Question about surface integration

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harulab 2016-2-7

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https://ww2.mathworks.cn/matlabcentral/answers/266954-question-about-surface-integration

评论： Torsten 2016-2-8

Hi, I'm facing a problem in calculating surface integration. I defined the function below which calculates surface integration for a discrete dataset using the trapezoidal rule.

function out = trapz2D(x,y,f)
    x = x(:);
    y = y(:);
    nx = length(x);
    ny = length(y);
    dx = diff(x);
    dy = diff(y);
    dS = dy*dx.';
    df = (f(1:ny-1,1:nx - 1) + f(2:ny,1:nx-1) + f(1:ny-1,2:nx) + f(2:ny,2:nx))/4;
    out = sum(sum(dS.*df));
end

I calculated surface integration using this function and the dataset attached, and then compare it to the value obtained from "trapz" which is a MATLAB built-in function.

surfInteg.m

clc
close all
clear
format long
load('dataset.mat')
I1 = trapz(y, trapz(x,Pz3,2));
I2 = trapz2D(x,y,Pz3);
disp([I1; I2])
>>>1.0e-12 *
   0.307618158054522 - 0.000000000004792i
   0.307618158054522 - 0.000000000004792i
I1 = trapz(y, trapz(x,Pz1,2));
I2 = trapz2D(x,y,Pz1);
disp([I1; I2])
>>>1.0e-27 *
   -0.135645057561047 + 0.013248760976931i
   -0.129284381233370 + 0.013497757971006i