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Numerical evaluation of the first and second complete elliptic integrals

To get a numerical evaluation of the first (K) and second (E) complete elliptic integrals: $$K(k)=\int_0^1\frac{dt}{(1-t^2)^{1/2}(1-k^2t^2)^{1/2}}, \ \ \ \ \ E(k)=\int_0^1\frac{(1-k^2t^2)^{1/2}}{(1-t^...
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votes
1answer
659 views

roots of polynomials of high degree: LinAlgError: Eigenvalues did not converge

I wrote a simple script to generate random polynoimals $\displaystyle f(z)= \sum_{k=0}^N a_k \frac{z^k}{\sqrt{k!}} $ of high degree and find their roots. For more discussion on random polyomials see ...
0
votes
2answers
2k views

scipy.integrate.odeint: how can odeint access a parameter set that is evolving independently of it?

I might have some non-linear ODEs that are being solved by scipy.integrate.odeint. However, a parameter at each time step might have to be updated by using a non-DE ...
0
votes
1answer
43 views

Confirmation of FSAL property for IMEX methods by Kennedy and Carpenter

This question is a continuation of Fourth order IMEX Runge-Kutta method and Implementation details for high order IMEX methods by Kennedy and Carpenter. I need confirmation that ARK3(2)4L[2]SA by ...
0
votes
1answer
127 views

Calculation of error

I have written a code in which I find the approximation of the solution of this elliptic problem. I calculated the error using the following part of code: http://pastebin.com/7b5mmuRW but I get the ...
0
votes
2answers
634 views

Mixed formulation of the Poisson equation (FEM)

I'm solving the Dirichlet problem for the Poisson equation in a 2d domain $D$: $$ \begin{cases} \Delta u = 0 \quad \text{in $D$}, \\ u|_{\partial D} = u_0. \end{cases} $$ I'm interested in ...
0
votes
1answer
249 views

Euler-Bernoulli beam element versus continuum beam element

I am using OpenSees to model a simply supported beam with a point load in the middle. The model is in consistent units. The beam is made up of bilinear quad elements. I have used 30 elements along the ...
0
votes
1answer
184 views

How to set an initial guess for the iterative solver in Comsol?

How to set the initial guess for the iterative solver GMRES or FGMRES for linear problems (Helmholtz equation of RF module) in Comsol?
0
votes
2answers
209 views

Convex quadratic problem solver gives different answers?

I am pretty sure that the following variance objective function should be a convex quadratic problem. My objective function is as follows: $$ \text{argmin } \text{var }(X*L) \xi \geq 1, \text{ where }...
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votes
2answers
288 views

Calculating integrals for a function approximated by Chebyshev polynomials

Setup (complete, but all very standard): My problem is how to best calculate the cumulative integral of a function which comes out of Spectral Collocation with a chebyshev basis. Take some function $...
0
votes
1answer
135 views

How does the animation work in eigenvalue problem of FEM

I have used free vibration analysis in FEM. After analysis, we can usually use animation to see the motion of each eigenmode (In Abaqus or Comsol, I would choose either half harmonic or full harmonic)...
0
votes
1answer
5k views

Python Finite Difference Schemes for 1D Heat Equation: How to express for loop using numpy expression

Hello all, I've recently been introduced to Python and Numpy, and am still a beginner in applying it for numerical methods. I've been performing simple 1D diffusion computations. I suppose my ...
0
votes
1answer
98 views

How to recognize boundary nodes and sides from the given element node connectivity data

I'm writing a code in C++ to parse abaqus/calculix input file for 2D plane stress problems. I'm not a user of abaqus/calculix but I noticed that the input file doesn't ask complete boundary details. ...
0
votes
1answer
1k views

Is it possible to output the matrix condition number from pardiso (MKL)? [closed]

I am assuming the pardiso solver calculates (or estimates) the condition number before proceeding to the solution phase. Is there a way to make pardiso output the condition number? Alternatively, ...
0
votes
1answer
95 views

Free access to Xeon Phi clusters

Apologies if this is not the right forum to ask, but there has been a somewhat related question here. I am working on a piece of software (nonlinear constrained optimisation, coded in C++11 and ...
0
votes
1answer
556 views

ZGETRF and ZGETRS from MKL - zgetrf fails and still zgetrs works?

I have a large system of equations $$Ax=b$$ and I know matrix $A$ and right-hand side vector $b$. I'm using MKL to solve this system. The matrices are complex. I have used the general solver ...
0
votes
0answers
70 views

Comparison of diffusion time - theoretical value vs computed

This is a follow up to my previous post I've been trying to compare the diffusion time obtained from theoretical derivation(answered in my previous post) and what is obtained computationally, for a ...
0
votes
0answers
31 views

Minimizing the ratio of two specific non negative quadratic convex functions

$F$ is $m\times m$ diagonal, with real non negative elements $D$ is $n \times m$ complex $P$ is $n \times 1$ complex $A$ is $m \times 1$ complex. Minimize $\Gamma(A)$, with respect to $A$. $$\...
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0answers
41 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 ...
-1
votes
2answers
220 views

$LU$ factorization

Our task is to implement a factorization routine that given A in a suitably efficient data structure returns the factors $L$ and $U$ where $L$ is unit lower triangular and $U$ is upper triangular. In ...
-1
votes
2answers
72 views

Is the sine function periodic in $x$ or $y$?

I know sine is $2\pi$-periodic, but some people say the motion is "periodic in..." Would it be periodic in $y$? If we move along the $x$-axis, the function values $y = \sin(x)$ will repeat, ...
-1
votes
1answer
360 views

Which ODE solver in Matlab allows me to advance in just one timestep only

[t,y] = odeXX(odefun,tspan,y0) I have a solver odeXX, and the tspan = [0 0.0001]. It seems that for any ode solver in MATLAB, they integrate by breaking ...
-3
votes
1answer
106 views

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