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Computational Science : Recent Questions and Answers (Page 12)

Find answers to your questions about Computational Science or help others by answering their Computational Science questions.

Pressure interpolation in the Q2-P1 element

The Q2-P1 element is one of the popular finite elements for incompressible flow problems in the mathematics community. For this element, the velocity field is approximated using bi-quadratic shape functions...

Asked on 08/22/2021

1 answer

Preconditioning the $[1 quad-2 quad 1]$ Finite Difference matrix

Let $A$ be the well known tridiagonal matrix coming from the 1D Finite difference discretization of the Laplacian, with stencil $frac{[1 quad-2 quad 1]}{h^2}$. The system $Ax...

Asked on 08/22/2021

0 answer

What is a dense ODE system? What is a sparse ODE system?

Can you provide a jargon-free (as much as possible) explanation of what is meant by "dense ODE systems", and "sparse ODE systems"? Some hints I have gotten from Googling:dense ODE...

Asked on 08/22/2021

1 answer

Maximum lossless compression ratio for floating point time series

I want to compress an array of time series floating point data as much as possible. Currently the only algorithm I've found for this is XOR compression which works well,...

Asked on 08/22/2021

1 answer

Can automatic differentiation be used on the parameters of an optimization problem?

If I wanted to perform an optimization using a Newton-based solver where the Hessian and gradient of a function are known analytically, and then use a package such as Adept...

Asked on 08/18/2021 by Sal L

0 answer

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...

Asked on 08/17/2021

1 answer

Finite elements with CFL condition - How to obtain correct order of convergence

I have discretized a PDE with continuous finite element method in spatial variable and with implicit Euler or Crank-Nicolson in temporal variable. In both cases, I have error estimates in...

Asked on 08/15/2021 by math_lover

1 answer

Solve two-player game - minimize the l-infinity norm of a matrix-vector product

I have a matrix $M$ with non-negative real entries, and I would like to minimize the objective function$$Phi(v) = |Mv|_infty,$$where $v$ is constrained to be...

Asked on 08/15/2021

2 answer

Clustering with points lying along different 3D planes

I have a bunch of data points in 3D that lie along a few planes. What would be the best approaches to estimate the normals of these planes? Edit:...

Asked on 08/15/2021

3 answer

FEM Stiffness Matrix is always close to Singular or Badly Scaled

I am making a code for an 18-node (3x3x2) 3D element FEM. However, even though I am (pretty) sure that all the shape functions are correct and whatnot, whenever I...

Asked on 08/13/2021 by Additional Pylons

2 answer

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