Computational Science Questions, Problems & Solutions : TransWikia.com ~ Page 7

Calculating residue of a rational function

I have a function$$f(z) = frac{1}{(z-z_1)(z-z_2)(z-z_3)(z-z_4)}$$All of ${z_1,z_2,z_3,z_4}$ are simple poles. The residuesfor this function are given as$$text{Res}(f(z),z_i)= limlimits_{zto zi}...

Asked on 10/23/2021

1 answer

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 10/23/2021

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 10/23/2021

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 10/23/2021

1 answer

Combined translational and rotational meshing in gmsh

For a flow simulation I am trying to reproduce a specific screw element design for an intermeshing co-rotating twin-screw extruder. I am using gmsh (v2.16) where the element is made...

Asked on 10/05/2021 by nluigi

2 answer

What are the best ways to interpolate a vector field inside (convex) polygons?

I want to interpolate a vector field inside convex polygons in a polygonal mesh. For triangular meshes the scheme uses a piecewise constant interpolation in the triangle, discretized at the...

Asked on 10/04/2021

2 answer

Does 'Recombine' work for this geometry in Gmsh?

I am struggling to recombine the remaining triangular cells into unstructured quadrangular ones in this geometry using Gmsh. Do I need to add auxiliary lines somewhere or do some geometries...

Asked on 10/03/2021

1 answer

Job Scheduler for Local Machine

I am used to running calculations on a server/cluster, and we have used both PBS and SLURM. However, I am looking to run some...

Asked on 10/03/2021 by kskinnerx16

2 answer

Can the mesh generation methods in FVM and FEM be totally based on the knowledge of the mesh generation theory in computer graphics?

The main references of mesh generation methods in computer graphics (CG) I found are discrete Differential Geometry [1] and a famous book "Polygon Mesh Processing" [2], while the "Handbook of...

Asked on 10/02/2021

4 answer

FFTW on subarray with MPI

With the guru interfaces of FFTW, I can apply transforms only to parts of a multidimensional array by modifying the fftw_iodim parameter (e.g., with fftw_plan_guru_r2r(...)). Unfortunately, there seems to be...

Asked on 10/01/2021 by Hannes

1 answer

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