0
votes
2answers
80 views

Relation between Time dependent problem and advection diffusion

Is there a relation between say the heat equation $u_t -\Delta u = f.$ and advection-diffusion equation $-\Delta u + c \cdot \nabla u = f$? I have heard several people use this argument in many talks ...
2
votes
0answers
36 views

Calculating theoretical order of accuracy of least squares fit advection scheme

I'm familiar with finding the order of accuracy using von Neumann analysis for finite difference schemes formulated using Taylor series expansions. But is there a similar technique for finding the ...
6
votes
0answers
59 views

Are there any standardized file formats for point group character tables?

Character tables are an important tool for symmetry analysis in many computational chemistry software packages. Are there any standardized file formats for point group character tables? This may seem ...
4
votes
1answer
51 views

transverse component for multidimensional advection in method of lines

So I inherited from some people a code that solves the advection-diffusion-reaction equation for a particular system. The original code was first implemented in 1D which worked fine in cartesian ...
1
vote
0answers
27 views

fixed point iteration to find out second order non-linear diff equations

I am working on some model analysis, getting two diff equations and after I convert them into matrix form, I have equations looks like $$ [A][X]=C\times\big(\exp([B][X])-1\big), $$ where $C$ is a ...
0
votes
1answer
54 views

Efficient method to multiply floating point matrix with binary matrix and get double precision results

I have a matrix A which is of size (n2, n1) and I am multiplying it by a matrix, B, of size ...
0
votes
0answers
17 views

Loading files into Magma? [on hold]

(First off, a disclaimer: I'm new to the site, and not quite sure this is the proper forum for this question. My apologies if it's out of place). I'm working on a computational algebra project and ...
0
votes
0answers
13 views

GAMS AND C++ CONNECTION [on hold]

I wrote a optimization model in GAMS and I want to solve the same model with about 100 different data. Instead of inputting the data one by one by hand, I need to do it with a for loop on C++. Is it ...
2
votes
1answer
55 views

minimization of normalized constrained quadratic function

I'm a computer science student. Please I need a help in solving a constrained normalized quadratic function. I'm familiar with solving quadratic constrained optimization function with matlab by ...
1
vote
1answer
46 views

Creating a 3D spatial density map from simulation results

I want so visualize the spatial density for my simulation. The result of my simulation is a (time-dependent) system of large number (~100k) of moving particles in a confined space. Each particle has ...
3
votes
1answer
89 views

How to calculate $det(X^TX)$ efficiently, update one column of X each time

$X_{1} = (A, b)$, where $X_{1}$ is a $n\times p$ matrix, $A$ is a $n\times (p-1)$ and $b$ is $n\times1$. First calculate $\det(X_{1}^T X_{1})$, then update $b$ with $c$, st. $X_{2} = (A, c)$ and ...
1
vote
0answers
51 views

Numerical Solution of the Advection Dispersion equation

I am facing a simple (at first glance) problem. I need to implement a numerical scheme for the solution of the first order wave propagation equation with chromatic dispersion included. My original ...
2
votes
0answers
166 views

Finite difference scheme for solving nonlinear least-squares problem

I am dealing with following problem: $$ \min_{u,\gamma}\Bigg\{ \frac{1}{1000} \iint_{S_2} {\gamma (x,y)^2 dxdy} + \iint_{S_2} {[u(x,y) - u_0 (x,y)]^2 dxdy} + \iint_{S_2} {[\Delta u(x,y) - \gamma ...
2
votes
1answer
98 views

How can I solve wave equation for circular membrabe in polar coordinates?

The original equation is $$\frac{1}{c^2} \frac{\partial^2 u}{\partial t^2} = \frac{\partial^2 u}{\partial r^2} + \frac{1}{r}\frac{\partial u}{\partial r} + \frac{1}{r^2}\frac{\partial^2 u}{\partial ...
9
votes
4answers
461 views

Modern C++ in scientific computing?

I am looking for books or articles, or blog-posts, or any published material in general, that address specifically the uses of C++ modern features (move semantics, the STL, iterators, lazy evaluation, ...
0
votes
0answers
56 views

Solving quasilinear/nonlinear equations obtained from the discretization of partial differential equations

When you solve numerically a (system of) linear partial differential equation (PDE) as for example Lapace's equation $\nabla^2\varphi = 0$ or Poisson's equation $\nabla^2\varphi = f$ you obtain a ...
2
votes
0answers
27 views

Fortran solver for the Sparse LSE problem

I was wondering if there is a Fortran library that contains a solver for the Sparse LSE(linear equality-constrained least squares) problem $$ min_{x}\|Cx-d\|^2 \text{ subject to } Ax=b $$ where $A$ ...
0
votes
1answer
28 views

How to represent a binary number in a matrix in Matlab?

This is a fairly simple question but my Matlab knowledge is still very limited. I want to take a given binary number (or rather, a bistring) of length $mn$ and generate an $m \times n$ matrix whose ...
4
votes
1answer
44 views

Is there an efficient $O(n^2)$ way to get the eigen decomposition given a LDL factorization?

Let's say I have a LDL factorization of a matrix A. Is there an efficient $O(n^2)$ way to get the eigen decomposition of A given it's LDL factorization? Is there a more efficient way, in case L and ...
1
vote
0answers
103 views

Differences in answers between Python and Fortran

I am translating a piece of Fortran code into Python and am testing my code with a certain test case. All the results differ with 0.04% compared to the Fortran results. This is a very small ...
4
votes
2answers
104 views

Absorbing boundary conditions for acoustics in Discontinuous Galerkin

Note: I'm trying to implement a Discontinuous Galerkin method, as kind of a way to learn about these things. As of now, I've taken the acoustic wave equation $c^2 \nabla \cdot \nabla u(x,t) - ...
2
votes
2answers
49 views

Scipy OdeInt solver with Neumann boundary conditions

I'm using scipy.odeint to solve Fisher-Kolmogorov equation: \begin{equation} u_t = u_{xx}+u(1-u) \end{equation} The code can be found here. From Ablowitz and ...
5
votes
1answer
28 views

Is there a way to ensure that PBS array jobs will be run in order?

I run many PBS scripts that take advantage of the job array structure for similar jobs (e.g. 12345[0] through 12345[9]). With the way that the code is written, job [0] needs to run first, and then any ...
1
vote
1answer
34 views

Raviart-Thomas elements global definition and compact support

As per the suggestion by Christian in the comments here, as part of my continuing quest to understand the Raviart-Thomas (RT) elements I'd like to know how exactly the RT elements are defined ...
2
votes
1answer
81 views

Finite difference for nonlinear system of equation

\begin{equation} \frac{\partial C_i}{\partial t} = D_i \nabla^2 C_i - \frac{I \cdot \nabla t_i}{z_i F} - \sum_{i'} \frac{z_{i'}}{z_i} D_{i'}\nabla \cdot (t_i\nabla C_{i'}) \end{equation} ...
6
votes
0answers
59 views

energy drift in molecular dynamics

I hope the following question will not be perceived as to vague. I am trying to ask the question directly, without going into too much information regarding my code. I am currently developing a ...
3
votes
2answers
57 views

Looking for reference on Streamline Upwind Petrov Galerkin finite elements for incompressible unsteady Navier-Stokes

I am looking for a relatively simple book/paper that explains the basic Streamline Upwind Petrov Galerkin (SUPG) method for solving the incompressible unsteady Navier-Stokes equations. Most of the ...
3
votes
1answer
45 views

Solve implicit ODE numerically in orbit simulation

I'm trying to plot the orbit of a compact binary star system where general relativistic effects become important. I'm using post-Newtonian approximation and I want to solve the orbit numerically based ...
5
votes
1answer
94 views

Raviart-Thomas elements on reference square

I'd like to learn how the Raviart-Thomas (RT) element works. To that end I'd like to analytically describe how the basis functions look on the reference square. The goal here is not to implement it ...
1
vote
1answer
45 views

Sparse generalized eigensolver using OpenCL

I would like to solve a generalized eigenproblem of real sparse symmetric matrices. Is there an efficient library which utilizes OpenCL in order to find a limited amount of the smallest eigenvalues in ...
0
votes
0answers
34 views

Debugging an implemented numerical method: which term gives the drop in accuracy?

I have a numerical scheme to solve an hyperbolic system of equations of this type (this a more simple version just for clarity): $$\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial ...
4
votes
1answer
100 views

H(curl) conforming Nédélec-Elements to satisfy div(B)=0

Most authors are very clear that it's very dangerous to just use $\mathrm{H}(curl)$ conforming edge elements, which are divergence free, to satisfy $\mathrm{div}(\mathbf{B})=0$ and implement this ...
0
votes
1answer
25 views

CPLEX in MATLAB - Asking for Help

I am using CPLEX in MATLAB. I want to optimize the following function $$\begin{align} &\min \Vert y\Vert\\ &\Vert y\Vert = \sum |y|\\ &\text{subject to } A y = 2B - A\, 13n \end{align}$$ ...
1
vote
3answers
95 views

Point inside curved finite element

I like to create interpolation functions for second order finite element meshes. For elements with straight edges all is good, but some of my elements may be curved edges as shown in the figure: I ...
0
votes
1answer
29 views

Interpolation of Data Value using Optimized Weighting of Its Features

Assume I have a data set $ { \left\{ {x}_{i} \right\} }_{i = 1}^{N} $ which represents the value of each data point. For each data we have its features $ {f}_{i} \in {\mathbb{R}}^{d} $. The model I ...
1
vote
0answers
41 views

solve linear system of equation of a large sparse symetric positive definite matrix

I want to invert large matrices ($10^4x10^4$ to $10^6x10^6$) but sparce (less than 100 non-zero entries per line) on clusters with 16 to 48 processors per node. I'm looking for an efficient method to ...

15 30 50 per page