Higher-Order FESpace mapped on mesh nodes

ekarabelas · November 18, 2021, 2:51pm

Hello,
I was wondering if there are routines in NGSolve to evaluate a FE-Function based on a higher order polynomial space (like the P2 in the Taylor-Hood Element) on the nodes of a mesh? I know, there is a VTK output routine, but this writes Files and I would like to evaluate the function in python and use it then as numpy-array for something else.

Best Regards
Elias

christopher · November 18, 2021, 4:28pm

Hi, yes you can create a numpy array of evaluation - points by giving an array of coordinates to the mesh and then put this array into the coefficientfunction to evaluate it:

xvals = np.linspace(0, 1, 1000)
pts = mesh(xvals, 0, 0)
vals = cf(pts)

Best
Christopher

joachim · November 18, 2021, 4:51pm

An alternativ is to define points on the reference element, and evaluate the function on the mapped points, simultaneously on all elements:

     pts = mesh.MapToAllElements({ngs.ET.TRIG: ir_trig, ngs.ET.QUAD: ir_quad}, vb)
     values = func(pts)

We use this in the webgui, see

github.com

NGSolve/ngsolve/blob/master/python/webgui.py

import math
import numpy as np
from time import time
import ngsolve as ngs
import os

from webgui_jupyter_widgets import BaseWebGuiScene, encodeData, WebGuiDocuWidget
import webgui_jupyter_widgets.widget as wg

def updatePMinMax( pmat, pmima=None ):
    pmima_new = [ngs.Vector(pmat[:,i], copy=False).MinMax(ignore_inf=True) for i in range(3)]

    if pmima is not None:
        for i in range(3):
            minmax = ( min(pmima[i][0], pmima_new[i][0]), max(pmima[i][1], pmima_new[i][1]) )
            pmima_new[i] = minmax

    return pmima_new

def getMinMax( vals, fmin=None, fmax=None ):

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Joachim

ekarabelas · November 19, 2021, 9:00am

Dear Joachim, dear Christopher,
thanks for the quick reply I will try this out.
Thanks
Elias

ekarabelas · November 19, 2021, 9:02am

One additional thing that wasn’t clear to me. When you guys speak of CoefficientFunction this is the same as a FE-Solution?

christopher · November 19, 2021, 9:22am

Yes, a fe solution GridFunction is derived from CoefficientFunction, so allows to evaluate itself like a CoefficientFunction. CoefficientFunction is any function on the mesh, like for example the coordinate-CFs x, y and z.

Also grad(u) is a coefficientfunction, also x * sin(u), …

All of these function can be evaluated on points in the mesh.