Questions tagged [numerics]
The numerics tag has no usage guidance.
853
questions
-1
votes
0answers
25 views
Is it ok to get the parameter of a random variable, from a random variable itself?
I want to generate the parameter, for a Poisson distribution, from a lognormal distribution. Has there been literature on if this is proper in probability & statistics, or are there nuances to ...
0
votes
1answer
86 views
Numerical solution of ill-conditioned differential equation
I want to solve the following Cauchy problem
\begin{equation}
y' = y^2 + \frac{t^4 - 6t^3 + 12t^2 - 14t + 9}{(1+t)^2}
\end{equation}
with initial condition: $y(0) = 2$ for $t \in [0,1.6]$ using a 3 ...
3
votes
1answer
55 views
How does the diffusion of a finite volume method with a WENO scheme compare with that of spectral methods?
I know that, in general, finite volume (FV) methods are more (numerically) diffusive than spectral methods. However, I can't find any information on how the advection scheme changes that.
For example, ...
-1
votes
1answer
56 views
Numerical solution of the advection equation with Crank–Nicolson finite difference method
I need to implement a numerical scheme for the solution of the one-dimensional advection equation
$$\\\frac{\partial u}{\partial t} + C(x, t) \frac{\partial u}{\partial x} = 0 \\\\$$
$$ \\ C(x,t) = \...
3
votes
2answers
129 views
Using the BDF and RK4 methods to solve this coupled system of ODEs in C++
I'm trying to solve a system of ODEs using the BDF order 4 method. I find the first 3 points using RK4, then for the implicit part of the BDF, I use Newton-Raphson iteration. Unfortunately my solution ...
0
votes
0answers
65 views
understanding the form of Steklov-Poincare operators
I am reading this paper https://paola-gervasio.unibs.it/Publications/pg_cmame.pdf and I fail to understand the local Steklov-Poincare operators defined in $3.2$. Please help me on that.
In my ...
2
votes
0answers
49 views
Book recommendation on numerical methods for solving Integro-Differential equations
I was wondering if anyone could recommend a good book or resource on numerical methods for solving integro-differential equations? Of course I am familiar with the methods for solving ODEs and PDEs ...
1
vote
1answer
58 views
Trouble with backwards time integration in Python
I am struggling with a rather basic numerical integration task: Using Python's scipy.integrate.solve_ivp module to integrate an ODE sytem backwards in time. As a test, I am using the following ODE ...
6
votes
0answers
97 views
A Question About a Claim from 1991 Computational EM paper about the Cancellation of certain Boundary Terms
Please let me know if this is not the appropriate site for this question. I found questions regarding EFIE/MFIE/CFIE on this site, so I thought my question might fit.
I am studying the paper by Putnam ...
1
vote
2answers
96 views
Software to build a mesh of a surface from points on the surface
I have a set of points $(x_i,y_i,u(x_i,y_i))\in\mathbb{R}^3$, $i=1,\dots N$, over a surface $S$ (from experimental data). I need to calculate the integral of a function $F$ over that surface.
If the ...
1
vote
1answer
23 views
Numerical stability of taking the `mean` of outputs from the simulation of a discrete stochastic dynamical system
I am writing a simulation for a discrete stochastic dynamical system. Since the simulation is stochastic, I need to run the simulation multiple times and then average the values of each timestep. I ...
2
votes
1answer
62 views
How to include negative number in the log-sum-exp?
I want to know summation of some small numbers, such as {e^-1000, -e^1001, e^1002...}
If all numbers are positive, I can use log-sum-exp algorithm. But unfortunately, negative numbers are also ...
1
vote
1answer
83 views
preconditioner for $u''(x)=\sin(x)$
I am interested in finding preconditioner to solve the problem for one dimensional problem $u''(x)=\sin(x), u(0)=u(1)=0$ using Dirichlet-Neumann method.
The preconditioner $M$ coming from Dirichlet-...
1
vote
0answers
54 views
Upper bound on condition number in linear preconditioning
I'm studying iterative methods for solving linear system, and I find the following setting in Wikipedia:
Consider a matrix splitting $A = M-N$, where $A,M,N$ are all symmetric and positive definite ...
2
votes
1answer
92 views
Numerical Linear Algebra: When to use Direct methods versus iterative methods to solve a linear system - for PDEs in particular
I am reading the Chapra and Canale book on numerical methods, and was working through the chapters on solving linear systems. Now the book goes through direct methods including Gaussian Elimination, ...
1
vote
0answers
17 views
Problem with recursive implementation of Subspace Iteration method in Numpy
I am having trouble with implementing the method of subspace iteration to find the eigenvalues and vectors of a random, symmetric matrix, A that is mxm with m = 10. ...
1
vote
0answers
265 views
Minimax optimization with an oracle
I have an optimization problem of the following form: $$\min_y\left[\max_x f(x,y)\right].$$ It is fairly straightforward to minimize $f(x,y)$ over $y$ with $x$ fixed, and similarly to maximize $f(x,...
0
votes
1answer
132 views
Conserve energy by message passing?
There are $N$ particles with positions $x_i(t)$ and velocities $v_i(t)$ and mass 1. There is a potential function $U_{i,j}(x_i, x_j)$ between each pair of particles, which is $0$ unless the particles ...
4
votes
1answer
148 views
Time Reversibility of Velocity Verlet Algorithm
I'm very new to computational Physics and am finding conflicting statements on whether the velocity Verlet algorithm, defined as:
$\begin{align}
x_{n+1} &= x_n + v_n \Delta t + \frac{1}{2} a_n \...
1
vote
0answers
32 views
How can I improve the accuracy of the calculation of the magnetic field in Gmsh/GetDP?
I need to calculate the magnetic field along a straight line in proximity of an array of 6 magnets. I used the tutorial files "magnets" included in Gmsh and I slightly modified the file in ...
4
votes
2answers
82 views
Dividing functions over a wide range-
I try to solve a system of coupled equations, where a very nasty division operation occurs. In fact, I need to compute a derivative of two exponential decaying functions. Let's illustrate this with ...
1
vote
1answer
52 views
2-DOF Robotic Manipulator Trajectory Tracking Simulation
I am trying to simulate a 2-DOF planar robotic manipulator (have its joints follow a predefined trajectory) that's described by its dynamic model:
$$ M(q)\ddot{q}+C(q,\dot{q})\dot{q}+G(q) = \tau $$
...
2
votes
1answer
81 views
Best practice for ADTs in computational science with Fortran
I have been writing a software package in Fortran for solution of the Vlasov-Poisson system in 2D2V. I want this software to be useful beyond its current application (e.g. systems with different ...
3
votes
1answer
68 views
Cauchy Lorentzian simulation on FFT with oscillation
Recently I do simulation on Lorentzian Function with FFT
Lorentzian Function is 2a/(x**2+a**2)
...
2
votes
2answers
136 views
Numerical Methods of solving a non-linear ODE?
I want to solve the nonlinear equation $\frac{d^2x}{dt^2} + k\sin x = 0$, numerically. I found that solving this elliptic integral would be cumbersome, so is there a numerical method i could use to ...
2
votes
0answers
81 views
Algorithm for computing inner products multiple times
I am taking a computational linear algebra course and i got stuck during a homework problem concerning the computation of inner products. I am supposed to compute the inner product:$$\mathrm{a}_{\...
0
votes
0answers
35 views
discretizing advection equation with variable wave speed + stability
I currently have a code that solves $u_t+ cu_x=0$ with periodic boundary conditions, and constant $c$ (using an upwind method). I'm wondering how I would alter this code to solve something of the form
...
2
votes
1answer
79 views
Rank of a double-precision augmented matrix
Let $A$ be a matrix with real entries, and let $A_+$ be $A$ augmented by a single column.
From linear algebra we know
\begin{equation}
\operatorname{rank}(A_+) = \operatorname{rank}(A) \hspace{10pt} ...
1
vote
1answer
122 views
Numerical integration problem: IntegrationWarning The integral is probably divergent, or slowly convergent
I am trying to get the numerical integration of a function using scipy's integrate.quad as follows.
$$
\begin{equation}
G (\alpha) = \frac{4\alpha}{\pi}\int_0^{\...
0
votes
0answers
65 views
Ill-conditioned stiffness matrix
I am writting a Fem code in c++ for a 2d plane stress model. My question is regarding the assembly stiffness matrix.I noticed that some elements of the matrix are not exactly zero but insted a number ...
1
vote
0answers
65 views
Error curve does not oscillate in between reference points using Remez
Using the Remez algorithm, implemented using multi-precision library, in certain functions that I want to approximate, the error curve does not oscillate in between reference points, and so no roots ...
0
votes
1answer
46 views
Linearization of Remez algorithm rational case
In the rational case, we are interested to find polynomials $P(x)$ and $Q(x)$ s.t.
$f(x_k)-P(x_k)/Q(x_k)=(-1)^kE$ for $k=1,2,\ldots, N$ where $N=deg(P)+deg(Q)+2$
This can be rewritten as
$$
(1)~~~~~~(...
1
vote
1answer
75 views
Least Square fit of a system of equations
I've a matrix equation $\bar z^{(r)}(k + 1) = \bar{DF} ~ \bar z^{(r)}(k)$. Now the $\bar z$'s and $\bar{DF}$ are $d \times d$ matrices. Now $\bar{DF} = \begin{pmatrix}
0 & 1 & 0 & 0 & \...
0
votes
0answers
22 views
offline Bin Packing problem with multiple size bins
As per my research on stack overflow communities, This is probably known as cutting stock problem / multiple Knapsack problem (a variant of the bin packing problem) which is NP hard.
here are the ...
2
votes
0answers
79 views
Remez algorithm convergence
I have implemented the Remez algorithm in Python where all calculations were done with the Python mpmath library. I have noticed that sometimes the $|E_{max}|$ and $|E_{min}|$ do not monotonically ...
2
votes
1answer
151 views
Finite element (1D) for steady state non-linear problem
I need to solve with linear finite elements the equation $$\frac{\partial }{\partial x}\Bigl(\text{sgn}(x) u \Big) +\frac{\partial}{\partial x} \Bigl[ \sqrt{u} \frac{\partial u}{\partial x} \Bigr] =0$...
1
vote
1answer
115 views
Non-Linear advection diffusion with nondifferetiable advection term
I'm looking at Murray's book: Mathematical biology: an introduction , first volume, pag. 404
In particular, I'm interested to solve the following PDE:
$$\partial_t u = \partial_x (\text{sign}(x) u) + \...
2
votes
1answer
115 views
Ill-condioned Linear System and Gaussian Elimination
Suppose that I have a linear system $Ax=b$ such that $A$ is ill-conditioned. Can I say that it is dangerous to find a solution with Gaussian Elimination for this system, or does there exist some class ...
1
vote
0answers
65 views
How can I practice multivariable root-finding?
Recently, I've been reading up on various root-finding / optimization algorithms such as the Levenberg-Marquardt method, Gauss-Newton, Conjugate Gradient, trust-region and trust-region-dogleg.
I've ...
1
vote
1answer
61 views
Imposing pressure variation instead of Dirichlet boundary conditions on Finite Element Method
I always see Finite Element codes solving PDE with Dirichlet or Neumann boundary conditions. But, I have a problem now consisting of a straight cylinder with a circular base (a simple 3D tube), with ...
0
votes
0answers
103 views
Solution of Cahn-Hilliard equation
I need to solve the Cahn-Hilliard equation
$$\frac{\partial u}{\partial t} = \Delta(f(u) - \epsilon^2\Delta u), \hspace{.5cm}(x, t)\in \Omega\times(0, T],$$
using mixed formulation
\begin{equation}\...
0
votes
0answers
45 views
Norm estimates if adjoints can't be computed
Assume that you have two linear maps $A$ and $V$. For a given $x$ (of appropriate dimension) you can compute $Ax$ numerically, and for any $y$ (of appropriate dimension) you can calculate $V^Ty$ ...
5
votes
1answer
114 views
Accurate and efficient computation of the logarithm of the ratio of two sines
For exploratory work related to special function implementations, I need to compute $\log \frac{\sin y}{\sin x} $, where $0 \le x \le y \le 2x < \frac{\pi}{2}$. Cases with $x \approx y$ in ...
2
votes
1answer
63 views
Parity for artificial dissipation term in a finite-difference solution
I have a doubt regarding the signal of the dissipative term in a finite difference solution for an equation of the form
$$
\frac{\partial u}{\partial x}+f(x)=0, u(0)=0
$$
In which $f$ is an odd ...
0
votes
0answers
48 views
numerical solution to pde on an ellipse
Looking for advice on discretization (preferably finite difference) schemes for pdes on curves in general, but in this case it is an ellipse (so given by $(a\cos(r), b\sin(r)$). The problem is the ...
3
votes
1answer
73 views
Find quadrature points and weights
I'm struggling with the following problem:
What is the maximum degree of exactness that we can obtain with the following quadrature >formula
$$\int_0^1 f(x)\frac{1}{\sqrt{x}}dx \approx w_0 f(x_0) +...
0
votes
1answer
71 views
Interpreting multivariable root-finding results from Matlab's fsolve algorithm
Edit: So I was able to get the same value of r that's given, when coding up the sum of squares of function values directly in the script file, rather than on the Command Window. So, maybe there's a ...
0
votes
2answers
132 views
No flux Neumann boundary condition for non-stationary PDE equivalent to Dirichlet boundary?
When using no flux Neumann boundary conditions (i.e. zero derivative to the normal on the boundary) in a non-stationary PDE, I don't seem to recognize the difference to using Dirichlet boundary ...
3
votes
1answer
162 views
How to use numerical integration to calculate the surface area of a superellipsoid?
I am working in an application in which I need to calculate the surface area of a superellipsoid. I have read that there is no closed form solution (see here), so I am trying to compute it using ...
0
votes
2answers
58 views
Grid Independence Study
Is the change in time step necessary for the grid independent study? As the CFL is based on the relation between dt and dx.
In mesh independent study, only change should be mesh i.e, dx isn't it so?
