add traction extraction demo to stfmm3dPerfTest.m

Author: ahbarnett

matlab/Contents.m

@@ -16,7 +16,7 @@
 %   hfmm3dTest
 %   emfmm3dTest
 %   stfmm3dTest
-%   stfmm3dPerfTest
+%   stfmm3dPerfTest - demo and math test for stokeslet & stresslet, traction
 %
 % For examples of use see:
 %   lfmm3d_example

matlab/stfmm3dPerfTest.m

@@ -1,11 +1,13 @@
 disp("Perf and math test matlab driver for FMM3D/Stokes")
-disp("Source to target, stokeslet+stresslet (1-vec), vel pot only...");
-% Barnett 8/4/23
+% Barnett 8/4/23. Added traction output test, 4/12/24.
 
 clear
 ns = 100000;
 nt = 100000;
 eps = 1e-3;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+disp("Source to target, stokeslet+stresslet (1-vec), vel pot only...");
 ifstrs = 1;       % include stresslets?
 ifppreg = 0;      % no eval at sources
 ifppregtarg = 1;  % just vel out
@@ -24,7 +26,7 @@
 t = toc;
 fprintf("%d to %d points, eps=%.3g, done in %.3g s (%.3g tot pts/sec)\n",ns,nt,eps,t,(ns+nt)/t)
 u = U.pottarg;
-i = randi(nt);   % which targ
+i = randi(nt);   % which targ to check
 fprintf("velpot targ(i=%d) =\n",i);
 disp(u(:,i))
 
@@ -42,6 +44,39 @@
   end
 end
 ui = 0.5 * ui;   % FMM3D is 1/4pi off from true 1/8pi prefactor
-fprintf("rel err vs direct at ith targ: %.3g\n",norm(u(:,i)-ui)/norm(ui))
+fprintf("rel err vs direct at ith targ: %.3g\n\n",norm(u(:,i)-ui)/norm(ui))
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+disp("Stokeslet sources to targets: compute vel pot, traction at oriented targs...");
+% just give the changes from the above setup...
+ifppregtarg = 3;  % request everything
+srcinfo = rmfield(srcinfo,{'strslet','strsvec'});
+targnor = rand(3,nt);   % normal vectors for targets (eg, surface normals)
+
+tic;
+U = stfmm3d(eps,srcinfo,ifppreg,targ,ifppregtarg);
+t = toc;
+fprintf("%d to %d points with u,p,gradu: done in %.3g s (%.3g tot pts/sec)\n",ns,nt,t,(ns+nt)/t)
+p = U.pretarg;         % pressure (1*ntarg)
+gradu = U.gradtarg;    % grad vel (3*3*ntarg)
+shearstress = gradu + permute(gradu,[2 1 3]);        % gradu + gradu^T
+% stress sigma = -pI + mu*(gradu+gradu^T),   then T = sigma.n    We assume mu=1.
+T = -(ones(3,1)*p).*targnor + squeeze(sum(shearstress .* reshape(kron(ones(3,1),targnor),3,3,nt),1));   % compute all tractions (painful tensor contraction in matlab)
+i = randi(nt);   % which targ to check
+%fprintf("targ(i=%d): p=%.15g,   gradu = \n",i,p(i)); disp(gradu(:,:,i))
+fprintf("targ(i=%d) traction T = \n",i);
+disp(T(:,i))
 
+% check T (target tractions) vs direct formula
+Ti = zeros(3,1);
+nori = targnor(:,i);
+for j=1:ns
+  R = targ(:,i) - srcinfo.sources(:,j);  % x-y with std sign (targ-src).
+  r = sqrt(sum(R.^2));                   % dist
+  f = srcinfo.stoklet(:,j);              % strength
+  Ti = Ti - (3/(4*pi))*(1/r^5)*R*dot(nori,R)*dot(f,R);  %  true T_{ijk} n_j f_k
+end
+Ti = Ti * (4*pi);   % FMM3D has 1/4pi missing in prefactor
+fprintf("rel err vs direct at ith targ: %.3g\n",norm(T(:,i)-Ti)/norm(Ti))