fixing transmission helper

chunkie/+chnk/+helm2d/fmm.m

@@ -46,7 +46,7 @@
 %
 % Optional Output:
 %   pot - potential/neumann data corresponding to the kernel at the target locations
-%   grad  - gradient at target locations
+%   grad - gradient at target locations
 %   hess - hessian at target locations
 
 if ( nargout == 0 )

chunkie/+chnk/+helm2d/transmission_helper.m

@@ -1,12 +1,17 @@
-function [kerns,varargout] = transmission_helper(chnkobj,ks,cs,coefs,varargin)
+function [kerns, varargout] = transmission_helper2(chnkobj,ks,cs,coefs,varargin)
 %CHNK.HELM2D.TRANSMISSION_HELPER builds the matrix of kernels required to call
 % chunkermat and generate boundary data which is appropriately scaled for the linear
 % system if requested.
 %
 % Syntax: kerns = transmission_helper(chnkrs,ks,cs,coefs), returns a matrix of kernels
-%         [kerns,bdrydata] = transmission_helper(chnkrs,ks,cs,coefs,opts), returns
+%         [kerns, bdrydata] = transmission_helper(chnkrs,ks,cs,coefs,opts), returns
 %            a matrix of kernels and the boundary data due to point sources or
 %            waves as prescribed by opts
+%         [kerns, bdrydata, kerns_eval] = 
+%            transmission_helper(chnkrs,ks,cs,coefs,opts), returns
+%            a matrix of kernels, the boundary data due to point sources or
+%            waves as prescribed by opts, and the evaluation matrix of
+%            kernels
 %
 % Note: Here we always assume that the transmission problem is either in
 %    the 'TE' or 'TM' polarization, which implies that the boundary conditions
@@ -22,9 +27,9 @@
 %    of the form
 %    [\beta u] = f. 
 %
-% Input:
+%  Input arguments:
 %   chnkrs - cell array of chunker objects describing the geometry (1,ncurve)
-%   ks - wavenumbers in different regions of teh plane
+%   ks - wavenumbers in different regions of the plane
 %   cs - cs(1,i), cs(2,i) denote the region number in the direction of the normal
 %          and opposite of the direction of the normal for curve chnkrs(i)
 %   coefs - denotes the scaling parameter for the jump in the neumann data, depends
@@ -38,6 +43,11 @@
 %      array of size (1,ncurve), with  opts.sources{i}.locs (2,m) locations 
 %      of charges which generate the data for region i, and .charges are the
 %      corresponding charge strengths
+%
+%  Output arguments:
+%    kerns - matrix of kernels for solving transmission boundary value problem
+%    bdrydata - boundary data
+%    kerns_eval - matrix of kernels for postprocessing transmission problem
 %           
 %
 
@@ -66,6 +76,8 @@
         error(msg)
     end
 
+    nreg = length(ks);
+
 
     bdry_data_type = 'pw';
     direction = 0;
@@ -93,11 +105,6 @@
     if(isfield(opts,'exposed_curves'))
         exposed_curves = opts.exposed_curves;
     end
-
-
-
-
-    kerns = cell(ncurve,ncurve);
 
     k1 = ks(cs(1,:));
     k2 = ks(cs(2,:));
@@ -108,7 +115,9 @@
 
 % First build system matrix without any corner corrections
     cc1 = zeros(2,2);
-    cc2 = zeros(2,2);  
+    cc2 = zeros(2,2); 
+
+    kerns(ncurve, ncurve) = kernel();
     for i=1:ncurve
 
         c1 = coefs(cs(1,i));
@@ -124,10 +133,12 @@
 
         cc1(2,2) = alpha2(i)/c1;
         cc2(2,2) = alpha2(i)/c2;
-
         for j=1:ncurve
-            kerns{i,j} = @(s,t) -(chnk.helm2d.kern(k1(i),s,t,'all',cc1)- ...
-                 chnk.helm2d.kern(k2(i),s,t,'all',cc2));
+            zks = [k1(i), k2(i)];
+            cc_use = cat(3, -cc1, -cc2);
+            kerns(i,j) = kernel('helmdiff', 'all', zks, cc_use);            
+%            kerns{i,j} = @(s,t) -(chnk.helm2d.kern(k1(i),s,t,'all',cc1)- ...
+%                 chnk.helm2d.kern(k2(i),s,t,'all',cc2));
         end  
     end
 
@@ -220,8 +231,15 @@
 
         end
         varargout{1} = bdry_data;
-
     end
-
 
+    if nargout > 2
+        kerns_eval(nreg,1) = kernel();
+        for i=1:nreg
+            Dk = coefs(i)*kernel('helm', 'd', ks(i));
+            Sk = kernel('helm', 's', ks(i));
+            kerns_eval(i) = kernel([Dk, Sk]);
+        end
+        varargout{2} = kerns_eval;
+    end
 end

chunkie/@kernel/helm2ddiff.m

@@ -24,7 +24,13 @@
 %   COEFS(1)*KERNEL.HELM2D('dp', ZKS(1)) -
 %   COEFS(2)*KERNEL.HELM2D('dp', ZKS(2))
 %
-%  COEFS is optional. If not given then COEFS is set to [1 1].
+%   KERNEL.HELM2DDIFF('all', ZKS, coefs) 
+%   constructs the (2x2) matrix of difference kernels of
+%   [D, S; D' S'] scaled by coefs where coefs is (2x2x2) tensor, i.e.
+%   D part is scaled as COEFS(1,1,1)*KERNEL.HELM2D('d', zks(1)) - 
+%   COEFS(1,1,2)*KERNEL.HELM2D('d', ZKS(2)), and so on.
+%
+%  COEFS is optional. If not given then COEFS is set to all ones.
 %
 % See also CHNK.HELM2D.KERN.
 
@@ -42,6 +48,9 @@
 obj.opdims = [1 1];
 if(nargin < 3)
     coefs = [1 1];
+    if strcmpi(type, 'all')
+      coefs = ones(2,2,2);
+    end
 end
 obj.params.coefs = coefs;
 
@@ -87,6 +96,18 @@
             obj.sing = 'hs';
         end
 
+    case {'all'}
+        obj.type = 'all';
+        obj.opdims = [2,2];
+        obj.eval = @(s,t) chnk.helm2d.kern(zks(1), s, t, 'all', coefs(:,:,1)) - ...
+                          chnk.helm2d.kern(zks(2), s, t, 'all', coefs(:,:,2));
+        obj.fmm  = []; 
+        if ( abs(coefs(2,1,1)-coefs(2,1,2)) < eps )
+            obj.sing = 'log';
+        else
+            obj.sing = 'hs';
+        end
+
     otherwise
         error('Unknown Helmholtz difference kernel type ''%s''.', type);
 

devtools/test/chunkgrphrcipTransmissionTest.m

@@ -5,12 +5,8 @@
 %            and tests the Helmholtz transmission problem
 %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%clear all
 clearvars
-addpaths_loc();
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 a = -1.0;
 b = 1.0;
 
@@ -37,15 +33,12 @@
 verts = exp(1i*2*pi*(0:4)/5);
 verts = [real(verts);imag(verts)];
 
-edge2verts = [-1, 1, 0, 0, 0; ...
-               0,-1, 1, 0, 0; ...
-               0, 0,-1, 1, 0; ...
-               0, 0, 0,-1, 1; ...
-               1, 0, 0, 0,-1];
-edge2verts = sparse(edge2verts);
+[~, nv] = size(verts);
+
+edgesendverts = [1:nv; [2:nv 1]];
+[~, ncurve] = size(edgesendverts);
 amp = 0.5;
 frq = 6;
-ncurve = size(edge2verts,1);
 
 fchnks    = cell(1,ncurve);
 cparams = cell(ncurve,1);
@@ -56,7 +49,7 @@
     cparams{icurve}.tb = 1;
 end
 
-[cgrph] = chunkgraph(verts,edge2verts,fchnks,cparams);
+[cgrph] = chunkgraph(verts, edgesendverts, fchnks, cparams);
 
 plot(cgrph); hold on;
 quiver(cgrph);
@@ -82,7 +75,8 @@
 opts.charges{1} = charges{1};
 opts.charges{2} = charges{2};
 
-[kerns, bdry_data] = chnk.helm2d.transmission_helper(cgrph,ks,cs,coefs,opts);
+[kerns, bdry_data, kerns_eval] = chnk.helm2d.transmission_helper(cgrph, ...
+                                   ks, cs, coefs, opts);
 
 
 opts = [];
@@ -94,7 +88,7 @@
 
 tic, dens = sysmat\bdry_data; toc;
 
-%%
+%% Postprocessing
 
 % generate some targets...
 
@@ -103,55 +97,27 @@
 [X,Y] = meshgrid(xs,ys);
 targs = [X(:).';Y(:).'];
 
-srcinfo = [];
-srcinfo.sources = cgrph.r(:,:);
-w = weights(cgrph);
-n = normals(cgrph);
-
-% a quick hack to find the interior points
-
-srcinfo.dipstr = w(:).';
-srcinfo.dipvec = n(:,:); 
-eps = 1E-8;
-pg  = 0;
-pgt = 1;
-[U] = lfmm2d(eps,srcinfo,pg,targs,pgt);
-U = U.pottarg;
-
-[~,nt] = size(targs);
-targdomain = ones(nt,1);
-inds = find(abs(U-2*pi)<pi/10);
-targdomain(inds) = 2;
-
-utarg = zeros(nt,1);
+opts_eval = [];
+opts_eval.forcesmooth = true;
+[utarg, targdomain] = chunkerkerneval(cgrph, kerns_eval, dens, targs, ...
+      opts_eval);
 
-nsys = size(sysmat,1);
-
-srcinfo.dipstr = (coefs(1)*w(:).*dens(1:2:nsys)).';
-srcinfo.charges = (w(:).*dens(2:2:nsys)).';
-srcinfo.dipvec = n(:,:); 
+[~, nt] = size(targs);
+true_sol = zeros(nt,1);
 
 iind1 = (targdomain == 1);
-fints = hfmm2d(eps,ks(1),srcinfo,pg,targs(:,iind1),pgt);
-utarg(iind1) = fints.pottarg;
-
-true_sol = zeros(nt,1);
 t.r = targs(:,iind1);
 s = [];
 s.r = sources{1};
-true_sol(iind1) = charges{1}*chnk.helm2d.kern(ks(1),s,t,'s');
+true_sol(iind1) = charges{1}*chnk.helm2d.kern(ks(1), s, t, 's');
 
 
-srcinfo.dipstr = (coefs(2)*w(:).*dens(1:2:nsys)).';
 iind2 = (targdomain == 2);
-fints = hfmm2d(eps,ks(2),srcinfo,pg,targs(:,iind2),pgt);
-utarg(iind2) = fints.pottarg;
 t.r = targs(:,iind2);
 s.r = sources{2};
 true_sol(iind2) = charges{2}*chnk.helm2d.kern(ks(2),s,t,'s');
 
 
-
 uerr = utarg - true_sol;
 uerr = reshape(uerr,size(X));
 figure
@@ -160,13 +126,6 @@
 plot(cgrph,'w-','LineWidth',2);
 caxis([-16,0])
 colorbar
-% 
-% utarg = reshape(utarg,size(X));
-% figure
-% h = pcolor(X,Y,imag(utarg));
-% set(h,'EdgeColor','None'); hold on;
-% plot(cgrph,'w-','LineWidth',2);
-% colorbar
 
 true_sol = reshape(true_sol,size(X));
 figure