--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+sbp/+grid/accurateBoundaryOptimizedGrid.m	Wed Jul 08 18:22:54 2020 +0200
@@ -0,0 +1,67 @@
+% Computes the grid points x and grid spacing h used by the boundary optimized SBP operators 
+% with improved boundary accuracy, presented in 
+% 'Boundary optimized diagonal-norm SBP operators - Mattsson, Almquist, van der Weide 2018'.
+%
+% lim - cell array with domain limits
+% N - Number of grid points
+% order - order of accuracy of sbp operator.
+function [x,h] = accurateBoundaryOptimizedGrid(lim,N,order)
+    assert(iscell(lim) && numel(lim) == 2,'The limit should be cell array 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 =  6.8764546205559e-01;
+            x2 =  1.8022115125776e+00;
+            xb = [x0 x1 x2]';
+        case 6
+            x0 =  0.0000000000000e+00;
+            x1 =  4.4090263368623e-01;
+            x2 =  1.2855984345073e+00;
+            x3 =  2.2638953951239e+00;
+            xb = [x0 x1 x2 x3]';
+        case 8
+            x0 =  0.0000000000000e+00;
+            x1 =  3.8118550247622e-01;
+            x2 =  1.1899550868338e+00;
+            x3 =  2.2476300175641e+00;
+            x4 =  3.3192851303204e+00;
+            xb = [x0 x1 x2 x3 x4]';
+        case 10
+            x0 =  0.0000000000000e+00;
+            x1 =  3.5902433622052e-01;
+            x2 =  1.1436659188355e+00;
+            x3 =  2.2144895894456e+00;
+            x4 =  3.3682742337736e+00;
+            x5 =  4.4309689056870e+00;
+            xb = [x0 x1 x2 x3 x4 x5]';
+        case 12
+            x0 =  0.0000000000000e+00;
+            x1 =  3.6098032343909e-01;
+            x2 =  1.1634317168086e+00;
+            x3 =  2.2975905356987e+00;
+            x4 =  3.6057529790929e+00;
+            x5 =  4.8918275675510e+00;
+            x6 =  6.0000000000000e+00;
+            xb = [x0 x1 x2 x3 x4 x5 x6]';
+        otherwise
+            error('Invalid operator order %d.',order);
+    end
+end
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