6
votes
1answer
24 views

Method to quantify geometric difference of two dissimilar meshes

I am looking for a method or algorithm to produce a value that describes how different two meshes are geometrically but that have different topologies. An example would be some CAD data that has had ...
0
votes
0answers
23 views

coriolis force in atmospheric modeling [migrated]

The coriolis force is not a real force, but depending on the reference system and how it does refer to an inertial system. Could this coriolis force as widely used in atmospheric/climate modeling be ...
3
votes
1answer
174 views

What are the differences between CFD simulations and realistic ocean/atmosphere model simulations?

The field of computational fluid dynamics (CFD) is dedicated to solving the Navier-Stokes equations (or some simplification of them). A subset of CFD, ocean and atmospheric models numerically solve ...
0
votes
0answers
18 views

Estimating mutual information of sine time series using 2D kernel density estimators

This is an attempt to reproduce Moon et al. 1995, and the author's copy can be obtained through here. As a benchmark, we estimate the time-lagged mutual information of a simple sine signal ...
1
vote
2answers
17 views

How best to use scipy.integrate's ODE solvers when state is not naturally stored as a vector?

I have a large system of ODEs. For various reasons, it is natural to store the values of the dependent variables in a multidimensional array. For example, these values might represent the solution ...
0
votes
2answers
60 views

Parallel solver for sparse matrices on unstructured grids

I am trying to solve Euler equations on unstructured grids. Consequently, the problem reduces to solving Ax=b where A is a ...
3
votes
1answer
45 views

Get symmetric Finite Difference matrix in non Laplacian settings

I would like to solve a system of differential equations $u+\nabla(\nabla\cdot u)=f$ or in more detail $a+\partial_t^2a+\partial_t\partial_xb+\partial_t\partial_yc=f$ ...
3
votes
0answers
42 views

Method with low memory requirement for large-scale eigenvalue problem

I am working on the flow stability problem. In this work the main complication is solving generalized eigenvalue problem for a large scale Non-Hermitian matrix. I need only one eigenvalue (most left ...
1
vote
0answers
30 views

2D Neumann Conditions on Irregular Domain

I would like to model the 2D diffusion equation with Neumann BC's inside the following egg-shaped domain: I would like to use the finite difference method with the discretization implied by the ...
0
votes
0answers
22 views

How do you decide on process order in a numerical model? [on hold]

Is there any generally applicable advice that can inform which processes are computed first in a numerical model? For example, if you're modelling the surface temperature of the earth, lots of ...
0
votes
1answer
26 views

Buckling reference using the FEM

I want to analyze buckling in a composite using the FEM. So far I have studied this references Zdenek P Bazant, Luigi Cedolin. Stability of Structures: Elastic, Inelastic, Fracture and Damage ...
0
votes
0answers
30 views

suggestion needed for solution algorithim non-linear differntial algebraic system

I have a nonlinear differential algebraic system in time arising from the weak formulation of coupled transient non-linear 1D problem. The system roughly looks like. ...
2
votes
2answers
67 views

Why does scipy's odeint function give a non-monotonic solution for a problem whose solution should be monotone?

The solution to the ode below looks like it is monotonically increasing: However on closer inspection we see that it is not: How can I ensure that the numerical solution is monotonically ...
-3
votes
0answers
43 views

ice (sleet, glaze ice) [on hold]

I must to forecast an ice (sleet, glaze ice). I have base of data with parameters to predict, but this data base have not some parametres. In one day I have three parametres in other day I have four ...
1
vote
1answer
59 views

How to deal with indeterminate function limit?

How do I ensure that my function below is well conditioned as $s$ approaches $\infty$? The problem I get is that for large $s$ the function returns an indeterminate form $\frac{0}{0}$. I would ...
2
votes
1answer
57 views

fastest and most efficent way to count all combinations in many sets and sum them together

I am a Java programmer who has reached the limits of brute computer power. My relational database (and non relational databases) is not producing results quick enough and I have hit a bottleneck in ...
5
votes
1answer
66 views

Numerical methods for boundary-value ODEs with a jump condition

I want to solve a non linear system of equations of a particular kind. I find it hard to formulate clearly so I directly give a simple example. $ f''=A(f,g)\\ g''=B(f,g) $ with the boundary ...
4
votes
0answers
90 views

Least-squares for a diagonal matrix

This is a follow-up to a different question I asked with more detail. For $v\in\mathbb{R}^n$, denote $D_v\in\mathbb{R}^n$ as the diagonal matrix with elements in $v$. Given a "tall" matrix ...
0
votes
0answers
16 views

Laplacian of Gaussian (LOG) for Edge Detection

The LOG is determined by the following function as given in this http://homepages.inf.ed.ac.uk/rbf/HIPR2/log.htm. I used Excel and also python to get the LOG kernel. But surprisingly my kernel values ...
3
votes
1answer
71 views

How to solve this optimization problem with abs object function?

Helo, every one. May I ask for help about how to solve this problem. $\begin{align} & \text{max}_{x_i} \quad |\sum_{i=1}^{4} a_i x_i | \\ & s.t. \quad \sum_{i=1}^4 x_i^2=1 \end{align} $ ...
0
votes
0answers
8 views

Wave Equation with Constant Boundary Conditions [migrated]

I need to find a formal solution to \begin{eqnarray} &u_{tt} &= c^2 u+{xx}, \;\;\;0<x<1, \mathrm{and \;}t>0\\ &u(x,0)&=x+1,\\ &u_t(x,0)&=x(1-x), \;\;\;\;0 \leq x \leq ...
2
votes
0answers
33 views

Deriving entropy function and entropy flux for a system of equations

I've been reading up on the concept of entropy as a useful way of developing a natural residual for a system of equations. For example, the entropy function for compressible Navier-Stokes is ...
2
votes
3answers
106 views

Large overdetermined system of linear equations

I'm looking for a method to solve a large overdetermined system of linear equations in a least squares sense. The matrix is dense. I'd like to use a method that works even with limited memory (we ...
4
votes
4answers
133 views

Mesh generator that can do 2D & 3D elements combined?

I'm trying to analyze a circuit card assembly (CCA). The biggest problem is always trying to mesh the thin copper layers along with the thicker epoxy layers between. I'm making the approximation that ...
2
votes
1answer
109 views

Is R or Matlab currently faster?

The most up-to-date performance benchmarks comparison between R and Matlab that I could find are several years out of date: 1 2 Is anyone aware of a more up-to-date comparison?
0
votes
0answers
26 views

Does cyclic reduction require a square mesh for 2D FEM/FDM?

In a 2-dimensional finite difference method or finite element method (triangular elements, each node is connected to 6 neighbors), each node has a matrix entry to its horizontal and vertical ...
4
votes
2answers
87 views

Solving “Hadamard systems”

Suppose we have two matrices $A$ and $B$ (we can assume they're symmetric; if absolutely necessary I think they may be positive definite). Then, is there any technique for solving $$(A\circ B)x=b,$$ ...
1
vote
1answer
29 views

Open source linux Maple Worksheet Interpreter/Converter?

I bought a book where the exercises are given in Maple worksheet format (.mw). Is there an open-source software in Linux able to interpret or to convert this specific file format ?
4
votes
1answer
97 views

Behavior of integration method

I was playing with N-body simulations of a game called Kerbal Space Program, which itself uses the patched conics approximation. I have read that for long term stability it is best to use symplectic ...
1
vote
2answers
84 views

(Fortran) Integrating/summing over complicated 3D domain

I have some function $F(k_x,k_y,k_z)$ that I wish to numerically integrate over a polygon domain - physically, I am integrating over the first Brillouin Zone (BZ) of the FCC lattice (a truncated ...
0
votes
2answers
48 views

Maths calculations for randomly generated numbers don't match computed averages

Ok, It was hard to explain my problem in the title. I hope it made enough sense to peak the curiosity of some of you. What I've been trying to do is find the relationship between the amount of random ...
0
votes
0answers
59 views

Using scipy.quad to calculate difficult integral

When evaluating the integral below in python using scipy.quad I get the following warning: UserWarning: The maximum number of subdivisions (50) has been achieved. If increasing the limit yields no ...
2
votes
2answers
75 views

How to implement Gauss-Laguerre Quadrature in Python?

To get the hang of Gauss-Laguerre integration I have decided to calculate the following integral numerically, which can be compared to the known analytical solution: \begin{align} \int_0^{\infty} ...
2
votes
1answer
86 views

Energy Conservation in Conservation Laws with Source Terms

I'm wondering if anyone can help me understand energy conservation when using conservation law methods (i.e. Riemann solver, High-Resolution Wave-Propagation Methods) with the addition of source ...
1
vote
1answer
33 views

Fortran 2003 ARPACK wrapper

I wrote a Fortran 2003 wrapper for the ARPACK routine znaupd, basically translating the the example driver routine zndrv1 into modern Fortran 2003 language with automatic arrays. I initialize every ...
2
votes
0answers
62 views

What is numerical damping in the context of time-dependent FEM solvers?

Comsol Multiphysics (a popular FEM package) includes two time-stepping algorithms (IDA aka BDF, and Generalized-alpha), described in their documentation as follows (quoted here under Fair Use; ...
1
vote
0answers
41 views

FEniCs: help in implementing the boundary condition for 1D problem [closed]

I have just started learning FEniCS and have used: http://www.scientificpython.net/pyblog/fenics-linear-two-point-bvp to write a script for solving: ...
2
votes
1answer
74 views

Is there a Gauss-Laguerre integration routine in Python?

I am reading the book "Numerical Recipes in Fortran 77: The Art of Scientific Computing" (Second Edition) and I came across some methods for numerical integration of 1D functions. More specifically ...
4
votes
0answers
118 views

Are there improved method of computing the following expression?

given a symmetric matrix $Y \in \mathbb{R}^{n \times n}$, and an arbitrary matrix $X \in \mathbb{R}^{n \times n}$, and a vector $v \in \mathbb{R}^{n \times 1}$, is it possible to compute the following ...
2
votes
2answers
85 views

Using Trilinos and/or Petsc in Windows with Visual Studio?

I am currently working on a project of building a simulator. Up till now I have mostly played around with very simple examples, but with regards to the future I have been thinking that it might be a ...
3
votes
1answer
90 views

steady state solution from parabolic problem vs solution of elliptic problem

My question is related, but not a duplicate of Asymptotic convergence of the solution to a parabolic pde to the solution of an elliptic pde Suppose I solve the parabolic PDE: $u_t = \Delta u + ...
2
votes
0answers
36 views

Treatment of Neumann (Traction) boundary conditions using projection methods

I am looking to solve the incompressible Navier-Stokes equations in 3D, using an inflow boundary condition specifying a velocity: $\mathbf{u} = \mathbf{g}_0 \,\, \forall \,\, \mathbf{x} \in \Gamma_u$ ...
2
votes
1answer
58 views

Testing 1D root-finding procedures for robustness

How can I test whether a given 1D root-finding procedure is robust? I know that there are data sets and resources online for different kinds of optimization, but I have yet to find anything with ...
0
votes
0answers
66 views

How to use the Freefem++ (or Fenics) for solving 3D Helmholtz equations or Maxwell equations

I recently want to solve the three-dimensional Helmholtz equations with ABCs via the edge element method. But I am familiar with the program of C++/Python (-type) language, so I want to obtain some ...
1
vote
1answer
51 views

3D Poisson equation, Fourier and Chebyshev

I am currently trying to solve the 3D Poisson equation with a Chebyshev discretisation in the $z$ direction (from -1 to 1) and Fourier in the $x$ and $y$ (from $-\pi$ to $\pi$) I have taken the code ...
0
votes
2answers
79 views

How to determine the number of c points in algebraic multi grid

I am trying to write an algebraic multi-grid solver (in c++). At a given level I determine which nodes are c-points and which nodes are f-points (where the total number of c and f points equals the ...
2
votes
2answers
66 views

How to generate a rotated (by 90 degrees) logistic sigmoid function in Python

I created this Python function to generate a sigmoid function where I can modify position and width: ...
4
votes
0answers
62 views

Policies Relating to Publication and Open Source Development of Code in Academia

Introduction Let me first state some conflicting assertions of the matter to illustrate what are the issues. Personally I would like to have my code open at every stage of development, since ...
3
votes
2answers
72 views

Should I pass command line arguments to MPI_Init or not?

When writing MPI 3.0 code, should I pass argc and argv to the MPI_Init call or not, and why? ...
2
votes
1answer
81 views

Is there a relatively simple way to extract the Jacobian from a Runge-Kutta 4/5 integrator?

I have a RKF45 numerical integrator that simulates polymerization of proteins using CUDA. It does so by tracking the populations of discrete length polymers, e.g. monomers, dimers, trimers, etc. all ...

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