--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+sbp/+grid/minimalBoundaryOptimizedGrid.m	Tue Jul 07 16:08:08 2020 +0200
@@ -0,0 +1,53 @@
+function [x,h] = minimalBoundaryOptimizedGrid(lim,N,order)
+	assert(iscell(lim) && numel(lim) == 2,'The limits should be cell arrays with 2 elements.');
+	L = lim{2} - lim{1};
+    assert(L>0,'Limits must be given in increasing order.');
+    %%%% Non-equidistant grid points %%%%%
+    xb = boundaryPoints(order);
+    m = length(xb)-1; % Number of non-equidistant points
+    assert(N-2*(m+1)>=0,'Not enough grid points to contain the boundary region. Requires at least %d points.',2*(m+1));
+    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+    %%%% Compute h %%%%%%%%%%
+    h = L/(2*xb(end) + N-1-2*m);
+    %%%%%%%%%%%%%%%%%%%%%%%%%
+
+    %%%% Define grid %%%%%%%%
+    x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
+    x = x + lim{1};
+    %%%%%%%%%%%%%%%%%%%%%%%%%
+end
+
+function xb = boundaryPoints(order)
+	switch order
+		case 4
+			x0 =  0.0000000000000e+00;
+			x1 =  7.7122987842562e-01;
+			xb = [x0 x1]';
+		case 6
+			x0 =  0.0000000000000e+00;
+			x1 =  4.0842950991998e-01;
+			x2 =  1.1968523189207e+00;
+			xb = [x0 x1 x2]';
+		case 8
+			x0 =  0.0000000000000e+00;
+			x1 =  4.9439570885261e-01;
+			x2 =  1.4051531374839e+00;
+			xb = [x0 x1 x2]';
+		case 10
+			x0 =  0.0000000000000e+00;
+			x1 =  5.8556160757529e-01;
+			x2 =  1.7473267488572e+00;
+			x3 =  3.0000000000000e+00;
+			xb = [x0 x1 x2 x3]';
+		case 12
+			x0 =  0.0000000000000e+00;
+			x1 =  4.6552112904489e-01;
+			x2 =  1.4647984306493e+00;
+			x3 =  2.7620429464763e+00;
+			x4 =  4.0000000000000e+00;
+			xb = [x0 x1 x2 x3 x4]';
+		otherwise
+			error('Invalid operator order %d.',order);
+	end
+end
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