Problem using quad2d with vector

Using below code with the variable t doesn't work, matrix dimensions don't agree, if the variable is replaced with a single number it does work (though that's not particularly useful), I've tried replacing it with a loop to no avail.

What am i missing?

lm = 1.75; 
Cm = 3.2E6;
fe = 1380;
H = 13.5;

% time and space
y = 0.0;
ro = 0.1;
x = ro;
ts = [0.1 97/24];           
Mt = 100; 
% t = logspace(log10(ts(1)*86400),log10(ts(2)*86400),Mt);   % [s]
t = linspace(ts(1)*86400, ts(2)*86400, Mt); % [s]

% calculated parameters
QL = fe/H;                   
z = H/2;
Dt = lm/Cm;             
r = sqrt(x.^2+y.^2);  

T = QL*(1/4/pi/lm)*...              
    (quad2d(@(f,ze) erfc(sqrt(r^2+ro^2-2*r*ro*cos(f)+(z-ze).^2)...
     /2/sqrt(Dt*t))/pi./sqrt(r^2+ro^2-2*r*ro*cos(f)+(z-ze).^2),0,pi,0,H)-...
     quad2d(@(f,ze) erfc(sqrt(r^2+ro^2-2*r*ro*cos(f)+(z-ze).^2)...
     /2/sqrt(Dt*t))/pi./sqrt(r^2+ro^2-2*r*ro*cos(f)+(z-ze).^2),0,pi,-H,0));

Answer 1

[KSSV]

You have to take care of element wise operations in that big expression T. As T is very big and clumsy, I have modified it to a loop, as below.

clc; clear all ;
lm = 1.75; 
Cm = 3.2E6;
fe = 1380;
H = 13.5;
% time and space
y = 0.0;
ro = 0.1;
x = ro;
ts = [0.1 97/24];           
Mt = 100; 
% t = logspace(log10(ts(1)*86400),log10(ts(2)*86400),Mt);   % [s]
tt = linspace(ts(1)*86400, ts(2)*86400, Mt); % [s]
% calculated parameters
QL = fe/H;                   
z = H/2;
Dt = lm/Cm;             
r = sqrt(x.^2+y.^2);  
T = zeros(size(tt)) ;
for i = 1:length(tt)
    t = tt(i) ;
T(i) = QL*(1/4/pi/lm)*...              
    (quad2d(@(f,ze) erfc(sqrt(r^2+ro^2-2*r*ro*cos(f)+(z-ze).^2)...
     /2/sqrt(Dt*t))/pi./sqrt(r^2+ro^2-2*r*ro*cos(f)+(z-ze).^2),0,pi,0,H)-...
     quad2d(@(f,ze) erfc(sqrt(r^2+ro^2-2*r*ro*cos(f)+(z-ze).^2)...
     /2/sqrt(Dt*t))/pi./sqrt(r^2+ro^2-2*r*ro*cos(f)+(z-ze).^2),0,pi,-H,0));
end

Though it is working, it is throwing some warning. I suggest you to check the expression for T.

[Scott Lines]

Thank you, I think I will need to go over the expression again but that's solved the first problem.

Answer 2

[Torsten]

There is no other way than to loop over the elements of t and call quad2d for each element separately.

MATLAB's "integral" has the option "ArrayValued=True", but as far as I know, integral2 or quad2d haven't.

Best wishes

Torsten.